Research ArticleDamage Deformation of Flexure-Yielding Steel-ReinforcedConcrete Coupling Beams Experimental andNumerical Investigation

Yinghui Li12 Huanjun Jiang 12 and T Y Yang23

1State Key Laboratory of Disaster Reduction in Civil Engineering Tongji University Shanghai China2e International Joint Research Laboratory of Earthquake Engineering Tongji University Shanghai China3Department of Civil Engineering University of British Columbia Vancouver Canada

Correspondence should be addressed to Huanjun Jiang jhj73tongjieducn

Received 20 February 2019 Revised 8 May 2019 Accepted 27 May 2019 Published 13 June 2019

Academic Editor Zhongguo John Ma

Copyright copy 2019 Yinghui Li et al is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

SRC coupling beams offer many significant advantages including the reduction in section depth reduced congestion at the wallboundary region improved degree of coupling for a given beam depth and improved deformation capacity In this paper 7 half-scale flexure-yielding SRC coupling beams designed according to Chinese approach have been tested under cyclic loads Detailedparameters such as aspect ratios steel reinforcement ratios and steel flange-web ratios were systematically studied and thedamage behavior of SRC coupling beams were presented in this paper e test results show that the aspect ratio steel ratio andsteel flange-web ratio have great influence on the damage behavior of SRC coupling beams ree-dimensional nonlinear finiteelement models were constructed and benchmarked through comparison with test results for both global and local damagedeformation behavior Based on the material damage and strength degradation four performance levels were defined andcorresponding chord rotation limits were obtained through the verified numerical analysis

1 Introduction

Reinforced concrete shear wall (RCSW) with the couplingbeam is one of the most prevalent seismic force resistingsystems used for medium- and high-rise constructionsworldwide [1] In this structural system seismic forces areresisted through a combination of flexural action of the shearwalls and frame action between the shear walls and couplingbeams Under such frame action the coupling beams shouldbe properly designed to transfer adequate forces betweenadjacent walls In addition coupling beams are expected tobe used as primary fuses to dissipate earthquake energy asthey undergo inelastic deformation [2] erefore the de-formation capacity and energy dissipation capacity are alsoimportant for coupling beams

Conventionally reinforced concrete coupling beam de-sign typically results in diagonally reinforced deep beam tosatisfy the stiffness strength and energy dissipation de-mands while creates constructability challenges and

increases construction time and cost Steel-reinforcedconcrete (SRC) coupling beams provide an attractive al-ternative thanks to its more attractive behavior SRC cou-pling beams offer potential advantages of reduced sectiondepth reduced congestion at the wall boundary regionimproved degree of coupling for a given beam depth andimproved deformation capacity [3] erefore reinforcedconcrete shear wall (RCSW) with steel-reinforced concrete(SRC) coupling beams is one of the new innovations in thecomposite seismic force resisting systems and has beenwidely used in Asia and North America

Gong and Shahrooz [4] tested four one-third-scaleshear-yielding SRC coupling beams and found that rein-forced encasement around the steel enhanced the strengthand stiffness Based on an equation developed and cali-brated to test results by Gong and Shahrooz [5] the 2010AISC Seismic Provisions [Eq (H5-3)] recommend com-puting the expected shear strength Vne of an SRC cou-pling beam as

HindawiAdvances in Civil EngineeringVolume 2019 Article ID 7071243 15 pageshttpsdoiorg10115520197071243

Vne 11Ry 06fatw Hs minus 2tf( 1113857( 1113857

+ 156 017

fc

1113969

bh0 +Astfyth0

s1113888 1113889

(1)

where fc is the nominal compressive strength of the con-crete bc is the beam section width h0 is the beam sectioneffective depth Ast is the area of transverse reinforcementfyt is the nominal yield strength of transverse reinforcements is the spacing of transverse reinforcement Ry is the ratio ofthe expected to nominal yield strength of structural steel fais the nominal yield strength of structural steel tw is the webthickness of encased steel Hs is the cross-sectional height ofencased steel and tf is the flange thickness of encased steelSu and Lam [6] tested eight half-scale steel plate-reinforcedconcrete coupling beams of short and medium-length spansand proposed a unified design approach Motter et al [3]tested four one-half scale flexure-yielding SRC couplingbeams embedded into reinforced concrete structural wallsfor realistic loading conditions and found that with adequateencased steel embedment and wall reinforcement theperformance of flexure-yielding SRC coupling beams canmeet or exceed that of conventionally or diagonally rein-forced concrete coupling beams Motter et al [7] modifiedequation (1) to calculate nominal shear strength of SRCcoupling beams as follows

Vn 06fatw Hs minus 2tf( 1113857 + 017

fc

1113969

bh0 +Astfyth0

s (2)

Although a number of SRC coupling beams have beentested [4ndash8] those results generally showed that SRC cou-pling beams can provide good seismic behavior stirrupslongitudinal rebars and embedment of encased steel have asignificant impact on the failure modes of SRC couplingbeams However those researches paid little attention toSRC coupling beam damage development during the wholeloading process which is an important reference in assessingthe seismic performance of structures or structural com-ponents [9 10] In addition there are two main types ofencased steel used in composite coupling beams which areH-shaped steel [3ndash5 7 8] and steel plate without flange [6]However the comparison research between these two typesof encased steel on seismic performance of coupling beams islimited

In this paper the cyclic test of 7 half-scale flexure-yielding SRC coupling beams designed according to Chi-nese code JGJ138-2016 [11] is presented and damage de-velopment was recorded throughout the whole loadingprocesse main design parameters studied are aspect ratio(span-to-depth ratio) steel ratio (ratio of encased steelsection area to beam section area) and steel flange-web ratio(ratio of flange steel section area to web steel section area ofencased steel) In order to develop further insight into theobserved experimental behavior this paper also presents thedevelopment and benchmarking of detailed 3D nonlinearfinite element models for predicting the damage behavior ofthe tested SRC coupling beams e models explicitly ac-count for material inelasticity including concrete cracking

and interaction behavior between rebar encased steel andconcrete and are benchmarked using results from the ex-perimental program Based on the damage characters andstrength degradation four performance levels were definedand corresponding chord rotation limits were obtainedthrough the verified numerical analysis

2 Test Program

21 Test Specimens Seven half-scale SRC coupling beamswith various span lengths and steel configurations weretested To ensure the SRC coupling beams are well connectedto the concrete pedestal an embedment length of encasedsteel welded with shear studs and longitudinal bars in thepedestal is selected as 700mm which is more than sufficientto be treated as a fixed boundary condition e calculationfor the embedment length of encased steel will be discussedat the end of this section Since this study just focuses on thedamage deformation of SRC coupling beams the damagedeformation of wall piers that are connected to SRC cou-pling beams is expected to be zero erefore the pedestal isconstructed not to simulate a shear wall but just to serve as arigid block to fix the SRC coupling beams and the rebar inpedestal is designed more than enough to resist shear andmoment from the coupling beam end In addition as theSRC coupling beams are designed as flexure-yielding whichbehavior is expected to be governed by flexure only half ofthe SRC coupling beam instead of the whole span is tested inthe laboratory which is similar to other researches [3ndash57]e beam specimens are free to elongate in this test since theaxial load from restrained adjacent coupled walls is ap-proximately 4ndash7 of axial load capacity of coupling beams[12] which is relatively small and is negligible in this re-search To ensure the bonding between the encased steel andconcrete 10mm diameter shear studs spaced at a distance of100mm were welded on the flange and web of encased steelaccording to Chinese code JGJ138-2016 [11]

e cross sections of specimens are identical that theheight is 500mm and width is 300mm and the longitudinaland transverse reinforcements of specimens are also iden-tical Figure 1 shows the dimensions of the specimens thesteel reinforcement and encased steel details and the per-spective view of the specimens e detailed design pa-rameters especially the beam length and encased steelconfiguration of specimens are shown in Table 1 SpecimensBeam1 Beam2 and Beam3 have all the parameters sameexcept the aspect ratio (span-to-depth ratio is equal to 2L500) Specimens Beam1 Beam4 and Beam5 have all theparameters same except the steel flange-web ratio (area ratioof flange steel to web steel of encased steel is equal to 2tfBs(Hsminus 2tf )tw) Specimens Beam2 Beam6 and Beam7 have allthe parameters same except the steel ratio (steel ratio is equalto (Hstw + 2(Bsminus tw)tf )150000) e tensile test results of thesteel plate and steel bar are listed in Table 2 e concretecubic compressive strength fcu is 578MPa

e flexural capacity and shear capacity of specimenswere calculated based on the tested material strength andthe corresponding resistance capacity of specimens is shownin Table 3 e flexural capacity was calculated using

2 Advances in Civil Engineering

equations in Chinese code JGJ138-2016 [11] and fiber sec-tion analysis respectively e shear capacity was calculatedby using equations in Chinese code JGJ138-2016 and

equation (2) proposed by Motter et al [7] respectively eflexural capacity and shear capacity equations of SRCcoupling beam with a symmetrical rebar and symmetrical

Lateral load

8 28

6 25

6 20

2 20

2 12

1260

1260

1275

500

2ndash2

1ndash1

860

51

5151

8181

8585

91700 90

85

51140 148 14080 85 85 80

1L70

0

22

1

300

500

(a)

BS

HS

t f

tw

300

500

(b)

Shear studs

Encased steel

Rigid pedestalBeam rebars

Pedestal rebars

Bolt hole

(c)

Figure 1 (a) Dimensions of the specimens and the steel reinforcement details (unit mm) (b) Encased steel details (unit mm)(c) Perspective view of the specimens

Table 1 Detailed parameters of specimens

Specimen number Loading pointdistance L (mm)

Cross-sectionaldimensions of

encased steel (mm) Steel ratio () Aspect ratio Steel flange-web ratio

Hs Bs tw tfBeam1 500 290 90 16 20 50 2 092Beam2 750 290 90 16 20 50 3 092Beam3 1250 290 90 16 20 50 5 092Beam4 500 292 80 20 16 50 2 046Beam5 500 300 mdash 25 mdash 50 2 0Beam6 750 300 120 20 20 67 3 092Beam7 750 310 120 25 25 83 3 092Notes Hs represents the cross sectional height Bs represents the flange width tw represents the web thickness tf represents the flange thickness

Advances in Civil Engineering 3

encased steel in Chinese code JGJ138-2016 are shown asfollows

Mn α1fcbx h0 minusx

21113874 1113875 + fyAs h0 minus asprime( 1113857

+ faAaf h0 minus aaprime( 1113857 + Maw

(3a)

α1fcbx + 25x

h0minus δ1 + δ2( 11138571113890 1113891twh0fa 0 (3b)

Maw 05 δ21 + δ221113872 1113873minus δ1 + δ2( 1113857 + 25x

h0minus 125

x

h01113888 1113889

2⎡⎣ ⎤⎦twh

20fa

(3c)

Vn

038ftbh0 + 09Astfyth0

s aspect ratiole 25

042ftbh0 +Astfyth0

s aspect ratiogt 25

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(4)

where α1 is the coefficient modifying the compression stressof concrete compression zone x is the effective depth ofconcrete compression zone fy is the nominal yieldstrength of longitudinal reinforcement As is the area oflongitudinal reinforcement asprime is the distance from centerof compression rebar to the edge of compression zone Aafis the area of encased steel flange aaprime is the distance fromcenter of compression encased steel flange to the edge ofcompression zone δ1h0 is the distance from upper edge ofencased steel web to the edge of compression zone δ2h0 isthe distance from lower edge of encased steel web to theedge of compression zone and ft is the nominal tensilestrength of the concrete A similar result for moment ca-pacity and shear capacity was obtained using differentequations or methods which proves the accuracy of the

equations or methods In addition the lateral load re-sistance capacity calculated by MnL is smaller than thatcalculated by Vn which testifies the flexure-yielding designintention

e minimum required embedment length of encasedsteel Le is determined using Equation H4-2 in the 2010 AISCSeismic Provisions by taking Vnembed equal to MnL whichequation is modified considering the effect of concrete cover[3] and is shown as follows

Vnembed 405

fc

1113969twall

Bs1113888 1113889

066

β1Bs Le minus c( 1113857

middot058minus 022β1

088 + (L + c) Le minus c( 1113857( 11138571113888 1113889

(5)

where Vnembed is the shear capacity of the embedded steeltwall is the thickness of the shear wall connected to SRCcoupling beams and is taken as 860mm in this study which isthe width of the pedestal β1 is the depth factor relating thedepth of the Whitney stress block to the neutral axis depthand c is the concrete cover thickness of the pedestal emaximum required embedment length of seven SRC cou-pling beam specimens calculated using equation (5) is435mm Considering the connection between lateral hy-draulic actuator and reaction wall in the laboratory theembedment length (the height of the pedestal) is determinedto be 700mm which is more than sufficient to fix the SRCcoupling beam specimens

22 Test Setup e test setup that is illustrated in Figure 2was used in this study which consists of a rigid floor areaction wall a hydraulic actuator instrumentations anddata acquisition systems e specimens were tested underreversed cyclic lateral load using the servo-controlled hy-draulic actuator Before the specimen reaching the yielding

Table 2 Tensile test results of the encased steel plate and steel bar

Dimension of thesteel plate or bar Yielding strength (MPa) Tensile strength (MPa) Elastic modulus (MPa) Yielding strain Tensile strain

Plate thickness of 16mm 2491 4112 195times105 128times10minus3 0214Plate thickness of 20mm 2820 4529 206times105 137times10minus3 0206Plate thickness of 25mm 2550 4095 206times105 124times10minus3 0215Rebar diameter of 12mm 4570 5556 190times105 241times 10minus3 0139Rebar diameter of 20mm 4375 5828 196times105 223times10minus3 0133

Table 3 Lateral load resistance capacity of specimens (kN)

Specimen numberCalculated by MnL Calculated by Vn

Fiber section Equation (3) Equation (2) Equation (4)Beam1 9514 9198 11891 11162Beam2 6343 6132 11891 12000Beam3 3806 3679 11891 12000Beam4 9636 9277 13900 13094Beam5 9044 8797 15354 14492Beam6 7739 7611 14312 14043Beam7 8415 8296 15463 15161

4 Advances in Civil Engineering

point which was monitored by the outmost strain gaugesattached to the encased steel the lateral load was controlledby force and just one reversed cycle was loaded during eachloading level en after that the lateral load was controlledby displacement and three reversed cycles were loadedduring each loading level e lateral loading protocol ofspecimen Beam1 is shown in Figure 3 and each reversedloading cycle was finished in 2minutes

Linear variable displacement transducers (LVDTs)were installed to the specimens to measure the lateraldisplacements and the curvatures in the critical regionsStrain gauges were attached to measure the strain of steelplates and steel bars at plastic hinge zonese values of thelateral load the global and local displacements and thestrains were recorded automatically through the data ac-quisition system throughout the whole loading processTypical damage states including crack evolution concretecrushing and spalling and rebar buckling and fracturewere recorded through observation and photographsduring the loading process During the first cycle of eachloading level the maximum crack width was measured atlargest lateral load or largest displacement and the cor-responding maximum residual crack width was measuredat zero loads e crack width was measured using thecrack comparison card which has a measurement range of002ndash5mm

3 Test Results

31 Damage Behavior e sequence of observed typicaldamage states is similar for all specimens and the typicaldamage states of specimen Beam1 at different loading levelsare illustrated in Figure 4 which is a representative for allspecimens In general the damage started by forminghorizontal cracks at the bottom of the specimen at thetension side as shown in Figure 4(a) en the obliquecracks started to appear when the lateral load reaches500 kN as shown in Figure 4(b) Tensile yielding of the steelflange was detected using strain gauges with the increase ofloading levels At this instant the force control loadingprotocol was switched to the displacement control modeAfterwards the initial concrete crushing of compressive sideat the bottom of the specimen was observed when lateraldisplacement reaches 10mm as shown in Figure 4(c) Underthe following load cycles the large cracks concentrated at theinterface as shown in Figure 4(d) en the spalling ofconcrete cover appeared when the lateral displacement

reaches 225mm as shown in Figure 4(e) At this loadinglevel the lateral load carrying capacity of specimen started tofall off After concrete cover of the specimen completelyspalled off the longitudinal bars and hoops outcropped andthen the longitudinal bars buckled during the followingcycles when the lateral displacement reaches 275mm asshown in Figure 4(f ) and the fracture of the longitudinalbars was observed at subsequent larger lateral displacementwhich is 325mm as shown in Figure 4(g) e test con-tinued with the lateral displacement increased graduallyuntil the global instability appeared when the lateral dis-placement reaches 425mm After the test the concrete wasremoved and the fracture of encased steel was observed asshown in Figure 4(h) and no encased steel buckling wasfound

e typical damage development was roughly the samefor the seven specimens All specimens exhibited flexure-yielding behavior since steel web yielding occurred later thansteel flange yielding and no hoop rebar of specimens wasfound yielding before longitudinal rebar buckling or frac-ture e typical damage development was as followshorizontal cracking on the tensile side of the specimentensile yielding of the steel plate and rebar principle tensileyielding of steel web concrete crushing and spalling on thecompressive side of the specimen and rebar buckling andfracture

e crack distribution of specimens Beam 1 Beam 2 andBeam 3with different aspect ratios before concrete spalling isshown in Figure 5 With the increase of aspect ratio thecracking region is enlarged and more flexural cracks andless diagonal cracks occurred e flange-web area ratio andsteel ratio have little influence on the crack distribution

32 Force and Deformation Characteristics Lateral loadversus chord rotation (lateral displacement divided byspecimen length) hysteretic curves of specimens andcorresponding skeleton curves with typical damage statesmarked on it are shown in Figure 6e hysteretic curves ofspecimens show SRC coupling beams exhibited littlepinching effect and small degradation behavior until thelongitudinal rebars were fractured which shows SRCcoupling beams have excellent energy dissipation capa-bility By comparing specimens Beam1 Beam2 and Beam3the hysteresis behavior is similar among these threespecimens In general the specimen with higher aspectratio results in smaller hysteresis loops since the lateral loadresistance capacity is lower at same lateral chord rotationBy comparing specimens Beam1 Beam4 and Beam5 in-crease flange-web area ratio results in fuller (smallerpinching) and more stable (smaller strength degradation)hysteresis loops since flange steel contributes to SRCcoupling beam flexural behavior more than web steel Bycomparing specimens Beam2 Beam6 and Beam7 in-creased steel ratio also results in fuller and more stablehysteresis loops as larger steel ratio leads to more flangesteel and more web steel

Table 4 lists the mean values of chord rotation at thedamage characteristic points in the specimensrsquo skeleton

Reac

tion

wal

l

Hydraulicactuator

Specimen

Pedestal

Loading head

Ground anchor

Figure 2 Schematic representation of test setup

Advances in Civil Engineering 5

curves in two opposite loading directions Experimentalresults show that although the longitudinal bars were placedoutside the encased steel encased steel still yielded before thelongitudinal bars since the yielding strain of the longitudinalbars is 75 larger than the encased steel (as shown in Ta-ble 2) After the longitudinal bars fractured the specimenscan still experience larger displacement with small lateral

load carrying capacity degradation because the encased steelplate possessing much larger deformation capacity than thesteel bar was still eective to resist the lateral load

For specimens Beam1 Beam2 and Beam3 with dierentaspect ratios specimen Beam1 with the aspect ratio of 2 hasthe largest lateral load carrying capacity which is 11487 kNand is 246 times that of specimen Beam3 and 153 times that

Horizontal cracks

(a)

Diagonal cracks

(b)

Concrete crushing

(c)

Interface crack

(d)

Concrete spalling

(e)

Longitudinal bar buckling

(f )

Longitudinal bar fracture

(g)

Steel fracture

(h)

Figure 4 Typical damage states of specimen Beam1 (a) 300 kN (00012 rad) (b) 500 kN (0003 rad) (c) 10mm (002 rad) (d) 125mm(0025 rad) (e) 225mm (0045 rad) (f ) 275mm (0055 rad) (g) 325mm (0065 rad) and (h) 425mm (0085 rad)

App

lied

disp

lace

men

t (m

m)

4 8 12 16 20 24 28 32ndash40ndash30ndash20ndash10

010203040

ndash8ndash6ndash4ndash202468Stage 3Stage 2

Chor

d ro

tatio

n (

)

Cycle no0 1 2 3 4

Stage 1

Cycle no

ndash600ndash400ndash200

0200400600

App

lied

load

(kN

)

Figure 3 Lateral loading protocol of specimen Beam1

6 Advances in Civil Engineering

(a) (b) (c)

Figure 5 Crack pattern of specimens before concrete crushing (a) Beam1 (b) Beam2 (c) Beam3

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200

ndash004 000 004 008ndash008Rotation (rad)

ndash40 ndash20 0 20 40Lateral displacement (mm)

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash40 ndash20 0 20 40

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(a)

Late

ral l

oad

(kN

)

ndash60 ndash30 0 30 60Lateral displacement (mm)

ndash800

ndash400

0

400

800

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

ndash004 000 004 008ndash008Rotation (rad)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash60 ndash30 0 30 60

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(b)

Figure 6 Continued

Advances in Civil Engineering 7

Late

ral l

oad

(kN

)

ndash100 ndash50 0 50 100Lateral displacement (mm)

ndash480

ndash320

ndash160

0

160

320

480

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

ndash004 000 004 008ndash008Rotation (rad)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash100 ndash50 0 50 100

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(c)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash40 ndash20 0 20 40

Lateral displacement (mm)

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

ndash004 000 004 008ndash008Rotation (rad)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash40 ndash20 0 20 40

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(d)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash40 ndash20 0 20 40

Lateral displacement (mm)

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

ndash004 000 004 008ndash008Rotation (rad)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash40 ndash20 0 20 40

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(e)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash60 ndash30 0 30 60

Lateral displacement (mm)

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

ndash004 000 004 008ndash008Rotation (rad)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash60 ndash30 0 30 60

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(f )

Figure 6 Continued

8 Advances in Civil Engineering

of specimen Beam2 which means that the lateral loadcarrying capacity changes in inverse proportion with theaspect ratio and all specimens reached its exural strengthIn general the larger aspect ratio specimen tends to havesmaller lateral load carrying capacity at the individualdamage characteristic point Considering displacements ofthe individual damage state the initial damage states(concrete cracking steel tensile yielding and rebar tensileyielding) of specimen Beam3 with a aspect ratio of 5 tend tooccur later than those of specimen Beam1 with a aspect ratioof 2 which is consistent with the elastic chord rotationequation of the Timoshenko cantilever beam which is asfollows

θ ΔLML

3EI+M

GAL (6)

where M is the xed end section moment of the cantileverbeam L is the length of the cantilever beam E is the elasticmodulus I is the section moment inertia G is the shearmodulus and A is the eective shear section area When L islarger than

3EIGA

radicasymp 08h (h is the beam section height)

chord rotation θ increases with the increase of the beamlength under the same xed end moment e damage statessuch as steel web principle yielding concrete crushingconcrete spalling rebar buckling and rebar fracture of

specimen Beam3 tend to occur earlier than those of spec-imen Beam1 because specimen Beam3 has a relativelysmaller moment gradient at the plastic zone which causesexural damages of Beam3 to occur easily and smaller shearforce in Beam3 leads to smaller shear deformation also

For specimens Beam1 Beam4 and Beam5 with dierentange-web area ratios of encased steel specimen Beam4witha ange-web ratio of 05 has the largest lateral load carryingcapacity which is 11866 kN and is 33 larger than that ofspecimen Beam1 and 225 larger than that of specimenBeam5 which means that the specimen without the ange ofencased steel has a signicant smaller lateral load carryingcapacity e reason that specimen Beam4 with a smallerange-web ratio has slightly larger lateral load capacity thanspecimen Beam1 is that the encased steel consists of steelplates with dierent thicknesses and dierent yieldingstrengths and the average yielding strength of encased steelof specimen Beam4 is slightly larger than that of specimenBeam1 e calculated lateral load capacity (MnL) forspecimens Beam4 and Beam1 shown in Table 3 veried thisexplanation Considering the displacements of individualdamage states except the damage states like steel tensileyielding and rebar tensile yielding the other damage states ofspecimen Beam1 with a ange-web ratio of 1 tend to occurlater than those of specimen Beam5 with a ange-web ratio

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash60 ndash30 0 30 60

Lateral displacement (mm)

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

ndash004 000 004 008ndash008Rotation (rad)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash60 ndash30 0 30 60

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(g)

Figure 6 Lateral load-chord rotation hysteretic curves and skeleton curves of specimens (a) Beam1 (b) Beam2 (c) Beam3 (d) Beam4(e) Beam5 (f ) Beam6 (g) Beam7

Table 4 Chord rotation of specimens at the individual damage characteristic point

Specimen number θc (rad) θsty (rad) θrty (rad) θswy (rad) θcc (rad) θcs (rad) θrb (rad) θrf (rad)Beam1 00012 00033 00072 00140 00238 00403 00502 00609Beam2 00013 00063 00065 00120 00192 00385 00451 00558Beam3 00014 00044 00091 00095 00139 00378 00478 00560Beam4 00009 00041 00072 00085 00233 00416 00485 00565Beam5 00008 00053 00078 00078 00179 00346 00444 00586Beam6 00010 00065 00065 00100 00237 00485 00522 00653Beam7 00013 00039 00105 00131 00201 00430 00511 00593Note θc θsty θrty θswy θcc θcs θrb and θrf represent the chord rotation of specimens at damage states of concrete cracking steel tensile yielding rebar tensileyielding steel web principle tensile yielding concrete crushing concrete spalling rebar buckling and rebar fracture respectively For Beam5 rebar tensileyielding and steel web principle tensile yielding occurred at the same time For Beam6 steel tensile yielding and rebar tensile yielding occurred at the sametime

Advances in Civil Engineering 9

of 0 is is because the flange steel enhances the com-pression behavior of the concrete and delays the concretecrushing and spalling In addition shear deformation ofspecimen Beam1 with smaller web steel is larger than that ofspecimen Beam5 at the same damage state

For specimens Beam2 Beam6 and Beam7 with theincrease of steel ratio from 5 to 83 the lateral loadcarrying capacity increases from 7503 kN to 9688 kN by292 which means that the lateral load carrying capacity ofSRC coupling beam was influenced largely by the steel ratioExcept initial damage states like concrete cracking rebartensile yielding and steel web principle tensile yielding theother damage states of specimen Beam6 with a steel ratio of67 tend to occur later than those of specimen Beam2 witha steel ratio of 5 and Beam7 with a steel ratio of 83

Concrete cover cracking influences the encased steelcorrosion initiation and the crack width influences thecorrosion propagation thus both influence the performanceof structures [13] e maximum residual crack width of allspecimens represented by Wmres was measured during thetest cycles before concrete cover crashed or spalled evariation of maximum residual crack width with the chordrotation is shown in Figure 7 Generally the maximumresidual crack width rises up with the increase of the chordrotation e maximum residual crack width of the speci-men at the same rotation tends to be smaller with the in-crease of the aspect ratio or steel ratio for the average value ofthat for both directions For specimens Beam1 Beam4 andBeam5 with different flange-web area ratios of encased steelBeam4 has the smallest maximum residual crack width whileBeam1 has the largest maximum residual crack width at thesame rotation

4 Numerical Analysis and Verification

41 Modeling ree-dimensional nonlinear finite elementmodels were developed to simulate the inelastic behavior oftested SRC coupling beam specimens using Abaqus [14] Notonly the global force-rotation behavior but also the localmaterial damage behavior during the test process includingconcrete (cracking crushing and spalling) steel yieldingand rebar (yielding buckling and fracture) was predictedthrough finite element analysis It has been reported [15ndash17]that material damage states ie spalling and yielding arenot dependent on the history of loading but are ratherclosely related to the maximum displacement that thestructure has experienced erefore a monotonic analysiswas sufficient for predicting damage deformation of flexure-yielding SRC coupling beams

Damaged plasticity model was used to simulate theconcrete inelastic behavior in SRC coupling beam specimensis model is applicable in the situation that the concrete is atlow confinement pressures (less than four to five times thelargest compressive stress that can be carried by the concretein uniaxial compression) which is suitable for SRC couplingbeams Moon et al [18] used this model to study the con-finement effect of steel tubes on the infilled concrete andBabazadeh et al [17] used this model to study the spalling ofthe concrete for RC bridge columnse uniaxial stress-strain

relationship for the concrete recommended in Chinese codeGB50010-2010 [19] was adopted here as shown in Figure 8(a)e compression strength of the concrete is 373MPa whichis the prismatic compression strength of concrete fck which iscalculated based on the conversion formula in Chinese code50010-2010 [19] and the tested cubic compression strength ofconcrete fcu is equal to 578MPa

Ductile damage plasticity model was used to simulate theencased steel and rebar inelastic behavior in SRC couplingbeam specimens is model offers a general capability forpredicting the onset of failure and a capability for modelingprogressive damage and failure of ductile metals Zhu et al[20] used this model to simulate the steel tearing of concrete-filled steel tube columns e strengthening stage of steeladopted a bilinear model hardening stiffness of which is 1of elastic stiffness and damage initiated at tensile strain anddamage evolution adopted a linear damage form Consid-ering the cyclic fatigue of longitudinal rebar under earth-quakes Priestley [21] suggested the tensile strain of thelongitudinal rebar to be reduced by 40 Shi et al [22]carried out the structural steel low cycle fatigue test andproved that the tensile strain of Q345B steel was reduced by203 and Q235B steel was reduced by 386 after cyclicloading e fracture strain was conservatively taken as twotimes tensile strain refer to the former test results euniaxial stress-strain relationship for the 12mm diameterrebar is shown in Figure 8(b)

Eight-node solid elements with reduced integration(C3D8R) were used for the concrete four-node shell ele-ments with reduced integration (S4R) were used for theencased steel and two-node linear displacement truss ele-ments were used for rebar A perfect bond was assumedbetween the steel rebar elements and the concrete parttherefore the truss elements and shell elements were em-bedded in the concrete instance using the lowastEMBEDDEDELEMENT option e bottom surface of the pedestal wasfixed against all degrees of freedom A reference point wasmodeled on the surface of the loading plate which wasconstrained with the surface of the loading plate using thelowastCOUPLING option available in the ABAQUS library

42 Analysis Results e global skeleton curves of all thespecimens obtained from the FEA are compared with theskeleton curves obtained from the test and two of them areshown in Figure 9 e FEA model gave a stiffer result in thepositive part and softer one in the negative part for specimenBeam1 compared to the experimental result which may bedue to the slippage of the pedestal or the gap between loadinghead and specimen in the test e local material damagesobtained from FEA are also compared with test results andconcrete spalling and rebar fracture are shown in Figure 10From the qualitative comparison good agreement isachieved between experimental and FEA results not only onthe global behavior but also on the local material damagebehavior

Concrete crushing and spalling were predicted throughthe compression strain of concrete Priestley [21] suggested avalue of 0004 for cover concrete edge compressive crushing

10 Advances in Civil Engineering

strain and Jiang et al [23] proposed an equation to calculatethe conned concrete edge compression spalling strainwhich is equal to 0005 for test specimense concrete crack

width was predicted through the tensile strain of rebarPriestley [21] suggested a value of 001 for longitudinal rebartensile strain to control the residual crack width within

Stre

ss (M

Pa)

ndash5

0

5

10

15

20

25

30

35

40

0002 0004 0006 0008 00100000Strain

(a)

Stre

ss (M

Pa)

0

100

200

300

400

500

600

004 008 012 016000Strain

(b)

Figure 8 Uniaxial constitutive relationships of materials (a) Concrete (b) Rebar 12mm

Wm

res (

mm

)

Beam1Beam2Beam3

00

05

10

15

20

ndash002 000 002 004ndash004Rotation (rad)

(a)W

mre

s (m

m)

Beam1Beam4Beam5

00

05

10

15

20

ndash002 000 002 004ndash004Rotation (rad)

(b)

Wm

res (

mm

)

Beam2Beam6Beam7

00

05

10

15

20

ndash002 000 002 004ndash004Rotation (rad)

(c)

Figure 7 Maximum residual crack width of specimens (a) Eect of aspect ratio (b) Eect of ange-web ratio (c) Eect of steel ratio

Late

ral l

oad

(kN

)

FEATest

ndash1200

ndash800

ndash400

0

400

800

1200

ndash006 ndash003 000 003 006 009ndash009Rotation (rad)

(a)

Late

ral l

oad

(kN

)

FEATest

ndash1200

ndash800

ndash400

0

400

800

1200

ndash006 ndash003 000 003 006 009ndash009Rotation (rad)

(b)

Figure 9 Comparison of experimental and numerical skeleton curves (a) Specimen Beam1 (b) Specimen Beam5

Advances in Civil Engineering 11

10mm e chord rotations corresponding to differentconcrete damage states obtained from finite element analysiswere compared with the test result as shown in Table 5From the quantitative comparison for concrete damagedeformation finite element analysis can only provide astatistically consistent simulation result not specifically ac-curate simulation result for each specimen e mean ro-tation ratios between FEA and the test for the concreteresidual crack width equal to 1mm concrete crushing and

concrete spalling are 099 083 and 074 respectively If thecover concrete edge compression crushing strain is revisedto 0005 and confined concrete edge compression spallingstrain is revised to 00075 the mean rotation ratios betweenFEA and the test for concrete crushing and concrete spallingare 104 and 103 respectively

Steel flange tensile yielding and web principle tensileyielding were predicted directly through steel yielding strainrecorded in Table 2 e chord rotations corresponding to

Rebar fracture

PE max principalSNEG(fraction = ndash10)(avg 75)

+1454e ndash 01+1333e ndash 01+1212e ndash 01+1090e ndash 01+9693e ndash 02+8481e ndash 02+7269e ndash 02+6058e ndash 02+4846e ndash 02+3635e ndash 02+2423e ndash 02+1212e ndash 02+0000e + 00

(a)

Concrete spalling

PEEQ(avg 75)

+4683e ndash 02+4292e ndash 02+3902e ndash 02+3512e ndash 02+3122e ndash 02+2731e ndash 02+2341e ndash 02+1951e ndash 02+1561e ndash 02+1171e ndash 02+7804e ndash 03+3902e ndash 03+0000e + 00

(b)

Figure 10 Comparison of experimental and numerical damages (a) Rebar fracture of specimen Beam1 (b) Concrete spalling of specimenBeam1

Table 5 Comparison of chord rotations of specimens for different concrete damage states

Specimen numberResidual crack width lt1mm Concrete crushing Concrete spallingTest FEA FEAtest Test FEA FEAtest Test FEA FEAtest

Beam1 00084 00157 187 00238 00231 097 00403 00442 110Beam2 00116 00141 122 00192 00137 071 00385 00244 063Beam3 00150 00155 103 00139 00143 103 00378 00256 068Beam4 00261 00145 056 00233 00185 079 00416 00288 069Beam5 00200 00149 075 00179 00196 109 00346 00363 105Beam6 00187 00140 075 00237 00133 056 00485 00233 048Beam7 00190 00141 074 00201 00130 065 00430 00225 052

12 Advances in Civil Engineering

different steel yielding states obtained from finite elementanalysis were compared with the test result as shown inTable 6 e finite element analysis can provide a statisticallyconsistent simulation result and the mean rotation ratiosbetween FEA and the test for steel flange tensile yielding andsteel web principle tensile yielding are 123 and 108respectively

Rebar tensile yielding and rebar fracture were pre-dicted directly through rebar yielding strain and tensilestrain recorded in Table 2 Rebar buckling was predictedthrough confined concrete ultimate compressive strainwhich is calculated using equation suggested by Priestley[21] e chord rotations corresponding to different rebardamage states obtained from finite element analysis werecompared with the test result as shown in Table 7 efinite element analysis can provide a statistically consis-tent simulation result and the mean rotation ratios be-tween FEA and the test for rebar tensile yielding rebarbuckling and rebar fracture are 074 103 and 090respectively

43 Performance Index Limit Analysis e seismic per-formance of SRC coupling beams is affected by the ma-terial damage which is related to the material strain Onthe other hand the degradation of the load carrying ca-pacity of SRC coupling beams affects its seismic perfor-mance also Based on the study on the material damagestrain limits [21 23] and component strength degradationlimits [24] four performance levels are defined as shownin Table 8 Since there is a lack of test records of speci-mensrsquo deformation at damage states of concrete strainequal to 0002 or crack width equal to 2mm the chordrotation of specimens at different performance levels canonly be obtained through FEA Table 9 shows the chord

rotations of SRC coupling beam specimens at differentperformance levels and then the mean values wereadopted as the performance index limits which were0005 rad 0014 rad 0024 rad and 0047 rad for the fourperformance levels

5 Summary and Conclusions

Seven half-scale flexural-yielding SRC coupling beamspecimens designed according to Chinese approach weretested under cyclic loade influence of design parameterssuch as aspect ratio flange-web area ratio of encased steeland steel ratio on damage development hysteretic be-havior strength and maximum residual crack width werediscussed Finite element analysis was conducted forspecimens both global skeleton curves and local materialdamage were simulated simultaneously rough quanti-tative comparison finite element analysis can provide astatistically consistent simulation result for materialdamages for each specimen Some conclusions are drawnfrom this research

(1) All specimens failed in flexural mode e damagedevelopment was roughly the same and the typicaldamage states were recorded through the wholeloading process which can be used in assessing theseismic performance level of SRC coupling beams

(2) With the increase of aspect ratio the lateral loadcarrying capacity drops down significantly and themaximum residual crack width tends to be smallerWith the increase of flange-web area ratio of encasedsteel the hysteretic curve gets fuller e specimenwith intermediate flange-web area ratio has thelargest lateral load carrying capacity but smallestmaximum residual crack width With the increase of

Table 6 Comparison of chord rotations of specimens for different steel damage states

Specimen numberSteel flange yielding Steel web yielding

Test FEA FEAtest Test FEA FEAtestBeam1 00033 00059 179 00140 00124 089Beam2 00063 00053 084 00120 00116 097Beam3 00044 00061 139 00095 00108 114Beam4 00041 00051 124 00085 00105 124Beam5 00053 00056 106 00078 00098 126Beam6 00065 00057 088 00100 00115 115Beam7 00039 00056 144 00131 00120 092

Table 7 Comparison of chord rotations of specimens for different rebar damage states

Specimen numberRebar yielding Rebar buckling Rebar fracture

Test FEA FEAtest Test FEA FEAtest Test FEA FEAtestBeam1 00072 00059 082 00502 00777 155 00609 00562 092Beam2 00065 00054 083 00451 00426 094 00558 00502 090Beam3 00091 00060 066 00478 00446 093 00560 00571 102Beam4 00072 00056 078 00485 00527 109 00565 00504 089Beam5 00078 00054 069 00444 00526 118 00586 00596 102Beam6 00065 00056 086 00522 00403 077 00653 00490 075Beam7 00105 00057 054 00511 00390 076 00593 00493 083

Advances in Civil Engineering 13

steel ratio the lateral load carrying capacity increasessignificantly while the maximum residual crackwidth drops down

(3) e finite element model was benchmarkedthrough comparison with test results for bothglobal load-deformation curves and local materialdamages Both qualitative and quantitative com-parisons testify the accuracy of finite elementmodels e cover concrete edge compressionstrain and confined concrete edge compressionstrain were recommended to be 0005 and 00075respectively for accurately modeling concretecrushing and spalling Based on the damagecharacters and strength degradation four perfor-mance levels were defined and correspondingchord rotation limits were obtained through theverified numerical analysis

Data Availability

All the data in this paper are obtained from tests and nu-merical analysis and no other data in the literature are usedto support this study

Conflicts of Interest

e authors declare that there are no potential conflicts ofinterest with respect to the research authorship and pub-lication of this article

Acknowledgments

e financial support from the Program of Shanghai Aca-demic Research Leader (grant number 18XD1403900) andthe National Key Research and Development Program ofChina (grant number 2017YFC1500701) is gratefullyacknowledged

References

[1] S El-Tawil K A Harries P J Fortney B M Shahrooz andY Kurama ldquoSeismic design of hybrid coupled wall systemsstate of the artrdquo Journal of structural engineering vol 136no 7 pp 755ndash769 2010

[2] C-C Hung and W-T Lu ldquoA performance-based designmethod for coupled wall structuresrdquo Journal of EarthquakeEngineering vol 21 no 4 pp 579ndash603 2016

[3] C J Motter D C Fields J D Hooper et al ldquoSteel-reinforcedconcrete coupling beams I testingrdquo Journal of StructuralEngineering vol 143 no 3 article 04016191 2016

[4] B Gong and B M Shahrooz ldquoConcrete-steel compositecoupling beams I component testingrdquo Journal of StructuralEngineering vol 127 no 6 pp 625ndash631 2001

[5] B Gong and B M Shahrooz ldquoConcrete-steel compositecoupling beams II subassembly testing and design verifi-cationrdquo Journal of Structural Engineering vol 127 no 6pp 632ndash638 2001

[6] R K L Su and W Y Lam ldquoA unified design approach forplate-reinforced composite coupling beamsrdquo Journal ofConstructional Steel Research vol 65 no 3 pp 675ndash6862009

Table 8 Method of defining performance levels for SRC coupling beams

Performance level Damage descriptionPerformance criterion

Rebar or steel strain Concretestrain Load carrying capacity

Being basically intact ere are fine cracks in concrete while steel or rebaris not yielding εy 0002 mdash

Slight damage Concrete cover is not crushing and residual crackwidth is less than 1mm 0015 0005 mdash

Moderate damage Concrete cover is not spalling and residual crackwidth is less than 2mm 003 00075 95 Pmax

Severe damage Concrete core is not crushing and rebar or steel isnot fracturing εsu εcu 85 Pmax

Note εy is the yielding strain of steel or rebar εsu is the tensile strain of steel or rebar εcu is the ultimate strain of the concrete Pmax is the lateral load carryingcapacity of specimens

Table 9 Chord rotations of SRC coupling beams at different performance levels (rad)

Specimen numberPerformance level

Being basically intact Slight damage Moderate damage Severe damageBeam1 00055 00157 00264 00562Beam2 00053 00137 00212 00426Beam3 00060 00143 00235 00446Beam4 00051 00145 00239 00504Beam5 00054 00149 00257 00526Beam6 00051 00133 00228 00403Beam7 00050 00130 00228 00390

14 Advances in Civil Engineering

[7] C J Motter D C Fields J D Hooper et al ldquoSteel-reinforcedconcrete coupling beams II Modelingrdquo Journal of StructuralEngineering vol 143 no 3 article 04016192 2016

[8] Q Z Liang and X L Han ldquoe behavior of stiffening beamsand lintel beams under cyclic loadingrdquo Journal of South ChinaUniversity of Technology vol 23 no 1 pp 27ndash33 1995 inChinese

[9] H Jiang B Wang and X Lu ldquoExperimental study on damagebehavior of reinforced concrete shear walls subjected to cyclicloadsrdquo Journal of Earthquake Engineering vol 17 no 7pp 958ndash971 2013

[10] J Yue J Qian and D E Beskos ldquoA generalized multi-levelseismic damage model for RC framed structuresrdquo Soil Dy-namics and Earthquake Engineering vol 80 pp 25ndash39 2016

[11] JGJ138-2016 Code for Design of Composite Structures ChinaArchitecture amp Building Press Beijing China 2016

[12] R D Lequesne G J Parra-Montesinos and J K WightldquoSeismic behavior and detailing of high-performance fiber-reinforced concrete coupling beams and coupled wall sys-temsrdquo Journal of Structural Engineering vol 139 no 8pp 1362ndash1370 2012

[13] M Otieno H Beushausen and M Alexander ldquoTowardsincorporating the influence of cover cracking on steel cor-rosion in RC design codes the concept of performance-basedcrack width limitsrdquo Materials and Structures vol 45 no 12pp 1805ndash1816 2012

[14] SIMULIA Dassault Systems ABAQUS Analysis UserrsquosManual Version 616 SIMULIA Johnston RI USA 2016

[15] J C Goodnight M J Kowalsky and J M Nau ldquoEffect of loadhistory on performance limit states of circular bridge col-umnsrdquo Journal of Bridge Engineering vol 18 no 12pp 1383ndash1396 2013

[16] R T Ranf ldquoDamage accumulation in lightly confined rein-forced concrete bridge columnsrdquo PEER Report PacificEarthquake Engineering Research Center University ofCalifornia Berkeley CA USA 2006

[17] A Babazadeh R Burguentildeo and P F Silva ldquoUse of 3D finite-element models for predicting intermediate damage limitstates in RC bridge columnsrdquo Journal of Structural Engi-neering vol 141 no 10 article 04015012 2015

[18] J Moon CW Roeder andH-E Lee ldquoAnalytical modeling ofbending of circular concrete-filled steel tubesrdquo EngineeringStructures vol 42 no 12 pp 349ndash361 2012

[19] GB50010-2010 Code for Design of Concrete Structures ChinaArchitecture amp Building Press Beijing China 2010

[20] H Zhu M T Stephens and D E Lehman ldquoInelastic responseprediction of CFST columns and connections subjected tolateral loadingrdquo Journal of Constructional Steel Researchvol 132 pp 130ndash140 2017

[21] M J N Priestley ldquoPerformance based seismic designrdquo inProceedings of 12th World Conference on EarthquakeEngineering Auckland New Zealand January 2000

[22] Y Shi M Wang and Y Wang ldquoExperimental and consti-tutive model study of structural steel under cyclic loadingrdquoJournal of Constructional Steel Research vol 67 no 8pp 1185ndash1197 2011

[23] H Jiang X Lu and T Kubo ldquoDamage displacement esti-mation of flexure-dominant RC columnsrdquo Advances inStructural Engineering vol 13 no 2 pp 357ndash368 2010

[24] GB50011-2010 Code for Seismic Design of Buildings ChinaArchitecture amp Building Press Beijing China 2010

Advances in Civil Engineering 15

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equations in Chinese code JGJ138-2016 [11] and fiber sec-tion analysis respectively e shear capacity was calculatedby using equations in Chinese code JGJ138-2016 and

equation (2) proposed by Motter et al [7] respectively eflexural capacity and shear capacity equations of SRCcoupling beam with a symmetrical rebar and symmetrical

Lateral load

8 28

6 25

6 20

2 20

2 12

1260

1260

1275

500

2ndash2

1ndash1

860

51

5151

8181

8585

91700 90

85

51140 148 14080 85 85 80

1L70

0

22

1

300

500

(a)

BS

HS

t f

tw

300

500

(b)

Shear studs

Encased steel

Rigid pedestalBeam rebars

Pedestal rebars

Bolt hole

(c)

Figure 1 (a) Dimensions of the specimens and the steel reinforcement details (unit mm) (b) Encased steel details (unit mm)(c) Perspective view of the specimens

Table 1 Detailed parameters of specimens

Specimen number Loading pointdistance L (mm)

Cross-sectionaldimensions of

encased steel (mm) Steel ratio () Aspect ratio Steel flange-web ratio

Hs Bs tw tfBeam1 500 290 90 16 20 50 2 092Beam2 750 290 90 16 20 50 3 092Beam3 1250 290 90 16 20 50 5 092Beam4 500 292 80 20 16 50 2 046Beam5 500 300 mdash 25 mdash 50 2 0Beam6 750 300 120 20 20 67 3 092Beam7 750 310 120 25 25 83 3 092Notes Hs represents the cross sectional height Bs represents the flange width tw represents the web thickness tf represents the flange thickness

Advances in Civil Engineering 3

encased steel in Chinese code JGJ138-2016 are shown asfollows

Mn α1fcbx h0 minusx

21113874 1113875 + fyAs h0 minus asprime( 1113857

+ faAaf h0 minus aaprime( 1113857 + Maw

(3a)

α1fcbx + 25x

h0minus δ1 + δ2( 11138571113890 1113891twh0fa 0 (3b)

Maw 05 δ21 + δ221113872 1113873minus δ1 + δ2( 1113857 + 25x

h0minus 125

x

h01113888 1113889

2⎡⎣ ⎤⎦twh

20fa

(3c)

Vn

038ftbh0 + 09Astfyth0

s aspect ratiole 25

042ftbh0 +Astfyth0

s aspect ratiogt 25

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(4)

where α1 is the coefficient modifying the compression stressof concrete compression zone x is the effective depth ofconcrete compression zone fy is the nominal yieldstrength of longitudinal reinforcement As is the area oflongitudinal reinforcement asprime is the distance from centerof compression rebar to the edge of compression zone Aafis the area of encased steel flange aaprime is the distance fromcenter of compression encased steel flange to the edge ofcompression zone δ1h0 is the distance from upper edge ofencased steel web to the edge of compression zone δ2h0 isthe distance from lower edge of encased steel web to theedge of compression zone and ft is the nominal tensilestrength of the concrete A similar result for moment ca-pacity and shear capacity was obtained using differentequations or methods which proves the accuracy of the

equations or methods In addition the lateral load re-sistance capacity calculated by MnL is smaller than thatcalculated by Vn which testifies the flexure-yielding designintention

e minimum required embedment length of encasedsteel Le is determined using Equation H4-2 in the 2010 AISCSeismic Provisions by taking Vnembed equal to MnL whichequation is modified considering the effect of concrete cover[3] and is shown as follows

Vnembed 405

fc

1113969twall

Bs1113888 1113889

066

β1Bs Le minus c( 1113857

middot058minus 022β1

088 + (L + c) Le minus c( 1113857( 11138571113888 1113889

(5)

where Vnembed is the shear capacity of the embedded steeltwall is the thickness of the shear wall connected to SRCcoupling beams and is taken as 860mm in this study which isthe width of the pedestal β1 is the depth factor relating thedepth of the Whitney stress block to the neutral axis depthand c is the concrete cover thickness of the pedestal emaximum required embedment length of seven SRC cou-pling beam specimens calculated using equation (5) is435mm Considering the connection between lateral hy-draulic actuator and reaction wall in the laboratory theembedment length (the height of the pedestal) is determinedto be 700mm which is more than sufficient to fix the SRCcoupling beam specimens

22 Test Setup e test setup that is illustrated in Figure 2was used in this study which consists of a rigid floor areaction wall a hydraulic actuator instrumentations anddata acquisition systems e specimens were tested underreversed cyclic lateral load using the servo-controlled hy-draulic actuator Before the specimen reaching the yielding

Table 2 Tensile test results of the encased steel plate and steel bar

Dimension of thesteel plate or bar Yielding strength (MPa) Tensile strength (MPa) Elastic modulus (MPa) Yielding strain Tensile strain

Plate thickness of 16mm 2491 4112 195times105 128times10minus3 0214Plate thickness of 20mm 2820 4529 206times105 137times10minus3 0206Plate thickness of 25mm 2550 4095 206times105 124times10minus3 0215Rebar diameter of 12mm 4570 5556 190times105 241times 10minus3 0139Rebar diameter of 20mm 4375 5828 196times105 223times10minus3 0133

Table 3 Lateral load resistance capacity of specimens (kN)

Specimen numberCalculated by MnL Calculated by Vn

Fiber section Equation (3) Equation (2) Equation (4)Beam1 9514 9198 11891 11162Beam2 6343 6132 11891 12000Beam3 3806 3679 11891 12000Beam4 9636 9277 13900 13094Beam5 9044 8797 15354 14492Beam6 7739 7611 14312 14043Beam7 8415 8296 15463 15161

4 Advances in Civil Engineering

point which was monitored by the outmost strain gaugesattached to the encased steel the lateral load was controlledby force and just one reversed cycle was loaded during eachloading level en after that the lateral load was controlledby displacement and three reversed cycles were loadedduring each loading level e lateral loading protocol ofspecimen Beam1 is shown in Figure 3 and each reversedloading cycle was finished in 2minutes

Linear variable displacement transducers (LVDTs)were installed to the specimens to measure the lateraldisplacements and the curvatures in the critical regionsStrain gauges were attached to measure the strain of steelplates and steel bars at plastic hinge zonese values of thelateral load the global and local displacements and thestrains were recorded automatically through the data ac-quisition system throughout the whole loading processTypical damage states including crack evolution concretecrushing and spalling and rebar buckling and fracturewere recorded through observation and photographsduring the loading process During the first cycle of eachloading level the maximum crack width was measured atlargest lateral load or largest displacement and the cor-responding maximum residual crack width was measuredat zero loads e crack width was measured using thecrack comparison card which has a measurement range of002ndash5mm

3 Test Results

31 Damage Behavior e sequence of observed typicaldamage states is similar for all specimens and the typicaldamage states of specimen Beam1 at different loading levelsare illustrated in Figure 4 which is a representative for allspecimens In general the damage started by forminghorizontal cracks at the bottom of the specimen at thetension side as shown in Figure 4(a) en the obliquecracks started to appear when the lateral load reaches500 kN as shown in Figure 4(b) Tensile yielding of the steelflange was detected using strain gauges with the increase ofloading levels At this instant the force control loadingprotocol was switched to the displacement control modeAfterwards the initial concrete crushing of compressive sideat the bottom of the specimen was observed when lateraldisplacement reaches 10mm as shown in Figure 4(c) Underthe following load cycles the large cracks concentrated at theinterface as shown in Figure 4(d) en the spalling ofconcrete cover appeared when the lateral displacement

reaches 225mm as shown in Figure 4(e) At this loadinglevel the lateral load carrying capacity of specimen started tofall off After concrete cover of the specimen completelyspalled off the longitudinal bars and hoops outcropped andthen the longitudinal bars buckled during the followingcycles when the lateral displacement reaches 275mm asshown in Figure 4(f ) and the fracture of the longitudinalbars was observed at subsequent larger lateral displacementwhich is 325mm as shown in Figure 4(g) e test con-tinued with the lateral displacement increased graduallyuntil the global instability appeared when the lateral dis-placement reaches 425mm After the test the concrete wasremoved and the fracture of encased steel was observed asshown in Figure 4(h) and no encased steel buckling wasfound

e typical damage development was roughly the samefor the seven specimens All specimens exhibited flexure-yielding behavior since steel web yielding occurred later thansteel flange yielding and no hoop rebar of specimens wasfound yielding before longitudinal rebar buckling or frac-ture e typical damage development was as followshorizontal cracking on the tensile side of the specimentensile yielding of the steel plate and rebar principle tensileyielding of steel web concrete crushing and spalling on thecompressive side of the specimen and rebar buckling andfracture

e crack distribution of specimens Beam 1 Beam 2 andBeam 3with different aspect ratios before concrete spalling isshown in Figure 5 With the increase of aspect ratio thecracking region is enlarged and more flexural cracks andless diagonal cracks occurred e flange-web area ratio andsteel ratio have little influence on the crack distribution

32 Force and Deformation Characteristics Lateral loadversus chord rotation (lateral displacement divided byspecimen length) hysteretic curves of specimens andcorresponding skeleton curves with typical damage statesmarked on it are shown in Figure 6e hysteretic curves ofspecimens show SRC coupling beams exhibited littlepinching effect and small degradation behavior until thelongitudinal rebars were fractured which shows SRCcoupling beams have excellent energy dissipation capa-bility By comparing specimens Beam1 Beam2 and Beam3the hysteresis behavior is similar among these threespecimens In general the specimen with higher aspectratio results in smaller hysteresis loops since the lateral loadresistance capacity is lower at same lateral chord rotationBy comparing specimens Beam1 Beam4 and Beam5 in-crease flange-web area ratio results in fuller (smallerpinching) and more stable (smaller strength degradation)hysteresis loops since flange steel contributes to SRCcoupling beam flexural behavior more than web steel Bycomparing specimens Beam2 Beam6 and Beam7 in-creased steel ratio also results in fuller and more stablehysteresis loops as larger steel ratio leads to more flangesteel and more web steel

Table 4 lists the mean values of chord rotation at thedamage characteristic points in the specimensrsquo skeleton

Reac

tion

wal

l

Hydraulicactuator

Specimen

Pedestal

Loading head

Ground anchor

Figure 2 Schematic representation of test setup

Advances in Civil Engineering 5

curves in two opposite loading directions Experimentalresults show that although the longitudinal bars were placedoutside the encased steel encased steel still yielded before thelongitudinal bars since the yielding strain of the longitudinalbars is 75 larger than the encased steel (as shown in Ta-ble 2) After the longitudinal bars fractured the specimenscan still experience larger displacement with small lateral

load carrying capacity degradation because the encased steelplate possessing much larger deformation capacity than thesteel bar was still eective to resist the lateral load

For specimens Beam1 Beam2 and Beam3 with dierentaspect ratios specimen Beam1 with the aspect ratio of 2 hasthe largest lateral load carrying capacity which is 11487 kNand is 246 times that of specimen Beam3 and 153 times that

Horizontal cracks

(a)

Diagonal cracks

(b)

Concrete crushing

(c)

Interface crack

(d)

Concrete spalling

(e)

Longitudinal bar buckling

(f )

Longitudinal bar fracture

(g)

Steel fracture

(h)

Figure 4 Typical damage states of specimen Beam1 (a) 300 kN (00012 rad) (b) 500 kN (0003 rad) (c) 10mm (002 rad) (d) 125mm(0025 rad) (e) 225mm (0045 rad) (f ) 275mm (0055 rad) (g) 325mm (0065 rad) and (h) 425mm (0085 rad)

App

lied

disp

lace

men

t (m

m)

4 8 12 16 20 24 28 32ndash40ndash30ndash20ndash10

010203040

ndash8ndash6ndash4ndash202468Stage 3Stage 2

Chor

d ro

tatio

n (

)

Cycle no0 1 2 3 4

Stage 1

Cycle no

ndash600ndash400ndash200

0200400600

App

lied

load

(kN

)

Figure 3 Lateral loading protocol of specimen Beam1

6 Advances in Civil Engineering

(a) (b) (c)

Figure 5 Crack pattern of specimens before concrete crushing (a) Beam1 (b) Beam2 (c) Beam3

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200

ndash004 000 004 008ndash008Rotation (rad)

ndash40 ndash20 0 20 40Lateral displacement (mm)

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash40 ndash20 0 20 40

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(a)

Late

ral l

oad

(kN

)

ndash60 ndash30 0 30 60Lateral displacement (mm)

ndash800

ndash400

0

400

800

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

ndash004 000 004 008ndash008Rotation (rad)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash60 ndash30 0 30 60

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(b)

Figure 6 Continued

Advances in Civil Engineering 7

Late

ral l

oad

(kN

)

ndash100 ndash50 0 50 100Lateral displacement (mm)

ndash480

ndash320

ndash160

0

160

320

480

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

ndash004 000 004 008ndash008Rotation (rad)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash100 ndash50 0 50 100

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(c)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash40 ndash20 0 20 40

Lateral displacement (mm)

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

ndash004 000 004 008ndash008Rotation (rad)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash40 ndash20 0 20 40

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(d)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash40 ndash20 0 20 40

Lateral displacement (mm)

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

ndash004 000 004 008ndash008Rotation (rad)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash40 ndash20 0 20 40

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(e)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash60 ndash30 0 30 60

Lateral displacement (mm)

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

ndash004 000 004 008ndash008Rotation (rad)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash60 ndash30 0 30 60

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(f )

Figure 6 Continued

8 Advances in Civil Engineering

of specimen Beam2 which means that the lateral loadcarrying capacity changes in inverse proportion with theaspect ratio and all specimens reached its exural strengthIn general the larger aspect ratio specimen tends to havesmaller lateral load carrying capacity at the individualdamage characteristic point Considering displacements ofthe individual damage state the initial damage states(concrete cracking steel tensile yielding and rebar tensileyielding) of specimen Beam3 with a aspect ratio of 5 tend tooccur later than those of specimen Beam1 with a aspect ratioof 2 which is consistent with the elastic chord rotationequation of the Timoshenko cantilever beam which is asfollows

θ ΔLML

3EI+M

GAL (6)

where M is the xed end section moment of the cantileverbeam L is the length of the cantilever beam E is the elasticmodulus I is the section moment inertia G is the shearmodulus and A is the eective shear section area When L islarger than

3EIGA

radicasymp 08h (h is the beam section height)

chord rotation θ increases with the increase of the beamlength under the same xed end moment e damage statessuch as steel web principle yielding concrete crushingconcrete spalling rebar buckling and rebar fracture of

specimen Beam3 tend to occur earlier than those of spec-imen Beam1 because specimen Beam3 has a relativelysmaller moment gradient at the plastic zone which causesexural damages of Beam3 to occur easily and smaller shearforce in Beam3 leads to smaller shear deformation also

For specimens Beam1 Beam4 and Beam5 with dierentange-web area ratios of encased steel specimen Beam4witha ange-web ratio of 05 has the largest lateral load carryingcapacity which is 11866 kN and is 33 larger than that ofspecimen Beam1 and 225 larger than that of specimenBeam5 which means that the specimen without the ange ofencased steel has a signicant smaller lateral load carryingcapacity e reason that specimen Beam4 with a smallerange-web ratio has slightly larger lateral load capacity thanspecimen Beam1 is that the encased steel consists of steelplates with dierent thicknesses and dierent yieldingstrengths and the average yielding strength of encased steelof specimen Beam4 is slightly larger than that of specimenBeam1 e calculated lateral load capacity (MnL) forspecimens Beam4 and Beam1 shown in Table 3 veried thisexplanation Considering the displacements of individualdamage states except the damage states like steel tensileyielding and rebar tensile yielding the other damage states ofspecimen Beam1 with a ange-web ratio of 1 tend to occurlater than those of specimen Beam5 with a ange-web ratio

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash60 ndash30 0 30 60

Lateral displacement (mm)

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

ndash004 000 004 008ndash008Rotation (rad)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash60 ndash30 0 30 60

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(g)

Figure 6 Lateral load-chord rotation hysteretic curves and skeleton curves of specimens (a) Beam1 (b) Beam2 (c) Beam3 (d) Beam4(e) Beam5 (f ) Beam6 (g) Beam7

Table 4 Chord rotation of specimens at the individual damage characteristic point

Specimen number θc (rad) θsty (rad) θrty (rad) θswy (rad) θcc (rad) θcs (rad) θrb (rad) θrf (rad)Beam1 00012 00033 00072 00140 00238 00403 00502 00609Beam2 00013 00063 00065 00120 00192 00385 00451 00558Beam3 00014 00044 00091 00095 00139 00378 00478 00560Beam4 00009 00041 00072 00085 00233 00416 00485 00565Beam5 00008 00053 00078 00078 00179 00346 00444 00586Beam6 00010 00065 00065 00100 00237 00485 00522 00653Beam7 00013 00039 00105 00131 00201 00430 00511 00593Note θc θsty θrty θswy θcc θcs θrb and θrf represent the chord rotation of specimens at damage states of concrete cracking steel tensile yielding rebar tensileyielding steel web principle tensile yielding concrete crushing concrete spalling rebar buckling and rebar fracture respectively For Beam5 rebar tensileyielding and steel web principle tensile yielding occurred at the same time For Beam6 steel tensile yielding and rebar tensile yielding occurred at the sametime

Advances in Civil Engineering 9

of 0 is is because the flange steel enhances the com-pression behavior of the concrete and delays the concretecrushing and spalling In addition shear deformation ofspecimen Beam1 with smaller web steel is larger than that ofspecimen Beam5 at the same damage state

For specimens Beam2 Beam6 and Beam7 with theincrease of steel ratio from 5 to 83 the lateral loadcarrying capacity increases from 7503 kN to 9688 kN by292 which means that the lateral load carrying capacity ofSRC coupling beam was influenced largely by the steel ratioExcept initial damage states like concrete cracking rebartensile yielding and steel web principle tensile yielding theother damage states of specimen Beam6 with a steel ratio of67 tend to occur later than those of specimen Beam2 witha steel ratio of 5 and Beam7 with a steel ratio of 83

Concrete cover cracking influences the encased steelcorrosion initiation and the crack width influences thecorrosion propagation thus both influence the performanceof structures [13] e maximum residual crack width of allspecimens represented by Wmres was measured during thetest cycles before concrete cover crashed or spalled evariation of maximum residual crack width with the chordrotation is shown in Figure 7 Generally the maximumresidual crack width rises up with the increase of the chordrotation e maximum residual crack width of the speci-men at the same rotation tends to be smaller with the in-crease of the aspect ratio or steel ratio for the average value ofthat for both directions For specimens Beam1 Beam4 andBeam5 with different flange-web area ratios of encased steelBeam4 has the smallest maximum residual crack width whileBeam1 has the largest maximum residual crack width at thesame rotation

4 Numerical Analysis and Verification

41 Modeling ree-dimensional nonlinear finite elementmodels were developed to simulate the inelastic behavior oftested SRC coupling beam specimens using Abaqus [14] Notonly the global force-rotation behavior but also the localmaterial damage behavior during the test process includingconcrete (cracking crushing and spalling) steel yieldingand rebar (yielding buckling and fracture) was predictedthrough finite element analysis It has been reported [15ndash17]that material damage states ie spalling and yielding arenot dependent on the history of loading but are ratherclosely related to the maximum displacement that thestructure has experienced erefore a monotonic analysiswas sufficient for predicting damage deformation of flexure-yielding SRC coupling beams

Damaged plasticity model was used to simulate theconcrete inelastic behavior in SRC coupling beam specimensis model is applicable in the situation that the concrete is atlow confinement pressures (less than four to five times thelargest compressive stress that can be carried by the concretein uniaxial compression) which is suitable for SRC couplingbeams Moon et al [18] used this model to study the con-finement effect of steel tubes on the infilled concrete andBabazadeh et al [17] used this model to study the spalling ofthe concrete for RC bridge columnse uniaxial stress-strain

relationship for the concrete recommended in Chinese codeGB50010-2010 [19] was adopted here as shown in Figure 8(a)e compression strength of the concrete is 373MPa whichis the prismatic compression strength of concrete fck which iscalculated based on the conversion formula in Chinese code50010-2010 [19] and the tested cubic compression strength ofconcrete fcu is equal to 578MPa

Ductile damage plasticity model was used to simulate theencased steel and rebar inelastic behavior in SRC couplingbeam specimens is model offers a general capability forpredicting the onset of failure and a capability for modelingprogressive damage and failure of ductile metals Zhu et al[20] used this model to simulate the steel tearing of concrete-filled steel tube columns e strengthening stage of steeladopted a bilinear model hardening stiffness of which is 1of elastic stiffness and damage initiated at tensile strain anddamage evolution adopted a linear damage form Consid-ering the cyclic fatigue of longitudinal rebar under earth-quakes Priestley [21] suggested the tensile strain of thelongitudinal rebar to be reduced by 40 Shi et al [22]carried out the structural steel low cycle fatigue test andproved that the tensile strain of Q345B steel was reduced by203 and Q235B steel was reduced by 386 after cyclicloading e fracture strain was conservatively taken as twotimes tensile strain refer to the former test results euniaxial stress-strain relationship for the 12mm diameterrebar is shown in Figure 8(b)

Eight-node solid elements with reduced integration(C3D8R) were used for the concrete four-node shell ele-ments with reduced integration (S4R) were used for theencased steel and two-node linear displacement truss ele-ments were used for rebar A perfect bond was assumedbetween the steel rebar elements and the concrete parttherefore the truss elements and shell elements were em-bedded in the concrete instance using the lowastEMBEDDEDELEMENT option e bottom surface of the pedestal wasfixed against all degrees of freedom A reference point wasmodeled on the surface of the loading plate which wasconstrained with the surface of the loading plate using thelowastCOUPLING option available in the ABAQUS library

42 Analysis Results e global skeleton curves of all thespecimens obtained from the FEA are compared with theskeleton curves obtained from the test and two of them areshown in Figure 9 e FEA model gave a stiffer result in thepositive part and softer one in the negative part for specimenBeam1 compared to the experimental result which may bedue to the slippage of the pedestal or the gap between loadinghead and specimen in the test e local material damagesobtained from FEA are also compared with test results andconcrete spalling and rebar fracture are shown in Figure 10From the qualitative comparison good agreement isachieved between experimental and FEA results not only onthe global behavior but also on the local material damagebehavior

Concrete crushing and spalling were predicted throughthe compression strain of concrete Priestley [21] suggested avalue of 0004 for cover concrete edge compressive crushing

10 Advances in Civil Engineering

strain and Jiang et al [23] proposed an equation to calculatethe conned concrete edge compression spalling strainwhich is equal to 0005 for test specimense concrete crack

width was predicted through the tensile strain of rebarPriestley [21] suggested a value of 001 for longitudinal rebartensile strain to control the residual crack width within

Stre

ss (M

Pa)

ndash5

0

5

10

15

20

25

30

35

40

0002 0004 0006 0008 00100000Strain

(a)

Stre

ss (M

Pa)

0

100

200

300

400

500

600

004 008 012 016000Strain

(b)

Figure 8 Uniaxial constitutive relationships of materials (a) Concrete (b) Rebar 12mm

Wm

res (

mm

)

Beam1Beam2Beam3

00

05

10

15

20

ndash002 000 002 004ndash004Rotation (rad)

(a)W

mre

s (m

m)

Beam1Beam4Beam5

00

05

10

15

20

ndash002 000 002 004ndash004Rotation (rad)

(b)

Wm

res (

mm

)

Beam2Beam6Beam7

00

05

10

15

20

ndash002 000 002 004ndash004Rotation (rad)

(c)

Figure 7 Maximum residual crack width of specimens (a) Eect of aspect ratio (b) Eect of ange-web ratio (c) Eect of steel ratio

Late

ral l

oad

(kN

)

FEATest

ndash1200

ndash800

ndash400

0

400

800

1200

ndash006 ndash003 000 003 006 009ndash009Rotation (rad)

(a)

Late

ral l

oad

(kN

)

FEATest

ndash1200

ndash800

ndash400

0

400

800

1200

ndash006 ndash003 000 003 006 009ndash009Rotation (rad)

(b)

Figure 9 Comparison of experimental and numerical skeleton curves (a) Specimen Beam1 (b) Specimen Beam5

Advances in Civil Engineering 11

10mm e chord rotations corresponding to differentconcrete damage states obtained from finite element analysiswere compared with the test result as shown in Table 5From the quantitative comparison for concrete damagedeformation finite element analysis can only provide astatistically consistent simulation result not specifically ac-curate simulation result for each specimen e mean ro-tation ratios between FEA and the test for the concreteresidual crack width equal to 1mm concrete crushing and

concrete spalling are 099 083 and 074 respectively If thecover concrete edge compression crushing strain is revisedto 0005 and confined concrete edge compression spallingstrain is revised to 00075 the mean rotation ratios betweenFEA and the test for concrete crushing and concrete spallingare 104 and 103 respectively

Steel flange tensile yielding and web principle tensileyielding were predicted directly through steel yielding strainrecorded in Table 2 e chord rotations corresponding to

Rebar fracture

PE max principalSNEG(fraction = ndash10)(avg 75)

+1454e ndash 01+1333e ndash 01+1212e ndash 01+1090e ndash 01+9693e ndash 02+8481e ndash 02+7269e ndash 02+6058e ndash 02+4846e ndash 02+3635e ndash 02+2423e ndash 02+1212e ndash 02+0000e + 00

(a)

Concrete spalling

PEEQ(avg 75)

+4683e ndash 02+4292e ndash 02+3902e ndash 02+3512e ndash 02+3122e ndash 02+2731e ndash 02+2341e ndash 02+1951e ndash 02+1561e ndash 02+1171e ndash 02+7804e ndash 03+3902e ndash 03+0000e + 00

(b)

Figure 10 Comparison of experimental and numerical damages (a) Rebar fracture of specimen Beam1 (b) Concrete spalling of specimenBeam1

Table 5 Comparison of chord rotations of specimens for different concrete damage states

Specimen numberResidual crack width lt1mm Concrete crushing Concrete spallingTest FEA FEAtest Test FEA FEAtest Test FEA FEAtest

Beam1 00084 00157 187 00238 00231 097 00403 00442 110Beam2 00116 00141 122 00192 00137 071 00385 00244 063Beam3 00150 00155 103 00139 00143 103 00378 00256 068Beam4 00261 00145 056 00233 00185 079 00416 00288 069Beam5 00200 00149 075 00179 00196 109 00346 00363 105Beam6 00187 00140 075 00237 00133 056 00485 00233 048Beam7 00190 00141 074 00201 00130 065 00430 00225 052

12 Advances in Civil Engineering

different steel yielding states obtained from finite elementanalysis were compared with the test result as shown inTable 6 e finite element analysis can provide a statisticallyconsistent simulation result and the mean rotation ratiosbetween FEA and the test for steel flange tensile yielding andsteel web principle tensile yielding are 123 and 108respectively

Rebar tensile yielding and rebar fracture were pre-dicted directly through rebar yielding strain and tensilestrain recorded in Table 2 Rebar buckling was predictedthrough confined concrete ultimate compressive strainwhich is calculated using equation suggested by Priestley[21] e chord rotations corresponding to different rebardamage states obtained from finite element analysis werecompared with the test result as shown in Table 7 efinite element analysis can provide a statistically consis-tent simulation result and the mean rotation ratios be-tween FEA and the test for rebar tensile yielding rebarbuckling and rebar fracture are 074 103 and 090respectively

43 Performance Index Limit Analysis e seismic per-formance of SRC coupling beams is affected by the ma-terial damage which is related to the material strain Onthe other hand the degradation of the load carrying ca-pacity of SRC coupling beams affects its seismic perfor-mance also Based on the study on the material damagestrain limits [21 23] and component strength degradationlimits [24] four performance levels are defined as shownin Table 8 Since there is a lack of test records of speci-mensrsquo deformation at damage states of concrete strainequal to 0002 or crack width equal to 2mm the chordrotation of specimens at different performance levels canonly be obtained through FEA Table 9 shows the chord

rotations of SRC coupling beam specimens at differentperformance levels and then the mean values wereadopted as the performance index limits which were0005 rad 0014 rad 0024 rad and 0047 rad for the fourperformance levels

5 Summary and Conclusions

Seven half-scale flexural-yielding SRC coupling beamspecimens designed according to Chinese approach weretested under cyclic loade influence of design parameterssuch as aspect ratio flange-web area ratio of encased steeland steel ratio on damage development hysteretic be-havior strength and maximum residual crack width werediscussed Finite element analysis was conducted forspecimens both global skeleton curves and local materialdamage were simulated simultaneously rough quanti-tative comparison finite element analysis can provide astatistically consistent simulation result for materialdamages for each specimen Some conclusions are drawnfrom this research

(1) All specimens failed in flexural mode e damagedevelopment was roughly the same and the typicaldamage states were recorded through the wholeloading process which can be used in assessing theseismic performance level of SRC coupling beams

(2) With the increase of aspect ratio the lateral loadcarrying capacity drops down significantly and themaximum residual crack width tends to be smallerWith the increase of flange-web area ratio of encasedsteel the hysteretic curve gets fuller e specimenwith intermediate flange-web area ratio has thelargest lateral load carrying capacity but smallestmaximum residual crack width With the increase of

Table 6 Comparison of chord rotations of specimens for different steel damage states

Specimen numberSteel flange yielding Steel web yielding

Test FEA FEAtest Test FEA FEAtestBeam1 00033 00059 179 00140 00124 089Beam2 00063 00053 084 00120 00116 097Beam3 00044 00061 139 00095 00108 114Beam4 00041 00051 124 00085 00105 124Beam5 00053 00056 106 00078 00098 126Beam6 00065 00057 088 00100 00115 115Beam7 00039 00056 144 00131 00120 092

Table 7 Comparison of chord rotations of specimens for different rebar damage states

Specimen numberRebar yielding Rebar buckling Rebar fracture

Test FEA FEAtest Test FEA FEAtest Test FEA FEAtestBeam1 00072 00059 082 00502 00777 155 00609 00562 092Beam2 00065 00054 083 00451 00426 094 00558 00502 090Beam3 00091 00060 066 00478 00446 093 00560 00571 102Beam4 00072 00056 078 00485 00527 109 00565 00504 089Beam5 00078 00054 069 00444 00526 118 00586 00596 102Beam6 00065 00056 086 00522 00403 077 00653 00490 075Beam7 00105 00057 054 00511 00390 076 00593 00493 083

Advances in Civil Engineering 13

steel ratio the lateral load carrying capacity increasessignificantly while the maximum residual crackwidth drops down

(3) e finite element model was benchmarkedthrough comparison with test results for bothglobal load-deformation curves and local materialdamages Both qualitative and quantitative com-parisons testify the accuracy of finite elementmodels e cover concrete edge compressionstrain and confined concrete edge compressionstrain were recommended to be 0005 and 00075respectively for accurately modeling concretecrushing and spalling Based on the damagecharacters and strength degradation four perfor-mance levels were defined and correspondingchord rotation limits were obtained through theverified numerical analysis

Data Availability

All the data in this paper are obtained from tests and nu-merical analysis and no other data in the literature are usedto support this study

Conflicts of Interest

e authors declare that there are no potential conflicts ofinterest with respect to the research authorship and pub-lication of this article

Acknowledgments

e financial support from the Program of Shanghai Aca-demic Research Leader (grant number 18XD1403900) andthe National Key Research and Development Program ofChina (grant number 2017YFC1500701) is gratefullyacknowledged

References

[1] S El-Tawil K A Harries P J Fortney B M Shahrooz andY Kurama ldquoSeismic design of hybrid coupled wall systemsstate of the artrdquo Journal of structural engineering vol 136no 7 pp 755ndash769 2010

[2] C-C Hung and W-T Lu ldquoA performance-based designmethod for coupled wall structuresrdquo Journal of EarthquakeEngineering vol 21 no 4 pp 579ndash603 2016

[3] C J Motter D C Fields J D Hooper et al ldquoSteel-reinforcedconcrete coupling beams I testingrdquo Journal of StructuralEngineering vol 143 no 3 article 04016191 2016

[4] B Gong and B M Shahrooz ldquoConcrete-steel compositecoupling beams I component testingrdquo Journal of StructuralEngineering vol 127 no 6 pp 625ndash631 2001

[5] B Gong and B M Shahrooz ldquoConcrete-steel compositecoupling beams II subassembly testing and design verifi-cationrdquo Journal of Structural Engineering vol 127 no 6pp 632ndash638 2001

[6] R K L Su and W Y Lam ldquoA unified design approach forplate-reinforced composite coupling beamsrdquo Journal ofConstructional Steel Research vol 65 no 3 pp 675ndash6862009

Table 8 Method of defining performance levels for SRC coupling beams

Performance level Damage descriptionPerformance criterion

Rebar or steel strain Concretestrain Load carrying capacity

Being basically intact ere are fine cracks in concrete while steel or rebaris not yielding εy 0002 mdash

Slight damage Concrete cover is not crushing and residual crackwidth is less than 1mm 0015 0005 mdash

Moderate damage Concrete cover is not spalling and residual crackwidth is less than 2mm 003 00075 95 Pmax

Severe damage Concrete core is not crushing and rebar or steel isnot fracturing εsu εcu 85 Pmax

Note εy is the yielding strain of steel or rebar εsu is the tensile strain of steel or rebar εcu is the ultimate strain of the concrete Pmax is the lateral load carryingcapacity of specimens

Table 9 Chord rotations of SRC coupling beams at different performance levels (rad)

Specimen numberPerformance level

Being basically intact Slight damage Moderate damage Severe damageBeam1 00055 00157 00264 00562Beam2 00053 00137 00212 00426Beam3 00060 00143 00235 00446Beam4 00051 00145 00239 00504Beam5 00054 00149 00257 00526Beam6 00051 00133 00228 00403Beam7 00050 00130 00228 00390

14 Advances in Civil Engineering

[7] C J Motter D C Fields J D Hooper et al ldquoSteel-reinforcedconcrete coupling beams II Modelingrdquo Journal of StructuralEngineering vol 143 no 3 article 04016192 2016

[8] Q Z Liang and X L Han ldquoe behavior of stiffening beamsand lintel beams under cyclic loadingrdquo Journal of South ChinaUniversity of Technology vol 23 no 1 pp 27ndash33 1995 inChinese

[9] H Jiang B Wang and X Lu ldquoExperimental study on damagebehavior of reinforced concrete shear walls subjected to cyclicloadsrdquo Journal of Earthquake Engineering vol 17 no 7pp 958ndash971 2013

[10] J Yue J Qian and D E Beskos ldquoA generalized multi-levelseismic damage model for RC framed structuresrdquo Soil Dy-namics and Earthquake Engineering vol 80 pp 25ndash39 2016

[11] JGJ138-2016 Code for Design of Composite Structures ChinaArchitecture amp Building Press Beijing China 2016

[12] R D Lequesne G J Parra-Montesinos and J K WightldquoSeismic behavior and detailing of high-performance fiber-reinforced concrete coupling beams and coupled wall sys-temsrdquo Journal of Structural Engineering vol 139 no 8pp 1362ndash1370 2012

[13] M Otieno H Beushausen and M Alexander ldquoTowardsincorporating the influence of cover cracking on steel cor-rosion in RC design codes the concept of performance-basedcrack width limitsrdquo Materials and Structures vol 45 no 12pp 1805ndash1816 2012

[14] SIMULIA Dassault Systems ABAQUS Analysis UserrsquosManual Version 616 SIMULIA Johnston RI USA 2016

[15] J C Goodnight M J Kowalsky and J M Nau ldquoEffect of loadhistory on performance limit states of circular bridge col-umnsrdquo Journal of Bridge Engineering vol 18 no 12pp 1383ndash1396 2013

[16] R T Ranf ldquoDamage accumulation in lightly confined rein-forced concrete bridge columnsrdquo PEER Report PacificEarthquake Engineering Research Center University ofCalifornia Berkeley CA USA 2006

[17] A Babazadeh R Burguentildeo and P F Silva ldquoUse of 3D finite-element models for predicting intermediate damage limitstates in RC bridge columnsrdquo Journal of Structural Engi-neering vol 141 no 10 article 04015012 2015

[18] J Moon CW Roeder andH-E Lee ldquoAnalytical modeling ofbending of circular concrete-filled steel tubesrdquo EngineeringStructures vol 42 no 12 pp 349ndash361 2012

[19] GB50010-2010 Code for Design of Concrete Structures ChinaArchitecture amp Building Press Beijing China 2010

[20] H Zhu M T Stephens and D E Lehman ldquoInelastic responseprediction of CFST columns and connections subjected tolateral loadingrdquo Journal of Constructional Steel Researchvol 132 pp 130ndash140 2017

[21] M J N Priestley ldquoPerformance based seismic designrdquo inProceedings of 12th World Conference on EarthquakeEngineering Auckland New Zealand January 2000

[22] Y Shi M Wang and Y Wang ldquoExperimental and consti-tutive model study of structural steel under cyclic loadingrdquoJournal of Constructional Steel Research vol 67 no 8pp 1185ndash1197 2011

[23] H Jiang X Lu and T Kubo ldquoDamage displacement esti-mation of flexure-dominant RC columnsrdquo Advances inStructural Engineering vol 13 no 2 pp 357ndash368 2010

[24] GB50011-2010 Code for Seismic Design of Buildings ChinaArchitecture amp Building Press Beijing China 2010

Advances in Civil Engineering 15

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encased steel in Chinese code JGJ138-2016 are shown asfollows

Mn α1fcbx h0 minusx

21113874 1113875 + fyAs h0 minus asprime( 1113857

+ faAaf h0 minus aaprime( 1113857 + Maw

(3a)

α1fcbx + 25x

h0minus δ1 + δ2( 11138571113890 1113891twh0fa 0 (3b)

Maw 05 δ21 + δ221113872 1113873minus δ1 + δ2( 1113857 + 25x

h0minus 125

x

h01113888 1113889

2⎡⎣ ⎤⎦twh

20fa

(3c)

Vn

038ftbh0 + 09Astfyth0

s aspect ratiole 25

042ftbh0 +Astfyth0

s aspect ratiogt 25

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(4)

where α1 is the coefficient modifying the compression stressof concrete compression zone x is the effective depth ofconcrete compression zone fy is the nominal yieldstrength of longitudinal reinforcement As is the area oflongitudinal reinforcement asprime is the distance from centerof compression rebar to the edge of compression zone Aafis the area of encased steel flange aaprime is the distance fromcenter of compression encased steel flange to the edge ofcompression zone δ1h0 is the distance from upper edge ofencased steel web to the edge of compression zone δ2h0 isthe distance from lower edge of encased steel web to theedge of compression zone and ft is the nominal tensilestrength of the concrete A similar result for moment ca-pacity and shear capacity was obtained using differentequations or methods which proves the accuracy of the

equations or methods In addition the lateral load re-sistance capacity calculated by MnL is smaller than thatcalculated by Vn which testifies the flexure-yielding designintention

e minimum required embedment length of encasedsteel Le is determined using Equation H4-2 in the 2010 AISCSeismic Provisions by taking Vnembed equal to MnL whichequation is modified considering the effect of concrete cover[3] and is shown as follows

Vnembed 405

fc

1113969twall

Bs1113888 1113889

066

β1Bs Le minus c( 1113857

middot058minus 022β1

088 + (L + c) Le minus c( 1113857( 11138571113888 1113889

(5)

where Vnembed is the shear capacity of the embedded steeltwall is the thickness of the shear wall connected to SRCcoupling beams and is taken as 860mm in this study which isthe width of the pedestal β1 is the depth factor relating thedepth of the Whitney stress block to the neutral axis depthand c is the concrete cover thickness of the pedestal emaximum required embedment length of seven SRC cou-pling beam specimens calculated using equation (5) is435mm Considering the connection between lateral hy-draulic actuator and reaction wall in the laboratory theembedment length (the height of the pedestal) is determinedto be 700mm which is more than sufficient to fix the SRCcoupling beam specimens

22 Test Setup e test setup that is illustrated in Figure 2was used in this study which consists of a rigid floor areaction wall a hydraulic actuator instrumentations anddata acquisition systems e specimens were tested underreversed cyclic lateral load using the servo-controlled hy-draulic actuator Before the specimen reaching the yielding

Table 2 Tensile test results of the encased steel plate and steel bar

Dimension of thesteel plate or bar Yielding strength (MPa) Tensile strength (MPa) Elastic modulus (MPa) Yielding strain Tensile strain

Plate thickness of 16mm 2491 4112 195times105 128times10minus3 0214Plate thickness of 20mm 2820 4529 206times105 137times10minus3 0206Plate thickness of 25mm 2550 4095 206times105 124times10minus3 0215Rebar diameter of 12mm 4570 5556 190times105 241times 10minus3 0139Rebar diameter of 20mm 4375 5828 196times105 223times10minus3 0133

Table 3 Lateral load resistance capacity of specimens (kN)

Specimen numberCalculated by MnL Calculated by Vn

Fiber section Equation (3) Equation (2) Equation (4)Beam1 9514 9198 11891 11162Beam2 6343 6132 11891 12000Beam3 3806 3679 11891 12000Beam4 9636 9277 13900 13094Beam5 9044 8797 15354 14492Beam6 7739 7611 14312 14043Beam7 8415 8296 15463 15161

4 Advances in Civil Engineering

point which was monitored by the outmost strain gaugesattached to the encased steel the lateral load was controlledby force and just one reversed cycle was loaded during eachloading level en after that the lateral load was controlledby displacement and three reversed cycles were loadedduring each loading level e lateral loading protocol ofspecimen Beam1 is shown in Figure 3 and each reversedloading cycle was finished in 2minutes

Linear variable displacement transducers (LVDTs)were installed to the specimens to measure the lateraldisplacements and the curvatures in the critical regionsStrain gauges were attached to measure the strain of steelplates and steel bars at plastic hinge zonese values of thelateral load the global and local displacements and thestrains were recorded automatically through the data ac-quisition system throughout the whole loading processTypical damage states including crack evolution concretecrushing and spalling and rebar buckling and fracturewere recorded through observation and photographsduring the loading process During the first cycle of eachloading level the maximum crack width was measured atlargest lateral load or largest displacement and the cor-responding maximum residual crack width was measuredat zero loads e crack width was measured using thecrack comparison card which has a measurement range of002ndash5mm

3 Test Results

31 Damage Behavior e sequence of observed typicaldamage states is similar for all specimens and the typicaldamage states of specimen Beam1 at different loading levelsare illustrated in Figure 4 which is a representative for allspecimens In general the damage started by forminghorizontal cracks at the bottom of the specimen at thetension side as shown in Figure 4(a) en the obliquecracks started to appear when the lateral load reaches500 kN as shown in Figure 4(b) Tensile yielding of the steelflange was detected using strain gauges with the increase ofloading levels At this instant the force control loadingprotocol was switched to the displacement control modeAfterwards the initial concrete crushing of compressive sideat the bottom of the specimen was observed when lateraldisplacement reaches 10mm as shown in Figure 4(c) Underthe following load cycles the large cracks concentrated at theinterface as shown in Figure 4(d) en the spalling ofconcrete cover appeared when the lateral displacement

reaches 225mm as shown in Figure 4(e) At this loadinglevel the lateral load carrying capacity of specimen started tofall off After concrete cover of the specimen completelyspalled off the longitudinal bars and hoops outcropped andthen the longitudinal bars buckled during the followingcycles when the lateral displacement reaches 275mm asshown in Figure 4(f ) and the fracture of the longitudinalbars was observed at subsequent larger lateral displacementwhich is 325mm as shown in Figure 4(g) e test con-tinued with the lateral displacement increased graduallyuntil the global instability appeared when the lateral dis-placement reaches 425mm After the test the concrete wasremoved and the fracture of encased steel was observed asshown in Figure 4(h) and no encased steel buckling wasfound

e typical damage development was roughly the samefor the seven specimens All specimens exhibited flexure-yielding behavior since steel web yielding occurred later thansteel flange yielding and no hoop rebar of specimens wasfound yielding before longitudinal rebar buckling or frac-ture e typical damage development was as followshorizontal cracking on the tensile side of the specimentensile yielding of the steel plate and rebar principle tensileyielding of steel web concrete crushing and spalling on thecompressive side of the specimen and rebar buckling andfracture

e crack distribution of specimens Beam 1 Beam 2 andBeam 3with different aspect ratios before concrete spalling isshown in Figure 5 With the increase of aspect ratio thecracking region is enlarged and more flexural cracks andless diagonal cracks occurred e flange-web area ratio andsteel ratio have little influence on the crack distribution

32 Force and Deformation Characteristics Lateral loadversus chord rotation (lateral displacement divided byspecimen length) hysteretic curves of specimens andcorresponding skeleton curves with typical damage statesmarked on it are shown in Figure 6e hysteretic curves ofspecimens show SRC coupling beams exhibited littlepinching effect and small degradation behavior until thelongitudinal rebars were fractured which shows SRCcoupling beams have excellent energy dissipation capa-bility By comparing specimens Beam1 Beam2 and Beam3the hysteresis behavior is similar among these threespecimens In general the specimen with higher aspectratio results in smaller hysteresis loops since the lateral loadresistance capacity is lower at same lateral chord rotationBy comparing specimens Beam1 Beam4 and Beam5 in-crease flange-web area ratio results in fuller (smallerpinching) and more stable (smaller strength degradation)hysteresis loops since flange steel contributes to SRCcoupling beam flexural behavior more than web steel Bycomparing specimens Beam2 Beam6 and Beam7 in-creased steel ratio also results in fuller and more stablehysteresis loops as larger steel ratio leads to more flangesteel and more web steel

Table 4 lists the mean values of chord rotation at thedamage characteristic points in the specimensrsquo skeleton

Reac

tion

wal

l

Hydraulicactuator

Specimen

Pedestal

Loading head

Ground anchor

Figure 2 Schematic representation of test setup

Advances in Civil Engineering 5

curves in two opposite loading directions Experimentalresults show that although the longitudinal bars were placedoutside the encased steel encased steel still yielded before thelongitudinal bars since the yielding strain of the longitudinalbars is 75 larger than the encased steel (as shown in Ta-ble 2) After the longitudinal bars fractured the specimenscan still experience larger displacement with small lateral

load carrying capacity degradation because the encased steelplate possessing much larger deformation capacity than thesteel bar was still eective to resist the lateral load

For specimens Beam1 Beam2 and Beam3 with dierentaspect ratios specimen Beam1 with the aspect ratio of 2 hasthe largest lateral load carrying capacity which is 11487 kNand is 246 times that of specimen Beam3 and 153 times that

Horizontal cracks

(a)

Diagonal cracks

(b)

Concrete crushing

(c)

Interface crack

(d)

Concrete spalling

(e)

Longitudinal bar buckling

(f )

Longitudinal bar fracture

(g)

Steel fracture

(h)

Figure 4 Typical damage states of specimen Beam1 (a) 300 kN (00012 rad) (b) 500 kN (0003 rad) (c) 10mm (002 rad) (d) 125mm(0025 rad) (e) 225mm (0045 rad) (f ) 275mm (0055 rad) (g) 325mm (0065 rad) and (h) 425mm (0085 rad)

App

lied

disp

lace

men

t (m

m)

4 8 12 16 20 24 28 32ndash40ndash30ndash20ndash10

010203040

ndash8ndash6ndash4ndash202468Stage 3Stage 2

Chor

d ro

tatio

n (

)

Cycle no0 1 2 3 4

Stage 1

Cycle no

ndash600ndash400ndash200

0200400600

App

lied

load

(kN

)

Figure 3 Lateral loading protocol of specimen Beam1

6 Advances in Civil Engineering

(a) (b) (c)

Figure 5 Crack pattern of specimens before concrete crushing (a) Beam1 (b) Beam2 (c) Beam3

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200

ndash004 000 004 008ndash008Rotation (rad)

ndash40 ndash20 0 20 40Lateral displacement (mm)

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash40 ndash20 0 20 40

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(a)

Late

ral l

oad

(kN

)

ndash60 ndash30 0 30 60Lateral displacement (mm)

ndash800

ndash400

0

400

800

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

ndash004 000 004 008ndash008Rotation (rad)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash60 ndash30 0 30 60

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(b)

Figure 6 Continued

Advances in Civil Engineering 7

Late

ral l

oad

(kN

)

ndash100 ndash50 0 50 100Lateral displacement (mm)

ndash480

ndash320

ndash160

0

160

320

480

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

ndash004 000 004 008ndash008Rotation (rad)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash100 ndash50 0 50 100

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(c)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash40 ndash20 0 20 40

Lateral displacement (mm)

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

ndash004 000 004 008ndash008Rotation (rad)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash40 ndash20 0 20 40

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(d)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash40 ndash20 0 20 40

Lateral displacement (mm)

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

ndash004 000 004 008ndash008Rotation (rad)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash40 ndash20 0 20 40

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(e)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash60 ndash30 0 30 60

Lateral displacement (mm)

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

ndash004 000 004 008ndash008Rotation (rad)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash60 ndash30 0 30 60

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(f )

Figure 6 Continued

8 Advances in Civil Engineering

of specimen Beam2 which means that the lateral loadcarrying capacity changes in inverse proportion with theaspect ratio and all specimens reached its exural strengthIn general the larger aspect ratio specimen tends to havesmaller lateral load carrying capacity at the individualdamage characteristic point Considering displacements ofthe individual damage state the initial damage states(concrete cracking steel tensile yielding and rebar tensileyielding) of specimen Beam3 with a aspect ratio of 5 tend tooccur later than those of specimen Beam1 with a aspect ratioof 2 which is consistent with the elastic chord rotationequation of the Timoshenko cantilever beam which is asfollows

θ ΔLML

3EI+M

GAL (6)

where M is the xed end section moment of the cantileverbeam L is the length of the cantilever beam E is the elasticmodulus I is the section moment inertia G is the shearmodulus and A is the eective shear section area When L islarger than

3EIGA

radicasymp 08h (h is the beam section height)

chord rotation θ increases with the increase of the beamlength under the same xed end moment e damage statessuch as steel web principle yielding concrete crushingconcrete spalling rebar buckling and rebar fracture of

specimen Beam3 tend to occur earlier than those of spec-imen Beam1 because specimen Beam3 has a relativelysmaller moment gradient at the plastic zone which causesexural damages of Beam3 to occur easily and smaller shearforce in Beam3 leads to smaller shear deformation also

For specimens Beam1 Beam4 and Beam5 with dierentange-web area ratios of encased steel specimen Beam4witha ange-web ratio of 05 has the largest lateral load carryingcapacity which is 11866 kN and is 33 larger than that ofspecimen Beam1 and 225 larger than that of specimenBeam5 which means that the specimen without the ange ofencased steel has a signicant smaller lateral load carryingcapacity e reason that specimen Beam4 with a smallerange-web ratio has slightly larger lateral load capacity thanspecimen Beam1 is that the encased steel consists of steelplates with dierent thicknesses and dierent yieldingstrengths and the average yielding strength of encased steelof specimen Beam4 is slightly larger than that of specimenBeam1 e calculated lateral load capacity (MnL) forspecimens Beam4 and Beam1 shown in Table 3 veried thisexplanation Considering the displacements of individualdamage states except the damage states like steel tensileyielding and rebar tensile yielding the other damage states ofspecimen Beam1 with a ange-web ratio of 1 tend to occurlater than those of specimen Beam5 with a ange-web ratio

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash60 ndash30 0 30 60

Lateral displacement (mm)

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

ndash004 000 004 008ndash008Rotation (rad)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash60 ndash30 0 30 60

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(g)

Figure 6 Lateral load-chord rotation hysteretic curves and skeleton curves of specimens (a) Beam1 (b) Beam2 (c) Beam3 (d) Beam4(e) Beam5 (f ) Beam6 (g) Beam7

Table 4 Chord rotation of specimens at the individual damage characteristic point

Specimen number θc (rad) θsty (rad) θrty (rad) θswy (rad) θcc (rad) θcs (rad) θrb (rad) θrf (rad)Beam1 00012 00033 00072 00140 00238 00403 00502 00609Beam2 00013 00063 00065 00120 00192 00385 00451 00558Beam3 00014 00044 00091 00095 00139 00378 00478 00560Beam4 00009 00041 00072 00085 00233 00416 00485 00565Beam5 00008 00053 00078 00078 00179 00346 00444 00586Beam6 00010 00065 00065 00100 00237 00485 00522 00653Beam7 00013 00039 00105 00131 00201 00430 00511 00593Note θc θsty θrty θswy θcc θcs θrb and θrf represent the chord rotation of specimens at damage states of concrete cracking steel tensile yielding rebar tensileyielding steel web principle tensile yielding concrete crushing concrete spalling rebar buckling and rebar fracture respectively For Beam5 rebar tensileyielding and steel web principle tensile yielding occurred at the same time For Beam6 steel tensile yielding and rebar tensile yielding occurred at the sametime

Advances in Civil Engineering 9

of 0 is is because the flange steel enhances the com-pression behavior of the concrete and delays the concretecrushing and spalling In addition shear deformation ofspecimen Beam1 with smaller web steel is larger than that ofspecimen Beam5 at the same damage state

For specimens Beam2 Beam6 and Beam7 with theincrease of steel ratio from 5 to 83 the lateral loadcarrying capacity increases from 7503 kN to 9688 kN by292 which means that the lateral load carrying capacity ofSRC coupling beam was influenced largely by the steel ratioExcept initial damage states like concrete cracking rebartensile yielding and steel web principle tensile yielding theother damage states of specimen Beam6 with a steel ratio of67 tend to occur later than those of specimen Beam2 witha steel ratio of 5 and Beam7 with a steel ratio of 83

Concrete cover cracking influences the encased steelcorrosion initiation and the crack width influences thecorrosion propagation thus both influence the performanceof structures [13] e maximum residual crack width of allspecimens represented by Wmres was measured during thetest cycles before concrete cover crashed or spalled evariation of maximum residual crack width with the chordrotation is shown in Figure 7 Generally the maximumresidual crack width rises up with the increase of the chordrotation e maximum residual crack width of the speci-men at the same rotation tends to be smaller with the in-crease of the aspect ratio or steel ratio for the average value ofthat for both directions For specimens Beam1 Beam4 andBeam5 with different flange-web area ratios of encased steelBeam4 has the smallest maximum residual crack width whileBeam1 has the largest maximum residual crack width at thesame rotation

4 Numerical Analysis and Verification

41 Modeling ree-dimensional nonlinear finite elementmodels were developed to simulate the inelastic behavior oftested SRC coupling beam specimens using Abaqus [14] Notonly the global force-rotation behavior but also the localmaterial damage behavior during the test process includingconcrete (cracking crushing and spalling) steel yieldingand rebar (yielding buckling and fracture) was predictedthrough finite element analysis It has been reported [15ndash17]that material damage states ie spalling and yielding arenot dependent on the history of loading but are ratherclosely related to the maximum displacement that thestructure has experienced erefore a monotonic analysiswas sufficient for predicting damage deformation of flexure-yielding SRC coupling beams

Damaged plasticity model was used to simulate theconcrete inelastic behavior in SRC coupling beam specimensis model is applicable in the situation that the concrete is atlow confinement pressures (less than four to five times thelargest compressive stress that can be carried by the concretein uniaxial compression) which is suitable for SRC couplingbeams Moon et al [18] used this model to study the con-finement effect of steel tubes on the infilled concrete andBabazadeh et al [17] used this model to study the spalling ofthe concrete for RC bridge columnse uniaxial stress-strain

relationship for the concrete recommended in Chinese codeGB50010-2010 [19] was adopted here as shown in Figure 8(a)e compression strength of the concrete is 373MPa whichis the prismatic compression strength of concrete fck which iscalculated based on the conversion formula in Chinese code50010-2010 [19] and the tested cubic compression strength ofconcrete fcu is equal to 578MPa

Ductile damage plasticity model was used to simulate theencased steel and rebar inelastic behavior in SRC couplingbeam specimens is model offers a general capability forpredicting the onset of failure and a capability for modelingprogressive damage and failure of ductile metals Zhu et al[20] used this model to simulate the steel tearing of concrete-filled steel tube columns e strengthening stage of steeladopted a bilinear model hardening stiffness of which is 1of elastic stiffness and damage initiated at tensile strain anddamage evolution adopted a linear damage form Consid-ering the cyclic fatigue of longitudinal rebar under earth-quakes Priestley [21] suggested the tensile strain of thelongitudinal rebar to be reduced by 40 Shi et al [22]carried out the structural steel low cycle fatigue test andproved that the tensile strain of Q345B steel was reduced by203 and Q235B steel was reduced by 386 after cyclicloading e fracture strain was conservatively taken as twotimes tensile strain refer to the former test results euniaxial stress-strain relationship for the 12mm diameterrebar is shown in Figure 8(b)

Eight-node solid elements with reduced integration(C3D8R) were used for the concrete four-node shell ele-ments with reduced integration (S4R) were used for theencased steel and two-node linear displacement truss ele-ments were used for rebar A perfect bond was assumedbetween the steel rebar elements and the concrete parttherefore the truss elements and shell elements were em-bedded in the concrete instance using the lowastEMBEDDEDELEMENT option e bottom surface of the pedestal wasfixed against all degrees of freedom A reference point wasmodeled on the surface of the loading plate which wasconstrained with the surface of the loading plate using thelowastCOUPLING option available in the ABAQUS library

42 Analysis Results e global skeleton curves of all thespecimens obtained from the FEA are compared with theskeleton curves obtained from the test and two of them areshown in Figure 9 e FEA model gave a stiffer result in thepositive part and softer one in the negative part for specimenBeam1 compared to the experimental result which may bedue to the slippage of the pedestal or the gap between loadinghead and specimen in the test e local material damagesobtained from FEA are also compared with test results andconcrete spalling and rebar fracture are shown in Figure 10From the qualitative comparison good agreement isachieved between experimental and FEA results not only onthe global behavior but also on the local material damagebehavior

Concrete crushing and spalling were predicted throughthe compression strain of concrete Priestley [21] suggested avalue of 0004 for cover concrete edge compressive crushing

10 Advances in Civil Engineering

strain and Jiang et al [23] proposed an equation to calculatethe conned concrete edge compression spalling strainwhich is equal to 0005 for test specimense concrete crack

width was predicted through the tensile strain of rebarPriestley [21] suggested a value of 001 for longitudinal rebartensile strain to control the residual crack width within

Stre

ss (M

Pa)

ndash5

0

5

10

15

20

25

30

35

40

0002 0004 0006 0008 00100000Strain

(a)

Stre

ss (M

Pa)

0

100

200

300

400

500

600

004 008 012 016000Strain

(b)

Figure 8 Uniaxial constitutive relationships of materials (a) Concrete (b) Rebar 12mm

Wm

res (

mm

)

Beam1Beam2Beam3

00

05

10

15

20

ndash002 000 002 004ndash004Rotation (rad)

(a)W

mre

s (m

m)

Beam1Beam4Beam5

00

05

10

15

20

ndash002 000 002 004ndash004Rotation (rad)

(b)

Wm

res (

mm

)

Beam2Beam6Beam7

00

05

10

15

20

ndash002 000 002 004ndash004Rotation (rad)

(c)

Figure 7 Maximum residual crack width of specimens (a) Eect of aspect ratio (b) Eect of ange-web ratio (c) Eect of steel ratio

Late

ral l

oad

(kN

)

FEATest

ndash1200

ndash800

ndash400

0

400

800

1200

ndash006 ndash003 000 003 006 009ndash009Rotation (rad)

(a)

Late

ral l

oad

(kN

)

FEATest

ndash1200

ndash800

ndash400

0

400

800

1200

ndash006 ndash003 000 003 006 009ndash009Rotation (rad)

(b)

Figure 9 Comparison of experimental and numerical skeleton curves (a) Specimen Beam1 (b) Specimen Beam5

Advances in Civil Engineering 11

10mm e chord rotations corresponding to differentconcrete damage states obtained from finite element analysiswere compared with the test result as shown in Table 5From the quantitative comparison for concrete damagedeformation finite element analysis can only provide astatistically consistent simulation result not specifically ac-curate simulation result for each specimen e mean ro-tation ratios between FEA and the test for the concreteresidual crack width equal to 1mm concrete crushing and

concrete spalling are 099 083 and 074 respectively If thecover concrete edge compression crushing strain is revisedto 0005 and confined concrete edge compression spallingstrain is revised to 00075 the mean rotation ratios betweenFEA and the test for concrete crushing and concrete spallingare 104 and 103 respectively

Steel flange tensile yielding and web principle tensileyielding were predicted directly through steel yielding strainrecorded in Table 2 e chord rotations corresponding to

Rebar fracture

PE max principalSNEG(fraction = ndash10)(avg 75)

+1454e ndash 01+1333e ndash 01+1212e ndash 01+1090e ndash 01+9693e ndash 02+8481e ndash 02+7269e ndash 02+6058e ndash 02+4846e ndash 02+3635e ndash 02+2423e ndash 02+1212e ndash 02+0000e + 00

(a)

Concrete spalling

PEEQ(avg 75)

+4683e ndash 02+4292e ndash 02+3902e ndash 02+3512e ndash 02+3122e ndash 02+2731e ndash 02+2341e ndash 02+1951e ndash 02+1561e ndash 02+1171e ndash 02+7804e ndash 03+3902e ndash 03+0000e + 00

(b)

Figure 10 Comparison of experimental and numerical damages (a) Rebar fracture of specimen Beam1 (b) Concrete spalling of specimenBeam1

Table 5 Comparison of chord rotations of specimens for different concrete damage states

Specimen numberResidual crack width lt1mm Concrete crushing Concrete spallingTest FEA FEAtest Test FEA FEAtest Test FEA FEAtest

Beam1 00084 00157 187 00238 00231 097 00403 00442 110Beam2 00116 00141 122 00192 00137 071 00385 00244 063Beam3 00150 00155 103 00139 00143 103 00378 00256 068Beam4 00261 00145 056 00233 00185 079 00416 00288 069Beam5 00200 00149 075 00179 00196 109 00346 00363 105Beam6 00187 00140 075 00237 00133 056 00485 00233 048Beam7 00190 00141 074 00201 00130 065 00430 00225 052

12 Advances in Civil Engineering

different steel yielding states obtained from finite elementanalysis were compared with the test result as shown inTable 6 e finite element analysis can provide a statisticallyconsistent simulation result and the mean rotation ratiosbetween FEA and the test for steel flange tensile yielding andsteel web principle tensile yielding are 123 and 108respectively

Rebar tensile yielding and rebar fracture were pre-dicted directly through rebar yielding strain and tensilestrain recorded in Table 2 Rebar buckling was predictedthrough confined concrete ultimate compressive strainwhich is calculated using equation suggested by Priestley[21] e chord rotations corresponding to different rebardamage states obtained from finite element analysis werecompared with the test result as shown in Table 7 efinite element analysis can provide a statistically consis-tent simulation result and the mean rotation ratios be-tween FEA and the test for rebar tensile yielding rebarbuckling and rebar fracture are 074 103 and 090respectively

43 Performance Index Limit Analysis e seismic per-formance of SRC coupling beams is affected by the ma-terial damage which is related to the material strain Onthe other hand the degradation of the load carrying ca-pacity of SRC coupling beams affects its seismic perfor-mance also Based on the study on the material damagestrain limits [21 23] and component strength degradationlimits [24] four performance levels are defined as shownin Table 8 Since there is a lack of test records of speci-mensrsquo deformation at damage states of concrete strainequal to 0002 or crack width equal to 2mm the chordrotation of specimens at different performance levels canonly be obtained through FEA Table 9 shows the chord

rotations of SRC coupling beam specimens at differentperformance levels and then the mean values wereadopted as the performance index limits which were0005 rad 0014 rad 0024 rad and 0047 rad for the fourperformance levels

5 Summary and Conclusions

Seven half-scale flexural-yielding SRC coupling beamspecimens designed according to Chinese approach weretested under cyclic loade influence of design parameterssuch as aspect ratio flange-web area ratio of encased steeland steel ratio on damage development hysteretic be-havior strength and maximum residual crack width werediscussed Finite element analysis was conducted forspecimens both global skeleton curves and local materialdamage were simulated simultaneously rough quanti-tative comparison finite element analysis can provide astatistically consistent simulation result for materialdamages for each specimen Some conclusions are drawnfrom this research

(1) All specimens failed in flexural mode e damagedevelopment was roughly the same and the typicaldamage states were recorded through the wholeloading process which can be used in assessing theseismic performance level of SRC coupling beams

(2) With the increase of aspect ratio the lateral loadcarrying capacity drops down significantly and themaximum residual crack width tends to be smallerWith the increase of flange-web area ratio of encasedsteel the hysteretic curve gets fuller e specimenwith intermediate flange-web area ratio has thelargest lateral load carrying capacity but smallestmaximum residual crack width With the increase of

Table 6 Comparison of chord rotations of specimens for different steel damage states

Specimen numberSteel flange yielding Steel web yielding

Test FEA FEAtest Test FEA FEAtestBeam1 00033 00059 179 00140 00124 089Beam2 00063 00053 084 00120 00116 097Beam3 00044 00061 139 00095 00108 114Beam4 00041 00051 124 00085 00105 124Beam5 00053 00056 106 00078 00098 126Beam6 00065 00057 088 00100 00115 115Beam7 00039 00056 144 00131 00120 092

Table 7 Comparison of chord rotations of specimens for different rebar damage states

Specimen numberRebar yielding Rebar buckling Rebar fracture

Test FEA FEAtest Test FEA FEAtest Test FEA FEAtestBeam1 00072 00059 082 00502 00777 155 00609 00562 092Beam2 00065 00054 083 00451 00426 094 00558 00502 090Beam3 00091 00060 066 00478 00446 093 00560 00571 102Beam4 00072 00056 078 00485 00527 109 00565 00504 089Beam5 00078 00054 069 00444 00526 118 00586 00596 102Beam6 00065 00056 086 00522 00403 077 00653 00490 075Beam7 00105 00057 054 00511 00390 076 00593 00493 083

Advances in Civil Engineering 13

steel ratio the lateral load carrying capacity increasessignificantly while the maximum residual crackwidth drops down

(3) e finite element model was benchmarkedthrough comparison with test results for bothglobal load-deformation curves and local materialdamages Both qualitative and quantitative com-parisons testify the accuracy of finite elementmodels e cover concrete edge compressionstrain and confined concrete edge compressionstrain were recommended to be 0005 and 00075respectively for accurately modeling concretecrushing and spalling Based on the damagecharacters and strength degradation four perfor-mance levels were defined and correspondingchord rotation limits were obtained through theverified numerical analysis

Data Availability

All the data in this paper are obtained from tests and nu-merical analysis and no other data in the literature are usedto support this study

Conflicts of Interest

e authors declare that there are no potential conflicts ofinterest with respect to the research authorship and pub-lication of this article

Acknowledgments

e financial support from the Program of Shanghai Aca-demic Research Leader (grant number 18XD1403900) andthe National Key Research and Development Program ofChina (grant number 2017YFC1500701) is gratefullyacknowledged

References

[1] S El-Tawil K A Harries P J Fortney B M Shahrooz andY Kurama ldquoSeismic design of hybrid coupled wall systemsstate of the artrdquo Journal of structural engineering vol 136no 7 pp 755ndash769 2010

[2] C-C Hung and W-T Lu ldquoA performance-based designmethod for coupled wall structuresrdquo Journal of EarthquakeEngineering vol 21 no 4 pp 579ndash603 2016

[3] C J Motter D C Fields J D Hooper et al ldquoSteel-reinforcedconcrete coupling beams I testingrdquo Journal of StructuralEngineering vol 143 no 3 article 04016191 2016

[4] B Gong and B M Shahrooz ldquoConcrete-steel compositecoupling beams I component testingrdquo Journal of StructuralEngineering vol 127 no 6 pp 625ndash631 2001

[5] B Gong and B M Shahrooz ldquoConcrete-steel compositecoupling beams II subassembly testing and design verifi-cationrdquo Journal of Structural Engineering vol 127 no 6pp 632ndash638 2001

[6] R K L Su and W Y Lam ldquoA unified design approach forplate-reinforced composite coupling beamsrdquo Journal ofConstructional Steel Research vol 65 no 3 pp 675ndash6862009

Table 8 Method of defining performance levels for SRC coupling beams

Performance level Damage descriptionPerformance criterion

Rebar or steel strain Concretestrain Load carrying capacity

Being basically intact ere are fine cracks in concrete while steel or rebaris not yielding εy 0002 mdash

Slight damage Concrete cover is not crushing and residual crackwidth is less than 1mm 0015 0005 mdash

Moderate damage Concrete cover is not spalling and residual crackwidth is less than 2mm 003 00075 95 Pmax

Severe damage Concrete core is not crushing and rebar or steel isnot fracturing εsu εcu 85 Pmax

Note εy is the yielding strain of steel or rebar εsu is the tensile strain of steel or rebar εcu is the ultimate strain of the concrete Pmax is the lateral load carryingcapacity of specimens

Table 9 Chord rotations of SRC coupling beams at different performance levels (rad)

Specimen numberPerformance level

Being basically intact Slight damage Moderate damage Severe damageBeam1 00055 00157 00264 00562Beam2 00053 00137 00212 00426Beam3 00060 00143 00235 00446Beam4 00051 00145 00239 00504Beam5 00054 00149 00257 00526Beam6 00051 00133 00228 00403Beam7 00050 00130 00228 00390

14 Advances in Civil Engineering

[7] C J Motter D C Fields J D Hooper et al ldquoSteel-reinforcedconcrete coupling beams II Modelingrdquo Journal of StructuralEngineering vol 143 no 3 article 04016192 2016

[8] Q Z Liang and X L Han ldquoe behavior of stiffening beamsand lintel beams under cyclic loadingrdquo Journal of South ChinaUniversity of Technology vol 23 no 1 pp 27ndash33 1995 inChinese

[9] H Jiang B Wang and X Lu ldquoExperimental study on damagebehavior of reinforced concrete shear walls subjected to cyclicloadsrdquo Journal of Earthquake Engineering vol 17 no 7pp 958ndash971 2013

[10] J Yue J Qian and D E Beskos ldquoA generalized multi-levelseismic damage model for RC framed structuresrdquo Soil Dy-namics and Earthquake Engineering vol 80 pp 25ndash39 2016

[11] JGJ138-2016 Code for Design of Composite Structures ChinaArchitecture amp Building Press Beijing China 2016

[12] R D Lequesne G J Parra-Montesinos and J K WightldquoSeismic behavior and detailing of high-performance fiber-reinforced concrete coupling beams and coupled wall sys-temsrdquo Journal of Structural Engineering vol 139 no 8pp 1362ndash1370 2012

[13] M Otieno H Beushausen and M Alexander ldquoTowardsincorporating the influence of cover cracking on steel cor-rosion in RC design codes the concept of performance-basedcrack width limitsrdquo Materials and Structures vol 45 no 12pp 1805ndash1816 2012

[14] SIMULIA Dassault Systems ABAQUS Analysis UserrsquosManual Version 616 SIMULIA Johnston RI USA 2016

[15] J C Goodnight M J Kowalsky and J M Nau ldquoEffect of loadhistory on performance limit states of circular bridge col-umnsrdquo Journal of Bridge Engineering vol 18 no 12pp 1383ndash1396 2013

[16] R T Ranf ldquoDamage accumulation in lightly confined rein-forced concrete bridge columnsrdquo PEER Report PacificEarthquake Engineering Research Center University ofCalifornia Berkeley CA USA 2006

[17] A Babazadeh R Burguentildeo and P F Silva ldquoUse of 3D finite-element models for predicting intermediate damage limitstates in RC bridge columnsrdquo Journal of Structural Engi-neering vol 141 no 10 article 04015012 2015

[18] J Moon CW Roeder andH-E Lee ldquoAnalytical modeling ofbending of circular concrete-filled steel tubesrdquo EngineeringStructures vol 42 no 12 pp 349ndash361 2012

[19] GB50010-2010 Code for Design of Concrete Structures ChinaArchitecture amp Building Press Beijing China 2010

[20] H Zhu M T Stephens and D E Lehman ldquoInelastic responseprediction of CFST columns and connections subjected tolateral loadingrdquo Journal of Constructional Steel Researchvol 132 pp 130ndash140 2017

[21] M J N Priestley ldquoPerformance based seismic designrdquo inProceedings of 12th World Conference on EarthquakeEngineering Auckland New Zealand January 2000

[22] Y Shi M Wang and Y Wang ldquoExperimental and consti-tutive model study of structural steel under cyclic loadingrdquoJournal of Constructional Steel Research vol 67 no 8pp 1185ndash1197 2011

[23] H Jiang X Lu and T Kubo ldquoDamage displacement esti-mation of flexure-dominant RC columnsrdquo Advances inStructural Engineering vol 13 no 2 pp 357ndash368 2010

[24] GB50011-2010 Code for Seismic Design of Buildings ChinaArchitecture amp Building Press Beijing China 2010

Advances in Civil Engineering 15

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point which was monitored by the outmost strain gaugesattached to the encased steel the lateral load was controlledby force and just one reversed cycle was loaded during eachloading level en after that the lateral load was controlledby displacement and three reversed cycles were loadedduring each loading level e lateral loading protocol ofspecimen Beam1 is shown in Figure 3 and each reversedloading cycle was finished in 2minutes

Linear variable displacement transducers (LVDTs)were installed to the specimens to measure the lateraldisplacements and the curvatures in the critical regionsStrain gauges were attached to measure the strain of steelplates and steel bars at plastic hinge zonese values of thelateral load the global and local displacements and thestrains were recorded automatically through the data ac-quisition system throughout the whole loading processTypical damage states including crack evolution concretecrushing and spalling and rebar buckling and fracturewere recorded through observation and photographsduring the loading process During the first cycle of eachloading level the maximum crack width was measured atlargest lateral load or largest displacement and the cor-responding maximum residual crack width was measuredat zero loads e crack width was measured using thecrack comparison card which has a measurement range of002ndash5mm

3 Test Results

31 Damage Behavior e sequence of observed typicaldamage states is similar for all specimens and the typicaldamage states of specimen Beam1 at different loading levelsare illustrated in Figure 4 which is a representative for allspecimens In general the damage started by forminghorizontal cracks at the bottom of the specimen at thetension side as shown in Figure 4(a) en the obliquecracks started to appear when the lateral load reaches500 kN as shown in Figure 4(b) Tensile yielding of the steelflange was detected using strain gauges with the increase ofloading levels At this instant the force control loadingprotocol was switched to the displacement control modeAfterwards the initial concrete crushing of compressive sideat the bottom of the specimen was observed when lateraldisplacement reaches 10mm as shown in Figure 4(c) Underthe following load cycles the large cracks concentrated at theinterface as shown in Figure 4(d) en the spalling ofconcrete cover appeared when the lateral displacement

reaches 225mm as shown in Figure 4(e) At this loadinglevel the lateral load carrying capacity of specimen started tofall off After concrete cover of the specimen completelyspalled off the longitudinal bars and hoops outcropped andthen the longitudinal bars buckled during the followingcycles when the lateral displacement reaches 275mm asshown in Figure 4(f ) and the fracture of the longitudinalbars was observed at subsequent larger lateral displacementwhich is 325mm as shown in Figure 4(g) e test con-tinued with the lateral displacement increased graduallyuntil the global instability appeared when the lateral dis-placement reaches 425mm After the test the concrete wasremoved and the fracture of encased steel was observed asshown in Figure 4(h) and no encased steel buckling wasfound

e typical damage development was roughly the samefor the seven specimens All specimens exhibited flexure-yielding behavior since steel web yielding occurred later thansteel flange yielding and no hoop rebar of specimens wasfound yielding before longitudinal rebar buckling or frac-ture e typical damage development was as followshorizontal cracking on the tensile side of the specimentensile yielding of the steel plate and rebar principle tensileyielding of steel web concrete crushing and spalling on thecompressive side of the specimen and rebar buckling andfracture

e crack distribution of specimens Beam 1 Beam 2 andBeam 3with different aspect ratios before concrete spalling isshown in Figure 5 With the increase of aspect ratio thecracking region is enlarged and more flexural cracks andless diagonal cracks occurred e flange-web area ratio andsteel ratio have little influence on the crack distribution

32 Force and Deformation Characteristics Lateral loadversus chord rotation (lateral displacement divided byspecimen length) hysteretic curves of specimens andcorresponding skeleton curves with typical damage statesmarked on it are shown in Figure 6e hysteretic curves ofspecimens show SRC coupling beams exhibited littlepinching effect and small degradation behavior until thelongitudinal rebars were fractured which shows SRCcoupling beams have excellent energy dissipation capa-bility By comparing specimens Beam1 Beam2 and Beam3the hysteresis behavior is similar among these threespecimens In general the specimen with higher aspectratio results in smaller hysteresis loops since the lateral loadresistance capacity is lower at same lateral chord rotationBy comparing specimens Beam1 Beam4 and Beam5 in-crease flange-web area ratio results in fuller (smallerpinching) and more stable (smaller strength degradation)hysteresis loops since flange steel contributes to SRCcoupling beam flexural behavior more than web steel Bycomparing specimens Beam2 Beam6 and Beam7 in-creased steel ratio also results in fuller and more stablehysteresis loops as larger steel ratio leads to more flangesteel and more web steel

Table 4 lists the mean values of chord rotation at thedamage characteristic points in the specimensrsquo skeleton

Reac

tion

wal

l

Hydraulicactuator

Specimen

Pedestal

Loading head

Ground anchor

Figure 2 Schematic representation of test setup

Advances in Civil Engineering 5

curves in two opposite loading directions Experimentalresults show that although the longitudinal bars were placedoutside the encased steel encased steel still yielded before thelongitudinal bars since the yielding strain of the longitudinalbars is 75 larger than the encased steel (as shown in Ta-ble 2) After the longitudinal bars fractured the specimenscan still experience larger displacement with small lateral

load carrying capacity degradation because the encased steelplate possessing much larger deformation capacity than thesteel bar was still eective to resist the lateral load

For specimens Beam1 Beam2 and Beam3 with dierentaspect ratios specimen Beam1 with the aspect ratio of 2 hasthe largest lateral load carrying capacity which is 11487 kNand is 246 times that of specimen Beam3 and 153 times that

Horizontal cracks

(a)

Diagonal cracks

(b)

Concrete crushing

(c)

Interface crack

(d)

Concrete spalling

(e)

Longitudinal bar buckling

(f )

Longitudinal bar fracture

(g)

Steel fracture

(h)

Figure 4 Typical damage states of specimen Beam1 (a) 300 kN (00012 rad) (b) 500 kN (0003 rad) (c) 10mm (002 rad) (d) 125mm(0025 rad) (e) 225mm (0045 rad) (f ) 275mm (0055 rad) (g) 325mm (0065 rad) and (h) 425mm (0085 rad)

App

lied

disp

lace

men

t (m

m)

4 8 12 16 20 24 28 32ndash40ndash30ndash20ndash10

010203040

ndash8ndash6ndash4ndash202468Stage 3Stage 2

Chor

d ro

tatio

n (

)

Cycle no0 1 2 3 4

Stage 1

Cycle no

ndash600ndash400ndash200

0200400600

App

lied

load

(kN

)

Figure 3 Lateral loading protocol of specimen Beam1

6 Advances in Civil Engineering

(a) (b) (c)

Figure 5 Crack pattern of specimens before concrete crushing (a) Beam1 (b) Beam2 (c) Beam3

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200

ndash004 000 004 008ndash008Rotation (rad)

ndash40 ndash20 0 20 40Lateral displacement (mm)

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash40 ndash20 0 20 40

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(a)

Late

ral l

oad

(kN

)

ndash60 ndash30 0 30 60Lateral displacement (mm)

ndash800

ndash400

0

400

800

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

ndash004 000 004 008ndash008Rotation (rad)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash60 ndash30 0 30 60

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(b)

Figure 6 Continued

Advances in Civil Engineering 7

Late

ral l

oad

(kN

)

ndash100 ndash50 0 50 100Lateral displacement (mm)

ndash480

ndash320

ndash160

0

160

320

480

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

ndash004 000 004 008ndash008Rotation (rad)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash100 ndash50 0 50 100

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(c)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash40 ndash20 0 20 40

Lateral displacement (mm)

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

ndash004 000 004 008ndash008Rotation (rad)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash40 ndash20 0 20 40

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(d)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash40 ndash20 0 20 40

Lateral displacement (mm)

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

ndash004 000 004 008ndash008Rotation (rad)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash40 ndash20 0 20 40

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(e)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash60 ndash30 0 30 60

Lateral displacement (mm)

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

ndash004 000 004 008ndash008Rotation (rad)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash60 ndash30 0 30 60

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(f )

Figure 6 Continued

8 Advances in Civil Engineering

of specimen Beam2 which means that the lateral loadcarrying capacity changes in inverse proportion with theaspect ratio and all specimens reached its exural strengthIn general the larger aspect ratio specimen tends to havesmaller lateral load carrying capacity at the individualdamage characteristic point Considering displacements ofthe individual damage state the initial damage states(concrete cracking steel tensile yielding and rebar tensileyielding) of specimen Beam3 with a aspect ratio of 5 tend tooccur later than those of specimen Beam1 with a aspect ratioof 2 which is consistent with the elastic chord rotationequation of the Timoshenko cantilever beam which is asfollows

θ ΔLML

3EI+M

GAL (6)

where M is the xed end section moment of the cantileverbeam L is the length of the cantilever beam E is the elasticmodulus I is the section moment inertia G is the shearmodulus and A is the eective shear section area When L islarger than

3EIGA

radicasymp 08h (h is the beam section height)

chord rotation θ increases with the increase of the beamlength under the same xed end moment e damage statessuch as steel web principle yielding concrete crushingconcrete spalling rebar buckling and rebar fracture of

specimen Beam3 tend to occur earlier than those of spec-imen Beam1 because specimen Beam3 has a relativelysmaller moment gradient at the plastic zone which causesexural damages of Beam3 to occur easily and smaller shearforce in Beam3 leads to smaller shear deformation also

For specimens Beam1 Beam4 and Beam5 with dierentange-web area ratios of encased steel specimen Beam4witha ange-web ratio of 05 has the largest lateral load carryingcapacity which is 11866 kN and is 33 larger than that ofspecimen Beam1 and 225 larger than that of specimenBeam5 which means that the specimen without the ange ofencased steel has a signicant smaller lateral load carryingcapacity e reason that specimen Beam4 with a smallerange-web ratio has slightly larger lateral load capacity thanspecimen Beam1 is that the encased steel consists of steelplates with dierent thicknesses and dierent yieldingstrengths and the average yielding strength of encased steelof specimen Beam4 is slightly larger than that of specimenBeam1 e calculated lateral load capacity (MnL) forspecimens Beam4 and Beam1 shown in Table 3 veried thisexplanation Considering the displacements of individualdamage states except the damage states like steel tensileyielding and rebar tensile yielding the other damage states ofspecimen Beam1 with a ange-web ratio of 1 tend to occurlater than those of specimen Beam5 with a ange-web ratio

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash60 ndash30 0 30 60

Lateral displacement (mm)

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

ndash004 000 004 008ndash008Rotation (rad)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash60 ndash30 0 30 60

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(g)

Figure 6 Lateral load-chord rotation hysteretic curves and skeleton curves of specimens (a) Beam1 (b) Beam2 (c) Beam3 (d) Beam4(e) Beam5 (f ) Beam6 (g) Beam7

Table 4 Chord rotation of specimens at the individual damage characteristic point

Specimen number θc (rad) θsty (rad) θrty (rad) θswy (rad) θcc (rad) θcs (rad) θrb (rad) θrf (rad)Beam1 00012 00033 00072 00140 00238 00403 00502 00609Beam2 00013 00063 00065 00120 00192 00385 00451 00558Beam3 00014 00044 00091 00095 00139 00378 00478 00560Beam4 00009 00041 00072 00085 00233 00416 00485 00565Beam5 00008 00053 00078 00078 00179 00346 00444 00586Beam6 00010 00065 00065 00100 00237 00485 00522 00653Beam7 00013 00039 00105 00131 00201 00430 00511 00593Note θc θsty θrty θswy θcc θcs θrb and θrf represent the chord rotation of specimens at damage states of concrete cracking steel tensile yielding rebar tensileyielding steel web principle tensile yielding concrete crushing concrete spalling rebar buckling and rebar fracture respectively For Beam5 rebar tensileyielding and steel web principle tensile yielding occurred at the same time For Beam6 steel tensile yielding and rebar tensile yielding occurred at the sametime

Advances in Civil Engineering 9

of 0 is is because the flange steel enhances the com-pression behavior of the concrete and delays the concretecrushing and spalling In addition shear deformation ofspecimen Beam1 with smaller web steel is larger than that ofspecimen Beam5 at the same damage state

For specimens Beam2 Beam6 and Beam7 with theincrease of steel ratio from 5 to 83 the lateral loadcarrying capacity increases from 7503 kN to 9688 kN by292 which means that the lateral load carrying capacity ofSRC coupling beam was influenced largely by the steel ratioExcept initial damage states like concrete cracking rebartensile yielding and steel web principle tensile yielding theother damage states of specimen Beam6 with a steel ratio of67 tend to occur later than those of specimen Beam2 witha steel ratio of 5 and Beam7 with a steel ratio of 83

Concrete cover cracking influences the encased steelcorrosion initiation and the crack width influences thecorrosion propagation thus both influence the performanceof structures [13] e maximum residual crack width of allspecimens represented by Wmres was measured during thetest cycles before concrete cover crashed or spalled evariation of maximum residual crack width with the chordrotation is shown in Figure 7 Generally the maximumresidual crack width rises up with the increase of the chordrotation e maximum residual crack width of the speci-men at the same rotation tends to be smaller with the in-crease of the aspect ratio or steel ratio for the average value ofthat for both directions For specimens Beam1 Beam4 andBeam5 with different flange-web area ratios of encased steelBeam4 has the smallest maximum residual crack width whileBeam1 has the largest maximum residual crack width at thesame rotation

4 Numerical Analysis and Verification

41 Modeling ree-dimensional nonlinear finite elementmodels were developed to simulate the inelastic behavior oftested SRC coupling beam specimens using Abaqus [14] Notonly the global force-rotation behavior but also the localmaterial damage behavior during the test process includingconcrete (cracking crushing and spalling) steel yieldingand rebar (yielding buckling and fracture) was predictedthrough finite element analysis It has been reported [15ndash17]that material damage states ie spalling and yielding arenot dependent on the history of loading but are ratherclosely related to the maximum displacement that thestructure has experienced erefore a monotonic analysiswas sufficient for predicting damage deformation of flexure-yielding SRC coupling beams

Damaged plasticity model was used to simulate theconcrete inelastic behavior in SRC coupling beam specimensis model is applicable in the situation that the concrete is atlow confinement pressures (less than four to five times thelargest compressive stress that can be carried by the concretein uniaxial compression) which is suitable for SRC couplingbeams Moon et al [18] used this model to study the con-finement effect of steel tubes on the infilled concrete andBabazadeh et al [17] used this model to study the spalling ofthe concrete for RC bridge columnse uniaxial stress-strain

relationship for the concrete recommended in Chinese codeGB50010-2010 [19] was adopted here as shown in Figure 8(a)e compression strength of the concrete is 373MPa whichis the prismatic compression strength of concrete fck which iscalculated based on the conversion formula in Chinese code50010-2010 [19] and the tested cubic compression strength ofconcrete fcu is equal to 578MPa

Ductile damage plasticity model was used to simulate theencased steel and rebar inelastic behavior in SRC couplingbeam specimens is model offers a general capability forpredicting the onset of failure and a capability for modelingprogressive damage and failure of ductile metals Zhu et al[20] used this model to simulate the steel tearing of concrete-filled steel tube columns e strengthening stage of steeladopted a bilinear model hardening stiffness of which is 1of elastic stiffness and damage initiated at tensile strain anddamage evolution adopted a linear damage form Consid-ering the cyclic fatigue of longitudinal rebar under earth-quakes Priestley [21] suggested the tensile strain of thelongitudinal rebar to be reduced by 40 Shi et al [22]carried out the structural steel low cycle fatigue test andproved that the tensile strain of Q345B steel was reduced by203 and Q235B steel was reduced by 386 after cyclicloading e fracture strain was conservatively taken as twotimes tensile strain refer to the former test results euniaxial stress-strain relationship for the 12mm diameterrebar is shown in Figure 8(b)

Eight-node solid elements with reduced integration(C3D8R) were used for the concrete four-node shell ele-ments with reduced integration (S4R) were used for theencased steel and two-node linear displacement truss ele-ments were used for rebar A perfect bond was assumedbetween the steel rebar elements and the concrete parttherefore the truss elements and shell elements were em-bedded in the concrete instance using the lowastEMBEDDEDELEMENT option e bottom surface of the pedestal wasfixed against all degrees of freedom A reference point wasmodeled on the surface of the loading plate which wasconstrained with the surface of the loading plate using thelowastCOUPLING option available in the ABAQUS library

42 Analysis Results e global skeleton curves of all thespecimens obtained from the FEA are compared with theskeleton curves obtained from the test and two of them areshown in Figure 9 e FEA model gave a stiffer result in thepositive part and softer one in the negative part for specimenBeam1 compared to the experimental result which may bedue to the slippage of the pedestal or the gap between loadinghead and specimen in the test e local material damagesobtained from FEA are also compared with test results andconcrete spalling and rebar fracture are shown in Figure 10From the qualitative comparison good agreement isachieved between experimental and FEA results not only onthe global behavior but also on the local material damagebehavior

Concrete crushing and spalling were predicted throughthe compression strain of concrete Priestley [21] suggested avalue of 0004 for cover concrete edge compressive crushing

10 Advances in Civil Engineering

strain and Jiang et al [23] proposed an equation to calculatethe conned concrete edge compression spalling strainwhich is equal to 0005 for test specimense concrete crack

width was predicted through the tensile strain of rebarPriestley [21] suggested a value of 001 for longitudinal rebartensile strain to control the residual crack width within

Stre

ss (M

Pa)

ndash5

0

5

10

15

20

25

30

35

40

0002 0004 0006 0008 00100000Strain

(a)

Stre

ss (M

Pa)

0

100

200

300

400

500

600

004 008 012 016000Strain

(b)

Figure 8 Uniaxial constitutive relationships of materials (a) Concrete (b) Rebar 12mm

Wm

res (

mm

)

Beam1Beam2Beam3

00

05

10

15

20

ndash002 000 002 004ndash004Rotation (rad)

(a)W

mre

s (m

m)

Beam1Beam4Beam5

00

05

10

15

20

ndash002 000 002 004ndash004Rotation (rad)

(b)

Wm

res (

mm

)

Beam2Beam6Beam7

00

05

10

15

20

ndash002 000 002 004ndash004Rotation (rad)

(c)

Figure 7 Maximum residual crack width of specimens (a) Eect of aspect ratio (b) Eect of ange-web ratio (c) Eect of steel ratio

Late

ral l

oad

(kN

)

FEATest

ndash1200

ndash800

ndash400

0

400

800

1200

ndash006 ndash003 000 003 006 009ndash009Rotation (rad)

(a)

Late

ral l

oad

(kN

)

FEATest

ndash1200

ndash800

ndash400

0

400

800

1200

ndash006 ndash003 000 003 006 009ndash009Rotation (rad)

(b)

Figure 9 Comparison of experimental and numerical skeleton curves (a) Specimen Beam1 (b) Specimen Beam5

Advances in Civil Engineering 11

10mm e chord rotations corresponding to differentconcrete damage states obtained from finite element analysiswere compared with the test result as shown in Table 5From the quantitative comparison for concrete damagedeformation finite element analysis can only provide astatistically consistent simulation result not specifically ac-curate simulation result for each specimen e mean ro-tation ratios between FEA and the test for the concreteresidual crack width equal to 1mm concrete crushing and

concrete spalling are 099 083 and 074 respectively If thecover concrete edge compression crushing strain is revisedto 0005 and confined concrete edge compression spallingstrain is revised to 00075 the mean rotation ratios betweenFEA and the test for concrete crushing and concrete spallingare 104 and 103 respectively

Steel flange tensile yielding and web principle tensileyielding were predicted directly through steel yielding strainrecorded in Table 2 e chord rotations corresponding to

Rebar fracture

PE max principalSNEG(fraction = ndash10)(avg 75)

+1454e ndash 01+1333e ndash 01+1212e ndash 01+1090e ndash 01+9693e ndash 02+8481e ndash 02+7269e ndash 02+6058e ndash 02+4846e ndash 02+3635e ndash 02+2423e ndash 02+1212e ndash 02+0000e + 00

(a)

Concrete spalling

PEEQ(avg 75)

+4683e ndash 02+4292e ndash 02+3902e ndash 02+3512e ndash 02+3122e ndash 02+2731e ndash 02+2341e ndash 02+1951e ndash 02+1561e ndash 02+1171e ndash 02+7804e ndash 03+3902e ndash 03+0000e + 00

(b)

Figure 10 Comparison of experimental and numerical damages (a) Rebar fracture of specimen Beam1 (b) Concrete spalling of specimenBeam1

Table 5 Comparison of chord rotations of specimens for different concrete damage states

Specimen numberResidual crack width lt1mm Concrete crushing Concrete spallingTest FEA FEAtest Test FEA FEAtest Test FEA FEAtest

Beam1 00084 00157 187 00238 00231 097 00403 00442 110Beam2 00116 00141 122 00192 00137 071 00385 00244 063Beam3 00150 00155 103 00139 00143 103 00378 00256 068Beam4 00261 00145 056 00233 00185 079 00416 00288 069Beam5 00200 00149 075 00179 00196 109 00346 00363 105Beam6 00187 00140 075 00237 00133 056 00485 00233 048Beam7 00190 00141 074 00201 00130 065 00430 00225 052

12 Advances in Civil Engineering

different steel yielding states obtained from finite elementanalysis were compared with the test result as shown inTable 6 e finite element analysis can provide a statisticallyconsistent simulation result and the mean rotation ratiosbetween FEA and the test for steel flange tensile yielding andsteel web principle tensile yielding are 123 and 108respectively

Rebar tensile yielding and rebar fracture were pre-dicted directly through rebar yielding strain and tensilestrain recorded in Table 2 Rebar buckling was predictedthrough confined concrete ultimate compressive strainwhich is calculated using equation suggested by Priestley[21] e chord rotations corresponding to different rebardamage states obtained from finite element analysis werecompared with the test result as shown in Table 7 efinite element analysis can provide a statistically consis-tent simulation result and the mean rotation ratios be-tween FEA and the test for rebar tensile yielding rebarbuckling and rebar fracture are 074 103 and 090respectively

43 Performance Index Limit Analysis e seismic per-formance of SRC coupling beams is affected by the ma-terial damage which is related to the material strain Onthe other hand the degradation of the load carrying ca-pacity of SRC coupling beams affects its seismic perfor-mance also Based on the study on the material damagestrain limits [21 23] and component strength degradationlimits [24] four performance levels are defined as shownin Table 8 Since there is a lack of test records of speci-mensrsquo deformation at damage states of concrete strainequal to 0002 or crack width equal to 2mm the chordrotation of specimens at different performance levels canonly be obtained through FEA Table 9 shows the chord

rotations of SRC coupling beam specimens at differentperformance levels and then the mean values wereadopted as the performance index limits which were0005 rad 0014 rad 0024 rad and 0047 rad for the fourperformance levels

5 Summary and Conclusions

Seven half-scale flexural-yielding SRC coupling beamspecimens designed according to Chinese approach weretested under cyclic loade influence of design parameterssuch as aspect ratio flange-web area ratio of encased steeland steel ratio on damage development hysteretic be-havior strength and maximum residual crack width werediscussed Finite element analysis was conducted forspecimens both global skeleton curves and local materialdamage were simulated simultaneously rough quanti-tative comparison finite element analysis can provide astatistically consistent simulation result for materialdamages for each specimen Some conclusions are drawnfrom this research

(1) All specimens failed in flexural mode e damagedevelopment was roughly the same and the typicaldamage states were recorded through the wholeloading process which can be used in assessing theseismic performance level of SRC coupling beams

(2) With the increase of aspect ratio the lateral loadcarrying capacity drops down significantly and themaximum residual crack width tends to be smallerWith the increase of flange-web area ratio of encasedsteel the hysteretic curve gets fuller e specimenwith intermediate flange-web area ratio has thelargest lateral load carrying capacity but smallestmaximum residual crack width With the increase of

Table 6 Comparison of chord rotations of specimens for different steel damage states

Specimen numberSteel flange yielding Steel web yielding

Test FEA FEAtest Test FEA FEAtestBeam1 00033 00059 179 00140 00124 089Beam2 00063 00053 084 00120 00116 097Beam3 00044 00061 139 00095 00108 114Beam4 00041 00051 124 00085 00105 124Beam5 00053 00056 106 00078 00098 126Beam6 00065 00057 088 00100 00115 115Beam7 00039 00056 144 00131 00120 092

Table 7 Comparison of chord rotations of specimens for different rebar damage states

Specimen numberRebar yielding Rebar buckling Rebar fracture

Test FEA FEAtest Test FEA FEAtest Test FEA FEAtestBeam1 00072 00059 082 00502 00777 155 00609 00562 092Beam2 00065 00054 083 00451 00426 094 00558 00502 090Beam3 00091 00060 066 00478 00446 093 00560 00571 102Beam4 00072 00056 078 00485 00527 109 00565 00504 089Beam5 00078 00054 069 00444 00526 118 00586 00596 102Beam6 00065 00056 086 00522 00403 077 00653 00490 075Beam7 00105 00057 054 00511 00390 076 00593 00493 083

Advances in Civil Engineering 13

steel ratio the lateral load carrying capacity increasessignificantly while the maximum residual crackwidth drops down

(3) e finite element model was benchmarkedthrough comparison with test results for bothglobal load-deformation curves and local materialdamages Both qualitative and quantitative com-parisons testify the accuracy of finite elementmodels e cover concrete edge compressionstrain and confined concrete edge compressionstrain were recommended to be 0005 and 00075respectively for accurately modeling concretecrushing and spalling Based on the damagecharacters and strength degradation four perfor-mance levels were defined and correspondingchord rotation limits were obtained through theverified numerical analysis

Data Availability

All the data in this paper are obtained from tests and nu-merical analysis and no other data in the literature are usedto support this study

Conflicts of Interest

e authors declare that there are no potential conflicts ofinterest with respect to the research authorship and pub-lication of this article

Acknowledgments

e financial support from the Program of Shanghai Aca-demic Research Leader (grant number 18XD1403900) andthe National Key Research and Development Program ofChina (grant number 2017YFC1500701) is gratefullyacknowledged

References

[1] S El-Tawil K A Harries P J Fortney B M Shahrooz andY Kurama ldquoSeismic design of hybrid coupled wall systemsstate of the artrdquo Journal of structural engineering vol 136no 7 pp 755ndash769 2010

[2] C-C Hung and W-T Lu ldquoA performance-based designmethod for coupled wall structuresrdquo Journal of EarthquakeEngineering vol 21 no 4 pp 579ndash603 2016

[3] C J Motter D C Fields J D Hooper et al ldquoSteel-reinforcedconcrete coupling beams I testingrdquo Journal of StructuralEngineering vol 143 no 3 article 04016191 2016

[4] B Gong and B M Shahrooz ldquoConcrete-steel compositecoupling beams I component testingrdquo Journal of StructuralEngineering vol 127 no 6 pp 625ndash631 2001

[5] B Gong and B M Shahrooz ldquoConcrete-steel compositecoupling beams II subassembly testing and design verifi-cationrdquo Journal of Structural Engineering vol 127 no 6pp 632ndash638 2001

[6] R K L Su and W Y Lam ldquoA unified design approach forplate-reinforced composite coupling beamsrdquo Journal ofConstructional Steel Research vol 65 no 3 pp 675ndash6862009

Table 8 Method of defining performance levels for SRC coupling beams

Performance level Damage descriptionPerformance criterion

Rebar or steel strain Concretestrain Load carrying capacity

Being basically intact ere are fine cracks in concrete while steel or rebaris not yielding εy 0002 mdash

Slight damage Concrete cover is not crushing and residual crackwidth is less than 1mm 0015 0005 mdash

Moderate damage Concrete cover is not spalling and residual crackwidth is less than 2mm 003 00075 95 Pmax

Severe damage Concrete core is not crushing and rebar or steel isnot fracturing εsu εcu 85 Pmax

Note εy is the yielding strain of steel or rebar εsu is the tensile strain of steel or rebar εcu is the ultimate strain of the concrete Pmax is the lateral load carryingcapacity of specimens

Table 9 Chord rotations of SRC coupling beams at different performance levels (rad)

Specimen numberPerformance level

Being basically intact Slight damage Moderate damage Severe damageBeam1 00055 00157 00264 00562Beam2 00053 00137 00212 00426Beam3 00060 00143 00235 00446Beam4 00051 00145 00239 00504Beam5 00054 00149 00257 00526Beam6 00051 00133 00228 00403Beam7 00050 00130 00228 00390

14 Advances in Civil Engineering

[7] C J Motter D C Fields J D Hooper et al ldquoSteel-reinforcedconcrete coupling beams II Modelingrdquo Journal of StructuralEngineering vol 143 no 3 article 04016192 2016

[8] Q Z Liang and X L Han ldquoe behavior of stiffening beamsand lintel beams under cyclic loadingrdquo Journal of South ChinaUniversity of Technology vol 23 no 1 pp 27ndash33 1995 inChinese

[9] H Jiang B Wang and X Lu ldquoExperimental study on damagebehavior of reinforced concrete shear walls subjected to cyclicloadsrdquo Journal of Earthquake Engineering vol 17 no 7pp 958ndash971 2013

[10] J Yue J Qian and D E Beskos ldquoA generalized multi-levelseismic damage model for RC framed structuresrdquo Soil Dy-namics and Earthquake Engineering vol 80 pp 25ndash39 2016

[11] JGJ138-2016 Code for Design of Composite Structures ChinaArchitecture amp Building Press Beijing China 2016

[12] R D Lequesne G J Parra-Montesinos and J K WightldquoSeismic behavior and detailing of high-performance fiber-reinforced concrete coupling beams and coupled wall sys-temsrdquo Journal of Structural Engineering vol 139 no 8pp 1362ndash1370 2012

[13] M Otieno H Beushausen and M Alexander ldquoTowardsincorporating the influence of cover cracking on steel cor-rosion in RC design codes the concept of performance-basedcrack width limitsrdquo Materials and Structures vol 45 no 12pp 1805ndash1816 2012

[14] SIMULIA Dassault Systems ABAQUS Analysis UserrsquosManual Version 616 SIMULIA Johnston RI USA 2016

[15] J C Goodnight M J Kowalsky and J M Nau ldquoEffect of loadhistory on performance limit states of circular bridge col-umnsrdquo Journal of Bridge Engineering vol 18 no 12pp 1383ndash1396 2013

[16] R T Ranf ldquoDamage accumulation in lightly confined rein-forced concrete bridge columnsrdquo PEER Report PacificEarthquake Engineering Research Center University ofCalifornia Berkeley CA USA 2006

[17] A Babazadeh R Burguentildeo and P F Silva ldquoUse of 3D finite-element models for predicting intermediate damage limitstates in RC bridge columnsrdquo Journal of Structural Engi-neering vol 141 no 10 article 04015012 2015

[18] J Moon CW Roeder andH-E Lee ldquoAnalytical modeling ofbending of circular concrete-filled steel tubesrdquo EngineeringStructures vol 42 no 12 pp 349ndash361 2012

[19] GB50010-2010 Code for Design of Concrete Structures ChinaArchitecture amp Building Press Beijing China 2010

[20] H Zhu M T Stephens and D E Lehman ldquoInelastic responseprediction of CFST columns and connections subjected tolateral loadingrdquo Journal of Constructional Steel Researchvol 132 pp 130ndash140 2017

[21] M J N Priestley ldquoPerformance based seismic designrdquo inProceedings of 12th World Conference on EarthquakeEngineering Auckland New Zealand January 2000

[22] Y Shi M Wang and Y Wang ldquoExperimental and consti-tutive model study of structural steel under cyclic loadingrdquoJournal of Constructional Steel Research vol 67 no 8pp 1185ndash1197 2011

[23] H Jiang X Lu and T Kubo ldquoDamage displacement esti-mation of flexure-dominant RC columnsrdquo Advances inStructural Engineering vol 13 no 2 pp 357ndash368 2010

[24] GB50011-2010 Code for Seismic Design of Buildings ChinaArchitecture amp Building Press Beijing China 2010

Advances in Civil Engineering 15

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curves in two opposite loading directions Experimentalresults show that although the longitudinal bars were placedoutside the encased steel encased steel still yielded before thelongitudinal bars since the yielding strain of the longitudinalbars is 75 larger than the encased steel (as shown in Ta-ble 2) After the longitudinal bars fractured the specimenscan still experience larger displacement with small lateral

load carrying capacity degradation because the encased steelplate possessing much larger deformation capacity than thesteel bar was still eective to resist the lateral load

For specimens Beam1 Beam2 and Beam3 with dierentaspect ratios specimen Beam1 with the aspect ratio of 2 hasthe largest lateral load carrying capacity which is 11487 kNand is 246 times that of specimen Beam3 and 153 times that

Horizontal cracks

(a)

Diagonal cracks

(b)

Concrete crushing

(c)

Interface crack

(d)

Concrete spalling

(e)

Longitudinal bar buckling

(f )

Longitudinal bar fracture

(g)

Steel fracture

(h)

Figure 4 Typical damage states of specimen Beam1 (a) 300 kN (00012 rad) (b) 500 kN (0003 rad) (c) 10mm (002 rad) (d) 125mm(0025 rad) (e) 225mm (0045 rad) (f ) 275mm (0055 rad) (g) 325mm (0065 rad) and (h) 425mm (0085 rad)

App

lied

disp

lace

men

t (m

m)

4 8 12 16 20 24 28 32ndash40ndash30ndash20ndash10

010203040

ndash8ndash6ndash4ndash202468Stage 3Stage 2

Chor

d ro

tatio

n (

)

Cycle no0 1 2 3 4

Stage 1

Cycle no

ndash600ndash400ndash200

0200400600

App

lied

load

(kN

)

Figure 3 Lateral loading protocol of specimen Beam1

6 Advances in Civil Engineering

(a) (b) (c)

Figure 5 Crack pattern of specimens before concrete crushing (a) Beam1 (b) Beam2 (c) Beam3

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200

ndash004 000 004 008ndash008Rotation (rad)

ndash40 ndash20 0 20 40Lateral displacement (mm)

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash40 ndash20 0 20 40

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(a)

Late

ral l

oad

(kN

)

ndash60 ndash30 0 30 60Lateral displacement (mm)

ndash800

ndash400

0

400

800

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

ndash004 000 004 008ndash008Rotation (rad)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash60 ndash30 0 30 60

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(b)

Figure 6 Continued

Advances in Civil Engineering 7

Late

ral l

oad

(kN

)

ndash100 ndash50 0 50 100Lateral displacement (mm)

ndash480

ndash320

ndash160

0

160

320

480

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

ndash004 000 004 008ndash008Rotation (rad)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash100 ndash50 0 50 100

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(c)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash40 ndash20 0 20 40

Lateral displacement (mm)

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

ndash004 000 004 008ndash008Rotation (rad)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash40 ndash20 0 20 40

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(d)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash40 ndash20 0 20 40

Lateral displacement (mm)

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

ndash004 000 004 008ndash008Rotation (rad)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash40 ndash20 0 20 40

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(e)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash60 ndash30 0 30 60

Lateral displacement (mm)

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

ndash004 000 004 008ndash008Rotation (rad)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash60 ndash30 0 30 60

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(f )

Figure 6 Continued

8 Advances in Civil Engineering

of specimen Beam2 which means that the lateral loadcarrying capacity changes in inverse proportion with theaspect ratio and all specimens reached its exural strengthIn general the larger aspect ratio specimen tends to havesmaller lateral load carrying capacity at the individualdamage characteristic point Considering displacements ofthe individual damage state the initial damage states(concrete cracking steel tensile yielding and rebar tensileyielding) of specimen Beam3 with a aspect ratio of 5 tend tooccur later than those of specimen Beam1 with a aspect ratioof 2 which is consistent with the elastic chord rotationequation of the Timoshenko cantilever beam which is asfollows

θ ΔLML

3EI+M

GAL (6)

where M is the xed end section moment of the cantileverbeam L is the length of the cantilever beam E is the elasticmodulus I is the section moment inertia G is the shearmodulus and A is the eective shear section area When L islarger than

3EIGA

radicasymp 08h (h is the beam section height)

chord rotation θ increases with the increase of the beamlength under the same xed end moment e damage statessuch as steel web principle yielding concrete crushingconcrete spalling rebar buckling and rebar fracture of

specimen Beam3 tend to occur earlier than those of spec-imen Beam1 because specimen Beam3 has a relativelysmaller moment gradient at the plastic zone which causesexural damages of Beam3 to occur easily and smaller shearforce in Beam3 leads to smaller shear deformation also

For specimens Beam1 Beam4 and Beam5 with dierentange-web area ratios of encased steel specimen Beam4witha ange-web ratio of 05 has the largest lateral load carryingcapacity which is 11866 kN and is 33 larger than that ofspecimen Beam1 and 225 larger than that of specimenBeam5 which means that the specimen without the ange ofencased steel has a signicant smaller lateral load carryingcapacity e reason that specimen Beam4 with a smallerange-web ratio has slightly larger lateral load capacity thanspecimen Beam1 is that the encased steel consists of steelplates with dierent thicknesses and dierent yieldingstrengths and the average yielding strength of encased steelof specimen Beam4 is slightly larger than that of specimenBeam1 e calculated lateral load capacity (MnL) forspecimens Beam4 and Beam1 shown in Table 3 veried thisexplanation Considering the displacements of individualdamage states except the damage states like steel tensileyielding and rebar tensile yielding the other damage states ofspecimen Beam1 with a ange-web ratio of 1 tend to occurlater than those of specimen Beam5 with a ange-web ratio

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash60 ndash30 0 30 60

Lateral displacement (mm)

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

ndash004 000 004 008ndash008Rotation (rad)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash60 ndash30 0 30 60

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(g)

Figure 6 Lateral load-chord rotation hysteretic curves and skeleton curves of specimens (a) Beam1 (b) Beam2 (c) Beam3 (d) Beam4(e) Beam5 (f ) Beam6 (g) Beam7

Table 4 Chord rotation of specimens at the individual damage characteristic point

Specimen number θc (rad) θsty (rad) θrty (rad) θswy (rad) θcc (rad) θcs (rad) θrb (rad) θrf (rad)Beam1 00012 00033 00072 00140 00238 00403 00502 00609Beam2 00013 00063 00065 00120 00192 00385 00451 00558Beam3 00014 00044 00091 00095 00139 00378 00478 00560Beam4 00009 00041 00072 00085 00233 00416 00485 00565Beam5 00008 00053 00078 00078 00179 00346 00444 00586Beam6 00010 00065 00065 00100 00237 00485 00522 00653Beam7 00013 00039 00105 00131 00201 00430 00511 00593Note θc θsty θrty θswy θcc θcs θrb and θrf represent the chord rotation of specimens at damage states of concrete cracking steel tensile yielding rebar tensileyielding steel web principle tensile yielding concrete crushing concrete spalling rebar buckling and rebar fracture respectively For Beam5 rebar tensileyielding and steel web principle tensile yielding occurred at the same time For Beam6 steel tensile yielding and rebar tensile yielding occurred at the sametime

Advances in Civil Engineering 9

of 0 is is because the flange steel enhances the com-pression behavior of the concrete and delays the concretecrushing and spalling In addition shear deformation ofspecimen Beam1 with smaller web steel is larger than that ofspecimen Beam5 at the same damage state

For specimens Beam2 Beam6 and Beam7 with theincrease of steel ratio from 5 to 83 the lateral loadcarrying capacity increases from 7503 kN to 9688 kN by292 which means that the lateral load carrying capacity ofSRC coupling beam was influenced largely by the steel ratioExcept initial damage states like concrete cracking rebartensile yielding and steel web principle tensile yielding theother damage states of specimen Beam6 with a steel ratio of67 tend to occur later than those of specimen Beam2 witha steel ratio of 5 and Beam7 with a steel ratio of 83

Concrete cover cracking influences the encased steelcorrosion initiation and the crack width influences thecorrosion propagation thus both influence the performanceof structures [13] e maximum residual crack width of allspecimens represented by Wmres was measured during thetest cycles before concrete cover crashed or spalled evariation of maximum residual crack width with the chordrotation is shown in Figure 7 Generally the maximumresidual crack width rises up with the increase of the chordrotation e maximum residual crack width of the speci-men at the same rotation tends to be smaller with the in-crease of the aspect ratio or steel ratio for the average value ofthat for both directions For specimens Beam1 Beam4 andBeam5 with different flange-web area ratios of encased steelBeam4 has the smallest maximum residual crack width whileBeam1 has the largest maximum residual crack width at thesame rotation

4 Numerical Analysis and Verification

41 Modeling ree-dimensional nonlinear finite elementmodels were developed to simulate the inelastic behavior oftested SRC coupling beam specimens using Abaqus [14] Notonly the global force-rotation behavior but also the localmaterial damage behavior during the test process includingconcrete (cracking crushing and spalling) steel yieldingand rebar (yielding buckling and fracture) was predictedthrough finite element analysis It has been reported [15ndash17]that material damage states ie spalling and yielding arenot dependent on the history of loading but are ratherclosely related to the maximum displacement that thestructure has experienced erefore a monotonic analysiswas sufficient for predicting damage deformation of flexure-yielding SRC coupling beams

Damaged plasticity model was used to simulate theconcrete inelastic behavior in SRC coupling beam specimensis model is applicable in the situation that the concrete is atlow confinement pressures (less than four to five times thelargest compressive stress that can be carried by the concretein uniaxial compression) which is suitable for SRC couplingbeams Moon et al [18] used this model to study the con-finement effect of steel tubes on the infilled concrete andBabazadeh et al [17] used this model to study the spalling ofthe concrete for RC bridge columnse uniaxial stress-strain

relationship for the concrete recommended in Chinese codeGB50010-2010 [19] was adopted here as shown in Figure 8(a)e compression strength of the concrete is 373MPa whichis the prismatic compression strength of concrete fck which iscalculated based on the conversion formula in Chinese code50010-2010 [19] and the tested cubic compression strength ofconcrete fcu is equal to 578MPa

Ductile damage plasticity model was used to simulate theencased steel and rebar inelastic behavior in SRC couplingbeam specimens is model offers a general capability forpredicting the onset of failure and a capability for modelingprogressive damage and failure of ductile metals Zhu et al[20] used this model to simulate the steel tearing of concrete-filled steel tube columns e strengthening stage of steeladopted a bilinear model hardening stiffness of which is 1of elastic stiffness and damage initiated at tensile strain anddamage evolution adopted a linear damage form Consid-ering the cyclic fatigue of longitudinal rebar under earth-quakes Priestley [21] suggested the tensile strain of thelongitudinal rebar to be reduced by 40 Shi et al [22]carried out the structural steel low cycle fatigue test andproved that the tensile strain of Q345B steel was reduced by203 and Q235B steel was reduced by 386 after cyclicloading e fracture strain was conservatively taken as twotimes tensile strain refer to the former test results euniaxial stress-strain relationship for the 12mm diameterrebar is shown in Figure 8(b)

Eight-node solid elements with reduced integration(C3D8R) were used for the concrete four-node shell ele-ments with reduced integration (S4R) were used for theencased steel and two-node linear displacement truss ele-ments were used for rebar A perfect bond was assumedbetween the steel rebar elements and the concrete parttherefore the truss elements and shell elements were em-bedded in the concrete instance using the lowastEMBEDDEDELEMENT option e bottom surface of the pedestal wasfixed against all degrees of freedom A reference point wasmodeled on the surface of the loading plate which wasconstrained with the surface of the loading plate using thelowastCOUPLING option available in the ABAQUS library

42 Analysis Results e global skeleton curves of all thespecimens obtained from the FEA are compared with theskeleton curves obtained from the test and two of them areshown in Figure 9 e FEA model gave a stiffer result in thepositive part and softer one in the negative part for specimenBeam1 compared to the experimental result which may bedue to the slippage of the pedestal or the gap between loadinghead and specimen in the test e local material damagesobtained from FEA are also compared with test results andconcrete spalling and rebar fracture are shown in Figure 10From the qualitative comparison good agreement isachieved between experimental and FEA results not only onthe global behavior but also on the local material damagebehavior

Concrete crushing and spalling were predicted throughthe compression strain of concrete Priestley [21] suggested avalue of 0004 for cover concrete edge compressive crushing

10 Advances in Civil Engineering

strain and Jiang et al [23] proposed an equation to calculatethe conned concrete edge compression spalling strainwhich is equal to 0005 for test specimense concrete crack

width was predicted through the tensile strain of rebarPriestley [21] suggested a value of 001 for longitudinal rebartensile strain to control the residual crack width within

Stre

ss (M

Pa)

ndash5

0

5

10

15

20

25

30

35

40

0002 0004 0006 0008 00100000Strain

(a)

Stre

ss (M

Pa)

0

100

200

300

400

500

600

004 008 012 016000Strain

(b)

Figure 8 Uniaxial constitutive relationships of materials (a) Concrete (b) Rebar 12mm

Wm

res (

mm

)

Beam1Beam2Beam3

00

05

10

15

20

ndash002 000 002 004ndash004Rotation (rad)

(a)W

mre

s (m

m)

Beam1Beam4Beam5

00

05

10

15

20

ndash002 000 002 004ndash004Rotation (rad)

(b)

Wm

res (

mm

)

Beam2Beam6Beam7

00

05

10

15

20

ndash002 000 002 004ndash004Rotation (rad)

(c)

Figure 7 Maximum residual crack width of specimens (a) Eect of aspect ratio (b) Eect of ange-web ratio (c) Eect of steel ratio

Late

ral l

oad

(kN

)

FEATest

ndash1200

ndash800

ndash400

0

400

800

1200

ndash006 ndash003 000 003 006 009ndash009Rotation (rad)

(a)

Late

ral l

oad

(kN

)

FEATest

ndash1200

ndash800

ndash400

0

400

800

1200

ndash006 ndash003 000 003 006 009ndash009Rotation (rad)

(b)

Figure 9 Comparison of experimental and numerical skeleton curves (a) Specimen Beam1 (b) Specimen Beam5

Advances in Civil Engineering 11

10mm e chord rotations corresponding to differentconcrete damage states obtained from finite element analysiswere compared with the test result as shown in Table 5From the quantitative comparison for concrete damagedeformation finite element analysis can only provide astatistically consistent simulation result not specifically ac-curate simulation result for each specimen e mean ro-tation ratios between FEA and the test for the concreteresidual crack width equal to 1mm concrete crushing and

concrete spalling are 099 083 and 074 respectively If thecover concrete edge compression crushing strain is revisedto 0005 and confined concrete edge compression spallingstrain is revised to 00075 the mean rotation ratios betweenFEA and the test for concrete crushing and concrete spallingare 104 and 103 respectively

Steel flange tensile yielding and web principle tensileyielding were predicted directly through steel yielding strainrecorded in Table 2 e chord rotations corresponding to

Rebar fracture

PE max principalSNEG(fraction = ndash10)(avg 75)

+1454e ndash 01+1333e ndash 01+1212e ndash 01+1090e ndash 01+9693e ndash 02+8481e ndash 02+7269e ndash 02+6058e ndash 02+4846e ndash 02+3635e ndash 02+2423e ndash 02+1212e ndash 02+0000e + 00

(a)

Concrete spalling

PEEQ(avg 75)

+4683e ndash 02+4292e ndash 02+3902e ndash 02+3512e ndash 02+3122e ndash 02+2731e ndash 02+2341e ndash 02+1951e ndash 02+1561e ndash 02+1171e ndash 02+7804e ndash 03+3902e ndash 03+0000e + 00

(b)

Figure 10 Comparison of experimental and numerical damages (a) Rebar fracture of specimen Beam1 (b) Concrete spalling of specimenBeam1

Table 5 Comparison of chord rotations of specimens for different concrete damage states

Specimen numberResidual crack width lt1mm Concrete crushing Concrete spallingTest FEA FEAtest Test FEA FEAtest Test FEA FEAtest

Beam1 00084 00157 187 00238 00231 097 00403 00442 110Beam2 00116 00141 122 00192 00137 071 00385 00244 063Beam3 00150 00155 103 00139 00143 103 00378 00256 068Beam4 00261 00145 056 00233 00185 079 00416 00288 069Beam5 00200 00149 075 00179 00196 109 00346 00363 105Beam6 00187 00140 075 00237 00133 056 00485 00233 048Beam7 00190 00141 074 00201 00130 065 00430 00225 052

12 Advances in Civil Engineering

different steel yielding states obtained from finite elementanalysis were compared with the test result as shown inTable 6 e finite element analysis can provide a statisticallyconsistent simulation result and the mean rotation ratiosbetween FEA and the test for steel flange tensile yielding andsteel web principle tensile yielding are 123 and 108respectively

Rebar tensile yielding and rebar fracture were pre-dicted directly through rebar yielding strain and tensilestrain recorded in Table 2 Rebar buckling was predictedthrough confined concrete ultimate compressive strainwhich is calculated using equation suggested by Priestley[21] e chord rotations corresponding to different rebardamage states obtained from finite element analysis werecompared with the test result as shown in Table 7 efinite element analysis can provide a statistically consis-tent simulation result and the mean rotation ratios be-tween FEA and the test for rebar tensile yielding rebarbuckling and rebar fracture are 074 103 and 090respectively

43 Performance Index Limit Analysis e seismic per-formance of SRC coupling beams is affected by the ma-terial damage which is related to the material strain Onthe other hand the degradation of the load carrying ca-pacity of SRC coupling beams affects its seismic perfor-mance also Based on the study on the material damagestrain limits [21 23] and component strength degradationlimits [24] four performance levels are defined as shownin Table 8 Since there is a lack of test records of speci-mensrsquo deformation at damage states of concrete strainequal to 0002 or crack width equal to 2mm the chordrotation of specimens at different performance levels canonly be obtained through FEA Table 9 shows the chord

rotations of SRC coupling beam specimens at differentperformance levels and then the mean values wereadopted as the performance index limits which were0005 rad 0014 rad 0024 rad and 0047 rad for the fourperformance levels

5 Summary and Conclusions

Seven half-scale flexural-yielding SRC coupling beamspecimens designed according to Chinese approach weretested under cyclic loade influence of design parameterssuch as aspect ratio flange-web area ratio of encased steeland steel ratio on damage development hysteretic be-havior strength and maximum residual crack width werediscussed Finite element analysis was conducted forspecimens both global skeleton curves and local materialdamage were simulated simultaneously rough quanti-tative comparison finite element analysis can provide astatistically consistent simulation result for materialdamages for each specimen Some conclusions are drawnfrom this research

(1) All specimens failed in flexural mode e damagedevelopment was roughly the same and the typicaldamage states were recorded through the wholeloading process which can be used in assessing theseismic performance level of SRC coupling beams

(2) With the increase of aspect ratio the lateral loadcarrying capacity drops down significantly and themaximum residual crack width tends to be smallerWith the increase of flange-web area ratio of encasedsteel the hysteretic curve gets fuller e specimenwith intermediate flange-web area ratio has thelargest lateral load carrying capacity but smallestmaximum residual crack width With the increase of

Table 6 Comparison of chord rotations of specimens for different steel damage states

Specimen numberSteel flange yielding Steel web yielding

Test FEA FEAtest Test FEA FEAtestBeam1 00033 00059 179 00140 00124 089Beam2 00063 00053 084 00120 00116 097Beam3 00044 00061 139 00095 00108 114Beam4 00041 00051 124 00085 00105 124Beam5 00053 00056 106 00078 00098 126Beam6 00065 00057 088 00100 00115 115Beam7 00039 00056 144 00131 00120 092

Table 7 Comparison of chord rotations of specimens for different rebar damage states

Specimen numberRebar yielding Rebar buckling Rebar fracture

Test FEA FEAtest Test FEA FEAtest Test FEA FEAtestBeam1 00072 00059 082 00502 00777 155 00609 00562 092Beam2 00065 00054 083 00451 00426 094 00558 00502 090Beam3 00091 00060 066 00478 00446 093 00560 00571 102Beam4 00072 00056 078 00485 00527 109 00565 00504 089Beam5 00078 00054 069 00444 00526 118 00586 00596 102Beam6 00065 00056 086 00522 00403 077 00653 00490 075Beam7 00105 00057 054 00511 00390 076 00593 00493 083

Advances in Civil Engineering 13

steel ratio the lateral load carrying capacity increasessignificantly while the maximum residual crackwidth drops down

(3) e finite element model was benchmarkedthrough comparison with test results for bothglobal load-deformation curves and local materialdamages Both qualitative and quantitative com-parisons testify the accuracy of finite elementmodels e cover concrete edge compressionstrain and confined concrete edge compressionstrain were recommended to be 0005 and 00075respectively for accurately modeling concretecrushing and spalling Based on the damagecharacters and strength degradation four perfor-mance levels were defined and correspondingchord rotation limits were obtained through theverified numerical analysis

Data Availability

All the data in this paper are obtained from tests and nu-merical analysis and no other data in the literature are usedto support this study

Conflicts of Interest

e authors declare that there are no potential conflicts ofinterest with respect to the research authorship and pub-lication of this article

Acknowledgments

e financial support from the Program of Shanghai Aca-demic Research Leader (grant number 18XD1403900) andthe National Key Research and Development Program ofChina (grant number 2017YFC1500701) is gratefullyacknowledged

References

[1] S El-Tawil K A Harries P J Fortney B M Shahrooz andY Kurama ldquoSeismic design of hybrid coupled wall systemsstate of the artrdquo Journal of structural engineering vol 136no 7 pp 755ndash769 2010

[2] C-C Hung and W-T Lu ldquoA performance-based designmethod for coupled wall structuresrdquo Journal of EarthquakeEngineering vol 21 no 4 pp 579ndash603 2016

[3] C J Motter D C Fields J D Hooper et al ldquoSteel-reinforcedconcrete coupling beams I testingrdquo Journal of StructuralEngineering vol 143 no 3 article 04016191 2016

[4] B Gong and B M Shahrooz ldquoConcrete-steel compositecoupling beams I component testingrdquo Journal of StructuralEngineering vol 127 no 6 pp 625ndash631 2001

[5] B Gong and B M Shahrooz ldquoConcrete-steel compositecoupling beams II subassembly testing and design verifi-cationrdquo Journal of Structural Engineering vol 127 no 6pp 632ndash638 2001

[6] R K L Su and W Y Lam ldquoA unified design approach forplate-reinforced composite coupling beamsrdquo Journal ofConstructional Steel Research vol 65 no 3 pp 675ndash6862009

Table 8 Method of defining performance levels for SRC coupling beams

Performance level Damage descriptionPerformance criterion

Rebar or steel strain Concretestrain Load carrying capacity

Being basically intact ere are fine cracks in concrete while steel or rebaris not yielding εy 0002 mdash

Slight damage Concrete cover is not crushing and residual crackwidth is less than 1mm 0015 0005 mdash

Moderate damage Concrete cover is not spalling and residual crackwidth is less than 2mm 003 00075 95 Pmax

Severe damage Concrete core is not crushing and rebar or steel isnot fracturing εsu εcu 85 Pmax

Note εy is the yielding strain of steel or rebar εsu is the tensile strain of steel or rebar εcu is the ultimate strain of the concrete Pmax is the lateral load carryingcapacity of specimens

Table 9 Chord rotations of SRC coupling beams at different performance levels (rad)

Specimen numberPerformance level

Being basically intact Slight damage Moderate damage Severe damageBeam1 00055 00157 00264 00562Beam2 00053 00137 00212 00426Beam3 00060 00143 00235 00446Beam4 00051 00145 00239 00504Beam5 00054 00149 00257 00526Beam6 00051 00133 00228 00403Beam7 00050 00130 00228 00390

14 Advances in Civil Engineering

[7] C J Motter D C Fields J D Hooper et al ldquoSteel-reinforcedconcrete coupling beams II Modelingrdquo Journal of StructuralEngineering vol 143 no 3 article 04016192 2016

[8] Q Z Liang and X L Han ldquoe behavior of stiffening beamsand lintel beams under cyclic loadingrdquo Journal of South ChinaUniversity of Technology vol 23 no 1 pp 27ndash33 1995 inChinese

[9] H Jiang B Wang and X Lu ldquoExperimental study on damagebehavior of reinforced concrete shear walls subjected to cyclicloadsrdquo Journal of Earthquake Engineering vol 17 no 7pp 958ndash971 2013

[10] J Yue J Qian and D E Beskos ldquoA generalized multi-levelseismic damage model for RC framed structuresrdquo Soil Dy-namics and Earthquake Engineering vol 80 pp 25ndash39 2016

[11] JGJ138-2016 Code for Design of Composite Structures ChinaArchitecture amp Building Press Beijing China 2016

[12] R D Lequesne G J Parra-Montesinos and J K WightldquoSeismic behavior and detailing of high-performance fiber-reinforced concrete coupling beams and coupled wall sys-temsrdquo Journal of Structural Engineering vol 139 no 8pp 1362ndash1370 2012

[13] M Otieno H Beushausen and M Alexander ldquoTowardsincorporating the influence of cover cracking on steel cor-rosion in RC design codes the concept of performance-basedcrack width limitsrdquo Materials and Structures vol 45 no 12pp 1805ndash1816 2012

[14] SIMULIA Dassault Systems ABAQUS Analysis UserrsquosManual Version 616 SIMULIA Johnston RI USA 2016

[15] J C Goodnight M J Kowalsky and J M Nau ldquoEffect of loadhistory on performance limit states of circular bridge col-umnsrdquo Journal of Bridge Engineering vol 18 no 12pp 1383ndash1396 2013

[16] R T Ranf ldquoDamage accumulation in lightly confined rein-forced concrete bridge columnsrdquo PEER Report PacificEarthquake Engineering Research Center University ofCalifornia Berkeley CA USA 2006

[17] A Babazadeh R Burguentildeo and P F Silva ldquoUse of 3D finite-element models for predicting intermediate damage limitstates in RC bridge columnsrdquo Journal of Structural Engi-neering vol 141 no 10 article 04015012 2015

[18] J Moon CW Roeder andH-E Lee ldquoAnalytical modeling ofbending of circular concrete-filled steel tubesrdquo EngineeringStructures vol 42 no 12 pp 349ndash361 2012

[19] GB50010-2010 Code for Design of Concrete Structures ChinaArchitecture amp Building Press Beijing China 2010

[20] H Zhu M T Stephens and D E Lehman ldquoInelastic responseprediction of CFST columns and connections subjected tolateral loadingrdquo Journal of Constructional Steel Researchvol 132 pp 130ndash140 2017

[21] M J N Priestley ldquoPerformance based seismic designrdquo inProceedings of 12th World Conference on EarthquakeEngineering Auckland New Zealand January 2000

[22] Y Shi M Wang and Y Wang ldquoExperimental and consti-tutive model study of structural steel under cyclic loadingrdquoJournal of Constructional Steel Research vol 67 no 8pp 1185ndash1197 2011

[23] H Jiang X Lu and T Kubo ldquoDamage displacement esti-mation of flexure-dominant RC columnsrdquo Advances inStructural Engineering vol 13 no 2 pp 357ndash368 2010

[24] GB50011-2010 Code for Seismic Design of Buildings ChinaArchitecture amp Building Press Beijing China 2010

Advances in Civil Engineering 15

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(a) (b) (c)

Figure 5 Crack pattern of specimens before concrete crushing (a) Beam1 (b) Beam2 (c) Beam3

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200

ndash004 000 004 008ndash008Rotation (rad)

ndash40 ndash20 0 20 40Lateral displacement (mm)

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash40 ndash20 0 20 40

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(a)

Late

ral l

oad

(kN

)

ndash60 ndash30 0 30 60Lateral displacement (mm)

ndash800

ndash400

0

400

800

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

ndash004 000 004 008ndash008Rotation (rad)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash60 ndash30 0 30 60

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(b)

Figure 6 Continued

Advances in Civil Engineering 7

Late

ral l

oad

(kN

)

ndash100 ndash50 0 50 100Lateral displacement (mm)

ndash480

ndash320

ndash160

0

160

320

480

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

ndash004 000 004 008ndash008Rotation (rad)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash100 ndash50 0 50 100

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(c)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash40 ndash20 0 20 40

Lateral displacement (mm)

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

ndash004 000 004 008ndash008Rotation (rad)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash40 ndash20 0 20 40

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(d)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash40 ndash20 0 20 40

Lateral displacement (mm)

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

ndash004 000 004 008ndash008Rotation (rad)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash40 ndash20 0 20 40

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(e)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash60 ndash30 0 30 60

Lateral displacement (mm)

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

ndash004 000 004 008ndash008Rotation (rad)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash60 ndash30 0 30 60

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(f )

Figure 6 Continued

8 Advances in Civil Engineering

of specimen Beam2 which means that the lateral loadcarrying capacity changes in inverse proportion with theaspect ratio and all specimens reached its exural strengthIn general the larger aspect ratio specimen tends to havesmaller lateral load carrying capacity at the individualdamage characteristic point Considering displacements ofthe individual damage state the initial damage states(concrete cracking steel tensile yielding and rebar tensileyielding) of specimen Beam3 with a aspect ratio of 5 tend tooccur later than those of specimen Beam1 with a aspect ratioof 2 which is consistent with the elastic chord rotationequation of the Timoshenko cantilever beam which is asfollows

θ ΔLML

3EI+M

GAL (6)

where M is the xed end section moment of the cantileverbeam L is the length of the cantilever beam E is the elasticmodulus I is the section moment inertia G is the shearmodulus and A is the eective shear section area When L islarger than

3EIGA

radicasymp 08h (h is the beam section height)

chord rotation θ increases with the increase of the beamlength under the same xed end moment e damage statessuch as steel web principle yielding concrete crushingconcrete spalling rebar buckling and rebar fracture of

specimen Beam3 tend to occur earlier than those of spec-imen Beam1 because specimen Beam3 has a relativelysmaller moment gradient at the plastic zone which causesexural damages of Beam3 to occur easily and smaller shearforce in Beam3 leads to smaller shear deformation also

For specimens Beam1 Beam4 and Beam5 with dierentange-web area ratios of encased steel specimen Beam4witha ange-web ratio of 05 has the largest lateral load carryingcapacity which is 11866 kN and is 33 larger than that ofspecimen Beam1 and 225 larger than that of specimenBeam5 which means that the specimen without the ange ofencased steel has a signicant smaller lateral load carryingcapacity e reason that specimen Beam4 with a smallerange-web ratio has slightly larger lateral load capacity thanspecimen Beam1 is that the encased steel consists of steelplates with dierent thicknesses and dierent yieldingstrengths and the average yielding strength of encased steelof specimen Beam4 is slightly larger than that of specimenBeam1 e calculated lateral load capacity (MnL) forspecimens Beam4 and Beam1 shown in Table 3 veried thisexplanation Considering the displacements of individualdamage states except the damage states like steel tensileyielding and rebar tensile yielding the other damage states ofspecimen Beam1 with a ange-web ratio of 1 tend to occurlater than those of specimen Beam5 with a ange-web ratio

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash60 ndash30 0 30 60

Lateral displacement (mm)

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

ndash004 000 004 008ndash008Rotation (rad)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash60 ndash30 0 30 60

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(g)

Figure 6 Lateral load-chord rotation hysteretic curves and skeleton curves of specimens (a) Beam1 (b) Beam2 (c) Beam3 (d) Beam4(e) Beam5 (f ) Beam6 (g) Beam7

Table 4 Chord rotation of specimens at the individual damage characteristic point

Specimen number θc (rad) θsty (rad) θrty (rad) θswy (rad) θcc (rad) θcs (rad) θrb (rad) θrf (rad)Beam1 00012 00033 00072 00140 00238 00403 00502 00609Beam2 00013 00063 00065 00120 00192 00385 00451 00558Beam3 00014 00044 00091 00095 00139 00378 00478 00560Beam4 00009 00041 00072 00085 00233 00416 00485 00565Beam5 00008 00053 00078 00078 00179 00346 00444 00586Beam6 00010 00065 00065 00100 00237 00485 00522 00653Beam7 00013 00039 00105 00131 00201 00430 00511 00593Note θc θsty θrty θswy θcc θcs θrb and θrf represent the chord rotation of specimens at damage states of concrete cracking steel tensile yielding rebar tensileyielding steel web principle tensile yielding concrete crushing concrete spalling rebar buckling and rebar fracture respectively For Beam5 rebar tensileyielding and steel web principle tensile yielding occurred at the same time For Beam6 steel tensile yielding and rebar tensile yielding occurred at the sametime

Advances in Civil Engineering 9

of 0 is is because the flange steel enhances the com-pression behavior of the concrete and delays the concretecrushing and spalling In addition shear deformation ofspecimen Beam1 with smaller web steel is larger than that ofspecimen Beam5 at the same damage state

For specimens Beam2 Beam6 and Beam7 with theincrease of steel ratio from 5 to 83 the lateral loadcarrying capacity increases from 7503 kN to 9688 kN by292 which means that the lateral load carrying capacity ofSRC coupling beam was influenced largely by the steel ratioExcept initial damage states like concrete cracking rebartensile yielding and steel web principle tensile yielding theother damage states of specimen Beam6 with a steel ratio of67 tend to occur later than those of specimen Beam2 witha steel ratio of 5 and Beam7 with a steel ratio of 83

Concrete cover cracking influences the encased steelcorrosion initiation and the crack width influences thecorrosion propagation thus both influence the performanceof structures [13] e maximum residual crack width of allspecimens represented by Wmres was measured during thetest cycles before concrete cover crashed or spalled evariation of maximum residual crack width with the chordrotation is shown in Figure 7 Generally the maximumresidual crack width rises up with the increase of the chordrotation e maximum residual crack width of the speci-men at the same rotation tends to be smaller with the in-crease of the aspect ratio or steel ratio for the average value ofthat for both directions For specimens Beam1 Beam4 andBeam5 with different flange-web area ratios of encased steelBeam4 has the smallest maximum residual crack width whileBeam1 has the largest maximum residual crack width at thesame rotation

4 Numerical Analysis and Verification

41 Modeling ree-dimensional nonlinear finite elementmodels were developed to simulate the inelastic behavior oftested SRC coupling beam specimens using Abaqus [14] Notonly the global force-rotation behavior but also the localmaterial damage behavior during the test process includingconcrete (cracking crushing and spalling) steel yieldingand rebar (yielding buckling and fracture) was predictedthrough finite element analysis It has been reported [15ndash17]that material damage states ie spalling and yielding arenot dependent on the history of loading but are ratherclosely related to the maximum displacement that thestructure has experienced erefore a monotonic analysiswas sufficient for predicting damage deformation of flexure-yielding SRC coupling beams

Damaged plasticity model was used to simulate theconcrete inelastic behavior in SRC coupling beam specimensis model is applicable in the situation that the concrete is atlow confinement pressures (less than four to five times thelargest compressive stress that can be carried by the concretein uniaxial compression) which is suitable for SRC couplingbeams Moon et al [18] used this model to study the con-finement effect of steel tubes on the infilled concrete andBabazadeh et al [17] used this model to study the spalling ofthe concrete for RC bridge columnse uniaxial stress-strain

relationship for the concrete recommended in Chinese codeGB50010-2010 [19] was adopted here as shown in Figure 8(a)e compression strength of the concrete is 373MPa whichis the prismatic compression strength of concrete fck which iscalculated based on the conversion formula in Chinese code50010-2010 [19] and the tested cubic compression strength ofconcrete fcu is equal to 578MPa

Ductile damage plasticity model was used to simulate theencased steel and rebar inelastic behavior in SRC couplingbeam specimens is model offers a general capability forpredicting the onset of failure and a capability for modelingprogressive damage and failure of ductile metals Zhu et al[20] used this model to simulate the steel tearing of concrete-filled steel tube columns e strengthening stage of steeladopted a bilinear model hardening stiffness of which is 1of elastic stiffness and damage initiated at tensile strain anddamage evolution adopted a linear damage form Consid-ering the cyclic fatigue of longitudinal rebar under earth-quakes Priestley [21] suggested the tensile strain of thelongitudinal rebar to be reduced by 40 Shi et al [22]carried out the structural steel low cycle fatigue test andproved that the tensile strain of Q345B steel was reduced by203 and Q235B steel was reduced by 386 after cyclicloading e fracture strain was conservatively taken as twotimes tensile strain refer to the former test results euniaxial stress-strain relationship for the 12mm diameterrebar is shown in Figure 8(b)

Eight-node solid elements with reduced integration(C3D8R) were used for the concrete four-node shell ele-ments with reduced integration (S4R) were used for theencased steel and two-node linear displacement truss ele-ments were used for rebar A perfect bond was assumedbetween the steel rebar elements and the concrete parttherefore the truss elements and shell elements were em-bedded in the concrete instance using the lowastEMBEDDEDELEMENT option e bottom surface of the pedestal wasfixed against all degrees of freedom A reference point wasmodeled on the surface of the loading plate which wasconstrained with the surface of the loading plate using thelowastCOUPLING option available in the ABAQUS library

42 Analysis Results e global skeleton curves of all thespecimens obtained from the FEA are compared with theskeleton curves obtained from the test and two of them areshown in Figure 9 e FEA model gave a stiffer result in thepositive part and softer one in the negative part for specimenBeam1 compared to the experimental result which may bedue to the slippage of the pedestal or the gap between loadinghead and specimen in the test e local material damagesobtained from FEA are also compared with test results andconcrete spalling and rebar fracture are shown in Figure 10From the qualitative comparison good agreement isachieved between experimental and FEA results not only onthe global behavior but also on the local material damagebehavior

Concrete crushing and spalling were predicted throughthe compression strain of concrete Priestley [21] suggested avalue of 0004 for cover concrete edge compressive crushing

10 Advances in Civil Engineering

strain and Jiang et al [23] proposed an equation to calculatethe conned concrete edge compression spalling strainwhich is equal to 0005 for test specimense concrete crack

width was predicted through the tensile strain of rebarPriestley [21] suggested a value of 001 for longitudinal rebartensile strain to control the residual crack width within

Stre

ss (M

Pa)

ndash5

0

5

10

15

20

25

30

35

40

0002 0004 0006 0008 00100000Strain

(a)

Stre

ss (M

Pa)

0

100

200

300

400

500

600

004 008 012 016000Strain

(b)

Figure 8 Uniaxial constitutive relationships of materials (a) Concrete (b) Rebar 12mm

Wm

res (

mm

)

Beam1Beam2Beam3

00

05

10

15

20

ndash002 000 002 004ndash004Rotation (rad)

(a)W

mre

s (m

m)

Beam1Beam4Beam5

00

05

10

15

20

ndash002 000 002 004ndash004Rotation (rad)

(b)

Wm

res (

mm

)

Beam2Beam6Beam7

00

05

10

15

20

ndash002 000 002 004ndash004Rotation (rad)

(c)

Figure 7 Maximum residual crack width of specimens (a) Eect of aspect ratio (b) Eect of ange-web ratio (c) Eect of steel ratio

Late

ral l

oad

(kN

)

FEATest

ndash1200

ndash800

ndash400

0

400

800

1200

ndash006 ndash003 000 003 006 009ndash009Rotation (rad)

(a)

Late

ral l

oad

(kN

)

FEATest

ndash1200

ndash800

ndash400

0

400

800

1200

ndash006 ndash003 000 003 006 009ndash009Rotation (rad)

(b)

Figure 9 Comparison of experimental and numerical skeleton curves (a) Specimen Beam1 (b) Specimen Beam5

Advances in Civil Engineering 11

10mm e chord rotations corresponding to differentconcrete damage states obtained from finite element analysiswere compared with the test result as shown in Table 5From the quantitative comparison for concrete damagedeformation finite element analysis can only provide astatistically consistent simulation result not specifically ac-curate simulation result for each specimen e mean ro-tation ratios between FEA and the test for the concreteresidual crack width equal to 1mm concrete crushing and

concrete spalling are 099 083 and 074 respectively If thecover concrete edge compression crushing strain is revisedto 0005 and confined concrete edge compression spallingstrain is revised to 00075 the mean rotation ratios betweenFEA and the test for concrete crushing and concrete spallingare 104 and 103 respectively

Steel flange tensile yielding and web principle tensileyielding were predicted directly through steel yielding strainrecorded in Table 2 e chord rotations corresponding to

Rebar fracture

PE max principalSNEG(fraction = ndash10)(avg 75)

+1454e ndash 01+1333e ndash 01+1212e ndash 01+1090e ndash 01+9693e ndash 02+8481e ndash 02+7269e ndash 02+6058e ndash 02+4846e ndash 02+3635e ndash 02+2423e ndash 02+1212e ndash 02+0000e + 00

(a)

Concrete spalling

PEEQ(avg 75)

+4683e ndash 02+4292e ndash 02+3902e ndash 02+3512e ndash 02+3122e ndash 02+2731e ndash 02+2341e ndash 02+1951e ndash 02+1561e ndash 02+1171e ndash 02+7804e ndash 03+3902e ndash 03+0000e + 00

(b)

Figure 10 Comparison of experimental and numerical damages (a) Rebar fracture of specimen Beam1 (b) Concrete spalling of specimenBeam1

Table 5 Comparison of chord rotations of specimens for different concrete damage states

Specimen numberResidual crack width lt1mm Concrete crushing Concrete spallingTest FEA FEAtest Test FEA FEAtest Test FEA FEAtest

Beam1 00084 00157 187 00238 00231 097 00403 00442 110Beam2 00116 00141 122 00192 00137 071 00385 00244 063Beam3 00150 00155 103 00139 00143 103 00378 00256 068Beam4 00261 00145 056 00233 00185 079 00416 00288 069Beam5 00200 00149 075 00179 00196 109 00346 00363 105Beam6 00187 00140 075 00237 00133 056 00485 00233 048Beam7 00190 00141 074 00201 00130 065 00430 00225 052

12 Advances in Civil Engineering

different steel yielding states obtained from finite elementanalysis were compared with the test result as shown inTable 6 e finite element analysis can provide a statisticallyconsistent simulation result and the mean rotation ratiosbetween FEA and the test for steel flange tensile yielding andsteel web principle tensile yielding are 123 and 108respectively

Rebar tensile yielding and rebar fracture were pre-dicted directly through rebar yielding strain and tensilestrain recorded in Table 2 Rebar buckling was predictedthrough confined concrete ultimate compressive strainwhich is calculated using equation suggested by Priestley[21] e chord rotations corresponding to different rebardamage states obtained from finite element analysis werecompared with the test result as shown in Table 7 efinite element analysis can provide a statistically consis-tent simulation result and the mean rotation ratios be-tween FEA and the test for rebar tensile yielding rebarbuckling and rebar fracture are 074 103 and 090respectively

43 Performance Index Limit Analysis e seismic per-formance of SRC coupling beams is affected by the ma-terial damage which is related to the material strain Onthe other hand the degradation of the load carrying ca-pacity of SRC coupling beams affects its seismic perfor-mance also Based on the study on the material damagestrain limits [21 23] and component strength degradationlimits [24] four performance levels are defined as shownin Table 8 Since there is a lack of test records of speci-mensrsquo deformation at damage states of concrete strainequal to 0002 or crack width equal to 2mm the chordrotation of specimens at different performance levels canonly be obtained through FEA Table 9 shows the chord

rotations of SRC coupling beam specimens at differentperformance levels and then the mean values wereadopted as the performance index limits which were0005 rad 0014 rad 0024 rad and 0047 rad for the fourperformance levels

5 Summary and Conclusions

Seven half-scale flexural-yielding SRC coupling beamspecimens designed according to Chinese approach weretested under cyclic loade influence of design parameterssuch as aspect ratio flange-web area ratio of encased steeland steel ratio on damage development hysteretic be-havior strength and maximum residual crack width werediscussed Finite element analysis was conducted forspecimens both global skeleton curves and local materialdamage were simulated simultaneously rough quanti-tative comparison finite element analysis can provide astatistically consistent simulation result for materialdamages for each specimen Some conclusions are drawnfrom this research

(1) All specimens failed in flexural mode e damagedevelopment was roughly the same and the typicaldamage states were recorded through the wholeloading process which can be used in assessing theseismic performance level of SRC coupling beams

(2) With the increase of aspect ratio the lateral loadcarrying capacity drops down significantly and themaximum residual crack width tends to be smallerWith the increase of flange-web area ratio of encasedsteel the hysteretic curve gets fuller e specimenwith intermediate flange-web area ratio has thelargest lateral load carrying capacity but smallestmaximum residual crack width With the increase of

Table 6 Comparison of chord rotations of specimens for different steel damage states

Specimen numberSteel flange yielding Steel web yielding

Test FEA FEAtest Test FEA FEAtestBeam1 00033 00059 179 00140 00124 089Beam2 00063 00053 084 00120 00116 097Beam3 00044 00061 139 00095 00108 114Beam4 00041 00051 124 00085 00105 124Beam5 00053 00056 106 00078 00098 126Beam6 00065 00057 088 00100 00115 115Beam7 00039 00056 144 00131 00120 092

Table 7 Comparison of chord rotations of specimens for different rebar damage states

Specimen numberRebar yielding Rebar buckling Rebar fracture

Test FEA FEAtest Test FEA FEAtest Test FEA FEAtestBeam1 00072 00059 082 00502 00777 155 00609 00562 092Beam2 00065 00054 083 00451 00426 094 00558 00502 090Beam3 00091 00060 066 00478 00446 093 00560 00571 102Beam4 00072 00056 078 00485 00527 109 00565 00504 089Beam5 00078 00054 069 00444 00526 118 00586 00596 102Beam6 00065 00056 086 00522 00403 077 00653 00490 075Beam7 00105 00057 054 00511 00390 076 00593 00493 083

Advances in Civil Engineering 13

steel ratio the lateral load carrying capacity increasessignificantly while the maximum residual crackwidth drops down

(3) e finite element model was benchmarkedthrough comparison with test results for bothglobal load-deformation curves and local materialdamages Both qualitative and quantitative com-parisons testify the accuracy of finite elementmodels e cover concrete edge compressionstrain and confined concrete edge compressionstrain were recommended to be 0005 and 00075respectively for accurately modeling concretecrushing and spalling Based on the damagecharacters and strength degradation four perfor-mance levels were defined and correspondingchord rotation limits were obtained through theverified numerical analysis

Data Availability

All the data in this paper are obtained from tests and nu-merical analysis and no other data in the literature are usedto support this study

Conflicts of Interest

e authors declare that there are no potential conflicts ofinterest with respect to the research authorship and pub-lication of this article

Acknowledgments

e financial support from the Program of Shanghai Aca-demic Research Leader (grant number 18XD1403900) andthe National Key Research and Development Program ofChina (grant number 2017YFC1500701) is gratefullyacknowledged

References

[1] S El-Tawil K A Harries P J Fortney B M Shahrooz andY Kurama ldquoSeismic design of hybrid coupled wall systemsstate of the artrdquo Journal of structural engineering vol 136no 7 pp 755ndash769 2010

[2] C-C Hung and W-T Lu ldquoA performance-based designmethod for coupled wall structuresrdquo Journal of EarthquakeEngineering vol 21 no 4 pp 579ndash603 2016

[3] C J Motter D C Fields J D Hooper et al ldquoSteel-reinforcedconcrete coupling beams I testingrdquo Journal of StructuralEngineering vol 143 no 3 article 04016191 2016

[4] B Gong and B M Shahrooz ldquoConcrete-steel compositecoupling beams I component testingrdquo Journal of StructuralEngineering vol 127 no 6 pp 625ndash631 2001

[5] B Gong and B M Shahrooz ldquoConcrete-steel compositecoupling beams II subassembly testing and design verifi-cationrdquo Journal of Structural Engineering vol 127 no 6pp 632ndash638 2001

[6] R K L Su and W Y Lam ldquoA unified design approach forplate-reinforced composite coupling beamsrdquo Journal ofConstructional Steel Research vol 65 no 3 pp 675ndash6862009

Table 8 Method of defining performance levels for SRC coupling beams

Performance level Damage descriptionPerformance criterion

Rebar or steel strain Concretestrain Load carrying capacity

Being basically intact ere are fine cracks in concrete while steel or rebaris not yielding εy 0002 mdash

Slight damage Concrete cover is not crushing and residual crackwidth is less than 1mm 0015 0005 mdash

Moderate damage Concrete cover is not spalling and residual crackwidth is less than 2mm 003 00075 95 Pmax

Severe damage Concrete core is not crushing and rebar or steel isnot fracturing εsu εcu 85 Pmax

Note εy is the yielding strain of steel or rebar εsu is the tensile strain of steel or rebar εcu is the ultimate strain of the concrete Pmax is the lateral load carryingcapacity of specimens

Table 9 Chord rotations of SRC coupling beams at different performance levels (rad)

Specimen numberPerformance level

Being basically intact Slight damage Moderate damage Severe damageBeam1 00055 00157 00264 00562Beam2 00053 00137 00212 00426Beam3 00060 00143 00235 00446Beam4 00051 00145 00239 00504Beam5 00054 00149 00257 00526Beam6 00051 00133 00228 00403Beam7 00050 00130 00228 00390

14 Advances in Civil Engineering

[7] C J Motter D C Fields J D Hooper et al ldquoSteel-reinforcedconcrete coupling beams II Modelingrdquo Journal of StructuralEngineering vol 143 no 3 article 04016192 2016

[8] Q Z Liang and X L Han ldquoe behavior of stiffening beamsand lintel beams under cyclic loadingrdquo Journal of South ChinaUniversity of Technology vol 23 no 1 pp 27ndash33 1995 inChinese

[9] H Jiang B Wang and X Lu ldquoExperimental study on damagebehavior of reinforced concrete shear walls subjected to cyclicloadsrdquo Journal of Earthquake Engineering vol 17 no 7pp 958ndash971 2013

[10] J Yue J Qian and D E Beskos ldquoA generalized multi-levelseismic damage model for RC framed structuresrdquo Soil Dy-namics and Earthquake Engineering vol 80 pp 25ndash39 2016

[11] JGJ138-2016 Code for Design of Composite Structures ChinaArchitecture amp Building Press Beijing China 2016

[12] R D Lequesne G J Parra-Montesinos and J K WightldquoSeismic behavior and detailing of high-performance fiber-reinforced concrete coupling beams and coupled wall sys-temsrdquo Journal of Structural Engineering vol 139 no 8pp 1362ndash1370 2012

[13] M Otieno H Beushausen and M Alexander ldquoTowardsincorporating the influence of cover cracking on steel cor-rosion in RC design codes the concept of performance-basedcrack width limitsrdquo Materials and Structures vol 45 no 12pp 1805ndash1816 2012

[14] SIMULIA Dassault Systems ABAQUS Analysis UserrsquosManual Version 616 SIMULIA Johnston RI USA 2016

[15] J C Goodnight M J Kowalsky and J M Nau ldquoEffect of loadhistory on performance limit states of circular bridge col-umnsrdquo Journal of Bridge Engineering vol 18 no 12pp 1383ndash1396 2013

[16] R T Ranf ldquoDamage accumulation in lightly confined rein-forced concrete bridge columnsrdquo PEER Report PacificEarthquake Engineering Research Center University ofCalifornia Berkeley CA USA 2006

[17] A Babazadeh R Burguentildeo and P F Silva ldquoUse of 3D finite-element models for predicting intermediate damage limitstates in RC bridge columnsrdquo Journal of Structural Engi-neering vol 141 no 10 article 04015012 2015

[18] J Moon CW Roeder andH-E Lee ldquoAnalytical modeling ofbending of circular concrete-filled steel tubesrdquo EngineeringStructures vol 42 no 12 pp 349ndash361 2012

[19] GB50010-2010 Code for Design of Concrete Structures ChinaArchitecture amp Building Press Beijing China 2010

[20] H Zhu M T Stephens and D E Lehman ldquoInelastic responseprediction of CFST columns and connections subjected tolateral loadingrdquo Journal of Constructional Steel Researchvol 132 pp 130ndash140 2017

[21] M J N Priestley ldquoPerformance based seismic designrdquo inProceedings of 12th World Conference on EarthquakeEngineering Auckland New Zealand January 2000

[22] Y Shi M Wang and Y Wang ldquoExperimental and consti-tutive model study of structural steel under cyclic loadingrdquoJournal of Constructional Steel Research vol 67 no 8pp 1185ndash1197 2011

[23] H Jiang X Lu and T Kubo ldquoDamage displacement esti-mation of flexure-dominant RC columnsrdquo Advances inStructural Engineering vol 13 no 2 pp 357ndash368 2010

[24] GB50011-2010 Code for Seismic Design of Buildings ChinaArchitecture amp Building Press Beijing China 2010

Advances in Civil Engineering 15

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Submit your manuscripts atwwwhindawicom

Late

ral l

oad

(kN

)

ndash100 ndash50 0 50 100Lateral displacement (mm)

ndash480

ndash320

ndash160

0

160

320

480

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

ndash004 000 004 008ndash008Rotation (rad)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash100 ndash50 0 50 100

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(c)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash40 ndash20 0 20 40

Lateral displacement (mm)

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

ndash004 000 004 008ndash008Rotation (rad)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash40 ndash20 0 20 40

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(d)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash40 ndash20 0 20 40

Lateral displacement (mm)

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

ndash004 000 004 008ndash008Rotation (rad)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash40 ndash20 0 20 40

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(e)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash60 ndash30 0 30 60

Lateral displacement (mm)

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

ndash004 000 004 008ndash008Rotation (rad)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash60 ndash30 0 30 60

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(f )

Figure 6 Continued

8 Advances in Civil Engineering

of specimen Beam2 which means that the lateral loadcarrying capacity changes in inverse proportion with theaspect ratio and all specimens reached its exural strengthIn general the larger aspect ratio specimen tends to havesmaller lateral load carrying capacity at the individualdamage characteristic point Considering displacements ofthe individual damage state the initial damage states(concrete cracking steel tensile yielding and rebar tensileyielding) of specimen Beam3 with a aspect ratio of 5 tend tooccur later than those of specimen Beam1 with a aspect ratioof 2 which is consistent with the elastic chord rotationequation of the Timoshenko cantilever beam which is asfollows

θ ΔLML

3EI+M

GAL (6)

where M is the xed end section moment of the cantileverbeam L is the length of the cantilever beam E is the elasticmodulus I is the section moment inertia G is the shearmodulus and A is the eective shear section area When L islarger than

3EIGA

radicasymp 08h (h is the beam section height)

chord rotation θ increases with the increase of the beamlength under the same xed end moment e damage statessuch as steel web principle yielding concrete crushingconcrete spalling rebar buckling and rebar fracture of

specimen Beam3 tend to occur earlier than those of spec-imen Beam1 because specimen Beam3 has a relativelysmaller moment gradient at the plastic zone which causesexural damages of Beam3 to occur easily and smaller shearforce in Beam3 leads to smaller shear deformation also

For specimens Beam1 Beam4 and Beam5 with dierentange-web area ratios of encased steel specimen Beam4witha ange-web ratio of 05 has the largest lateral load carryingcapacity which is 11866 kN and is 33 larger than that ofspecimen Beam1 and 225 larger than that of specimenBeam5 which means that the specimen without the ange ofencased steel has a signicant smaller lateral load carryingcapacity e reason that specimen Beam4 with a smallerange-web ratio has slightly larger lateral load capacity thanspecimen Beam1 is that the encased steel consists of steelplates with dierent thicknesses and dierent yieldingstrengths and the average yielding strength of encased steelof specimen Beam4 is slightly larger than that of specimenBeam1 e calculated lateral load capacity (MnL) forspecimens Beam4 and Beam1 shown in Table 3 veried thisexplanation Considering the displacements of individualdamage states except the damage states like steel tensileyielding and rebar tensile yielding the other damage states ofspecimen Beam1 with a ange-web ratio of 1 tend to occurlater than those of specimen Beam5 with a ange-web ratio

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash60 ndash30 0 30 60

Lateral displacement (mm)

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

ndash004 000 004 008ndash008Rotation (rad)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash60 ndash30 0 30 60

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(g)

Figure 6 Lateral load-chord rotation hysteretic curves and skeleton curves of specimens (a) Beam1 (b) Beam2 (c) Beam3 (d) Beam4(e) Beam5 (f ) Beam6 (g) Beam7

Table 4 Chord rotation of specimens at the individual damage characteristic point

Specimen number θc (rad) θsty (rad) θrty (rad) θswy (rad) θcc (rad) θcs (rad) θrb (rad) θrf (rad)Beam1 00012 00033 00072 00140 00238 00403 00502 00609Beam2 00013 00063 00065 00120 00192 00385 00451 00558Beam3 00014 00044 00091 00095 00139 00378 00478 00560Beam4 00009 00041 00072 00085 00233 00416 00485 00565Beam5 00008 00053 00078 00078 00179 00346 00444 00586Beam6 00010 00065 00065 00100 00237 00485 00522 00653Beam7 00013 00039 00105 00131 00201 00430 00511 00593Note θc θsty θrty θswy θcc θcs θrb and θrf represent the chord rotation of specimens at damage states of concrete cracking steel tensile yielding rebar tensileyielding steel web principle tensile yielding concrete crushing concrete spalling rebar buckling and rebar fracture respectively For Beam5 rebar tensileyielding and steel web principle tensile yielding occurred at the same time For Beam6 steel tensile yielding and rebar tensile yielding occurred at the sametime

Advances in Civil Engineering 9

of 0 is is because the flange steel enhances the com-pression behavior of the concrete and delays the concretecrushing and spalling In addition shear deformation ofspecimen Beam1 with smaller web steel is larger than that ofspecimen Beam5 at the same damage state

For specimens Beam2 Beam6 and Beam7 with theincrease of steel ratio from 5 to 83 the lateral loadcarrying capacity increases from 7503 kN to 9688 kN by292 which means that the lateral load carrying capacity ofSRC coupling beam was influenced largely by the steel ratioExcept initial damage states like concrete cracking rebartensile yielding and steel web principle tensile yielding theother damage states of specimen Beam6 with a steel ratio of67 tend to occur later than those of specimen Beam2 witha steel ratio of 5 and Beam7 with a steel ratio of 83

Concrete cover cracking influences the encased steelcorrosion initiation and the crack width influences thecorrosion propagation thus both influence the performanceof structures [13] e maximum residual crack width of allspecimens represented by Wmres was measured during thetest cycles before concrete cover crashed or spalled evariation of maximum residual crack width with the chordrotation is shown in Figure 7 Generally the maximumresidual crack width rises up with the increase of the chordrotation e maximum residual crack width of the speci-men at the same rotation tends to be smaller with the in-crease of the aspect ratio or steel ratio for the average value ofthat for both directions For specimens Beam1 Beam4 andBeam5 with different flange-web area ratios of encased steelBeam4 has the smallest maximum residual crack width whileBeam1 has the largest maximum residual crack width at thesame rotation

4 Numerical Analysis and Verification

41 Modeling ree-dimensional nonlinear finite elementmodels were developed to simulate the inelastic behavior oftested SRC coupling beam specimens using Abaqus [14] Notonly the global force-rotation behavior but also the localmaterial damage behavior during the test process includingconcrete (cracking crushing and spalling) steel yieldingand rebar (yielding buckling and fracture) was predictedthrough finite element analysis It has been reported [15ndash17]that material damage states ie spalling and yielding arenot dependent on the history of loading but are ratherclosely related to the maximum displacement that thestructure has experienced erefore a monotonic analysiswas sufficient for predicting damage deformation of flexure-yielding SRC coupling beams

Damaged plasticity model was used to simulate theconcrete inelastic behavior in SRC coupling beam specimensis model is applicable in the situation that the concrete is atlow confinement pressures (less than four to five times thelargest compressive stress that can be carried by the concretein uniaxial compression) which is suitable for SRC couplingbeams Moon et al [18] used this model to study the con-finement effect of steel tubes on the infilled concrete andBabazadeh et al [17] used this model to study the spalling ofthe concrete for RC bridge columnse uniaxial stress-strain

relationship for the concrete recommended in Chinese codeGB50010-2010 [19] was adopted here as shown in Figure 8(a)e compression strength of the concrete is 373MPa whichis the prismatic compression strength of concrete fck which iscalculated based on the conversion formula in Chinese code50010-2010 [19] and the tested cubic compression strength ofconcrete fcu is equal to 578MPa

Ductile damage plasticity model was used to simulate theencased steel and rebar inelastic behavior in SRC couplingbeam specimens is model offers a general capability forpredicting the onset of failure and a capability for modelingprogressive damage and failure of ductile metals Zhu et al[20] used this model to simulate the steel tearing of concrete-filled steel tube columns e strengthening stage of steeladopted a bilinear model hardening stiffness of which is 1of elastic stiffness and damage initiated at tensile strain anddamage evolution adopted a linear damage form Consid-ering the cyclic fatigue of longitudinal rebar under earth-quakes Priestley [21] suggested the tensile strain of thelongitudinal rebar to be reduced by 40 Shi et al [22]carried out the structural steel low cycle fatigue test andproved that the tensile strain of Q345B steel was reduced by203 and Q235B steel was reduced by 386 after cyclicloading e fracture strain was conservatively taken as twotimes tensile strain refer to the former test results euniaxial stress-strain relationship for the 12mm diameterrebar is shown in Figure 8(b)

Eight-node solid elements with reduced integration(C3D8R) were used for the concrete four-node shell ele-ments with reduced integration (S4R) were used for theencased steel and two-node linear displacement truss ele-ments were used for rebar A perfect bond was assumedbetween the steel rebar elements and the concrete parttherefore the truss elements and shell elements were em-bedded in the concrete instance using the lowastEMBEDDEDELEMENT option e bottom surface of the pedestal wasfixed against all degrees of freedom A reference point wasmodeled on the surface of the loading plate which wasconstrained with the surface of the loading plate using thelowastCOUPLING option available in the ABAQUS library

42 Analysis Results e global skeleton curves of all thespecimens obtained from the FEA are compared with theskeleton curves obtained from the test and two of them areshown in Figure 9 e FEA model gave a stiffer result in thepositive part and softer one in the negative part for specimenBeam1 compared to the experimental result which may bedue to the slippage of the pedestal or the gap between loadinghead and specimen in the test e local material damagesobtained from FEA are also compared with test results andconcrete spalling and rebar fracture are shown in Figure 10From the qualitative comparison good agreement isachieved between experimental and FEA results not only onthe global behavior but also on the local material damagebehavior

Concrete crushing and spalling were predicted throughthe compression strain of concrete Priestley [21] suggested avalue of 0004 for cover concrete edge compressive crushing

10 Advances in Civil Engineering

strain and Jiang et al [23] proposed an equation to calculatethe conned concrete edge compression spalling strainwhich is equal to 0005 for test specimense concrete crack

width was predicted through the tensile strain of rebarPriestley [21] suggested a value of 001 for longitudinal rebartensile strain to control the residual crack width within

Stre

ss (M

Pa)

ndash5

0

5

10

15

20

25

30

35

40

0002 0004 0006 0008 00100000Strain

(a)

Stre

ss (M

Pa)

0

100

200

300

400

500

600

004 008 012 016000Strain

(b)

Figure 8 Uniaxial constitutive relationships of materials (a) Concrete (b) Rebar 12mm

Wm

res (

mm

)

Beam1Beam2Beam3

00

05

10

15

20

ndash002 000 002 004ndash004Rotation (rad)

(a)W

mre

s (m

m)

Beam1Beam4Beam5

00

05

10

15

20

ndash002 000 002 004ndash004Rotation (rad)

(b)

Wm

res (

mm

)

Beam2Beam6Beam7

00

05

10

15

20

ndash002 000 002 004ndash004Rotation (rad)

(c)

Figure 7 Maximum residual crack width of specimens (a) Eect of aspect ratio (b) Eect of ange-web ratio (c) Eect of steel ratio

Late

ral l

oad

(kN

)

FEATest

ndash1200

ndash800

ndash400

0

400

800

1200

ndash006 ndash003 000 003 006 009ndash009Rotation (rad)

(a)

Late

ral l

oad

(kN

)

FEATest

ndash1200

ndash800

ndash400

0

400

800

1200

ndash006 ndash003 000 003 006 009ndash009Rotation (rad)

(b)

Figure 9 Comparison of experimental and numerical skeleton curves (a) Specimen Beam1 (b) Specimen Beam5

Advances in Civil Engineering 11

10mm e chord rotations corresponding to differentconcrete damage states obtained from finite element analysiswere compared with the test result as shown in Table 5From the quantitative comparison for concrete damagedeformation finite element analysis can only provide astatistically consistent simulation result not specifically ac-curate simulation result for each specimen e mean ro-tation ratios between FEA and the test for the concreteresidual crack width equal to 1mm concrete crushing and

concrete spalling are 099 083 and 074 respectively If thecover concrete edge compression crushing strain is revisedto 0005 and confined concrete edge compression spallingstrain is revised to 00075 the mean rotation ratios betweenFEA and the test for concrete crushing and concrete spallingare 104 and 103 respectively

Steel flange tensile yielding and web principle tensileyielding were predicted directly through steel yielding strainrecorded in Table 2 e chord rotations corresponding to

Rebar fracture

PE max principalSNEG(fraction = ndash10)(avg 75)

+1454e ndash 01+1333e ndash 01+1212e ndash 01+1090e ndash 01+9693e ndash 02+8481e ndash 02+7269e ndash 02+6058e ndash 02+4846e ndash 02+3635e ndash 02+2423e ndash 02+1212e ndash 02+0000e + 00

(a)

Concrete spalling

PEEQ(avg 75)

+4683e ndash 02+4292e ndash 02+3902e ndash 02+3512e ndash 02+3122e ndash 02+2731e ndash 02+2341e ndash 02+1951e ndash 02+1561e ndash 02+1171e ndash 02+7804e ndash 03+3902e ndash 03+0000e + 00

(b)

Figure 10 Comparison of experimental and numerical damages (a) Rebar fracture of specimen Beam1 (b) Concrete spalling of specimenBeam1

Table 5 Comparison of chord rotations of specimens for different concrete damage states

Specimen numberResidual crack width lt1mm Concrete crushing Concrete spallingTest FEA FEAtest Test FEA FEAtest Test FEA FEAtest

Beam1 00084 00157 187 00238 00231 097 00403 00442 110Beam2 00116 00141 122 00192 00137 071 00385 00244 063Beam3 00150 00155 103 00139 00143 103 00378 00256 068Beam4 00261 00145 056 00233 00185 079 00416 00288 069Beam5 00200 00149 075 00179 00196 109 00346 00363 105Beam6 00187 00140 075 00237 00133 056 00485 00233 048Beam7 00190 00141 074 00201 00130 065 00430 00225 052

12 Advances in Civil Engineering

different steel yielding states obtained from finite elementanalysis were compared with the test result as shown inTable 6 e finite element analysis can provide a statisticallyconsistent simulation result and the mean rotation ratiosbetween FEA and the test for steel flange tensile yielding andsteel web principle tensile yielding are 123 and 108respectively

Rebar tensile yielding and rebar fracture were pre-dicted directly through rebar yielding strain and tensilestrain recorded in Table 2 Rebar buckling was predictedthrough confined concrete ultimate compressive strainwhich is calculated using equation suggested by Priestley[21] e chord rotations corresponding to different rebardamage states obtained from finite element analysis werecompared with the test result as shown in Table 7 efinite element analysis can provide a statistically consis-tent simulation result and the mean rotation ratios be-tween FEA and the test for rebar tensile yielding rebarbuckling and rebar fracture are 074 103 and 090respectively

43 Performance Index Limit Analysis e seismic per-formance of SRC coupling beams is affected by the ma-terial damage which is related to the material strain Onthe other hand the degradation of the load carrying ca-pacity of SRC coupling beams affects its seismic perfor-mance also Based on the study on the material damagestrain limits [21 23] and component strength degradationlimits [24] four performance levels are defined as shownin Table 8 Since there is a lack of test records of speci-mensrsquo deformation at damage states of concrete strainequal to 0002 or crack width equal to 2mm the chordrotation of specimens at different performance levels canonly be obtained through FEA Table 9 shows the chord

rotations of SRC coupling beam specimens at differentperformance levels and then the mean values wereadopted as the performance index limits which were0005 rad 0014 rad 0024 rad and 0047 rad for the fourperformance levels

5 Summary and Conclusions

Seven half-scale flexural-yielding SRC coupling beamspecimens designed according to Chinese approach weretested under cyclic loade influence of design parameterssuch as aspect ratio flange-web area ratio of encased steeland steel ratio on damage development hysteretic be-havior strength and maximum residual crack width werediscussed Finite element analysis was conducted forspecimens both global skeleton curves and local materialdamage were simulated simultaneously rough quanti-tative comparison finite element analysis can provide astatistically consistent simulation result for materialdamages for each specimen Some conclusions are drawnfrom this research

(1) All specimens failed in flexural mode e damagedevelopment was roughly the same and the typicaldamage states were recorded through the wholeloading process which can be used in assessing theseismic performance level of SRC coupling beams

(2) With the increase of aspect ratio the lateral loadcarrying capacity drops down significantly and themaximum residual crack width tends to be smallerWith the increase of flange-web area ratio of encasedsteel the hysteretic curve gets fuller e specimenwith intermediate flange-web area ratio has thelargest lateral load carrying capacity but smallestmaximum residual crack width With the increase of

Table 6 Comparison of chord rotations of specimens for different steel damage states

Specimen numberSteel flange yielding Steel web yielding

Test FEA FEAtest Test FEA FEAtestBeam1 00033 00059 179 00140 00124 089Beam2 00063 00053 084 00120 00116 097Beam3 00044 00061 139 00095 00108 114Beam4 00041 00051 124 00085 00105 124Beam5 00053 00056 106 00078 00098 126Beam6 00065 00057 088 00100 00115 115Beam7 00039 00056 144 00131 00120 092

Table 7 Comparison of chord rotations of specimens for different rebar damage states

Specimen numberRebar yielding Rebar buckling Rebar fracture

Test FEA FEAtest Test FEA FEAtest Test FEA FEAtestBeam1 00072 00059 082 00502 00777 155 00609 00562 092Beam2 00065 00054 083 00451 00426 094 00558 00502 090Beam3 00091 00060 066 00478 00446 093 00560 00571 102Beam4 00072 00056 078 00485 00527 109 00565 00504 089Beam5 00078 00054 069 00444 00526 118 00586 00596 102Beam6 00065 00056 086 00522 00403 077 00653 00490 075Beam7 00105 00057 054 00511 00390 076 00593 00493 083

Advances in Civil Engineering 13

steel ratio the lateral load carrying capacity increasessignificantly while the maximum residual crackwidth drops down

(3) e finite element model was benchmarkedthrough comparison with test results for bothglobal load-deformation curves and local materialdamages Both qualitative and quantitative com-parisons testify the accuracy of finite elementmodels e cover concrete edge compressionstrain and confined concrete edge compressionstrain were recommended to be 0005 and 00075respectively for accurately modeling concretecrushing and spalling Based on the damagecharacters and strength degradation four perfor-mance levels were defined and correspondingchord rotation limits were obtained through theverified numerical analysis

Data Availability

All the data in this paper are obtained from tests and nu-merical analysis and no other data in the literature are usedto support this study

Conflicts of Interest

e authors declare that there are no potential conflicts ofinterest with respect to the research authorship and pub-lication of this article

Acknowledgments

e financial support from the Program of Shanghai Aca-demic Research Leader (grant number 18XD1403900) andthe National Key Research and Development Program ofChina (grant number 2017YFC1500701) is gratefullyacknowledged

References

[1] S El-Tawil K A Harries P J Fortney B M Shahrooz andY Kurama ldquoSeismic design of hybrid coupled wall systemsstate of the artrdquo Journal of structural engineering vol 136no 7 pp 755ndash769 2010

[2] C-C Hung and W-T Lu ldquoA performance-based designmethod for coupled wall structuresrdquo Journal of EarthquakeEngineering vol 21 no 4 pp 579ndash603 2016

[3] C J Motter D C Fields J D Hooper et al ldquoSteel-reinforcedconcrete coupling beams I testingrdquo Journal of StructuralEngineering vol 143 no 3 article 04016191 2016

[4] B Gong and B M Shahrooz ldquoConcrete-steel compositecoupling beams I component testingrdquo Journal of StructuralEngineering vol 127 no 6 pp 625ndash631 2001

[5] B Gong and B M Shahrooz ldquoConcrete-steel compositecoupling beams II subassembly testing and design verifi-cationrdquo Journal of Structural Engineering vol 127 no 6pp 632ndash638 2001

[6] R K L Su and W Y Lam ldquoA unified design approach forplate-reinforced composite coupling beamsrdquo Journal ofConstructional Steel Research vol 65 no 3 pp 675ndash6862009

Table 8 Method of defining performance levels for SRC coupling beams

Performance level Damage descriptionPerformance criterion

Rebar or steel strain Concretestrain Load carrying capacity

Being basically intact ere are fine cracks in concrete while steel or rebaris not yielding εy 0002 mdash

Slight damage Concrete cover is not crushing and residual crackwidth is less than 1mm 0015 0005 mdash

Moderate damage Concrete cover is not spalling and residual crackwidth is less than 2mm 003 00075 95 Pmax

Severe damage Concrete core is not crushing and rebar or steel isnot fracturing εsu εcu 85 Pmax

Note εy is the yielding strain of steel or rebar εsu is the tensile strain of steel or rebar εcu is the ultimate strain of the concrete Pmax is the lateral load carryingcapacity of specimens

Table 9 Chord rotations of SRC coupling beams at different performance levels (rad)

Specimen numberPerformance level

Being basically intact Slight damage Moderate damage Severe damageBeam1 00055 00157 00264 00562Beam2 00053 00137 00212 00426Beam3 00060 00143 00235 00446Beam4 00051 00145 00239 00504Beam5 00054 00149 00257 00526Beam6 00051 00133 00228 00403Beam7 00050 00130 00228 00390

14 Advances in Civil Engineering

[7] C J Motter D C Fields J D Hooper et al ldquoSteel-reinforcedconcrete coupling beams II Modelingrdquo Journal of StructuralEngineering vol 143 no 3 article 04016192 2016

[8] Q Z Liang and X L Han ldquoe behavior of stiffening beamsand lintel beams under cyclic loadingrdquo Journal of South ChinaUniversity of Technology vol 23 no 1 pp 27ndash33 1995 inChinese

[9] H Jiang B Wang and X Lu ldquoExperimental study on damagebehavior of reinforced concrete shear walls subjected to cyclicloadsrdquo Journal of Earthquake Engineering vol 17 no 7pp 958ndash971 2013

[10] J Yue J Qian and D E Beskos ldquoA generalized multi-levelseismic damage model for RC framed structuresrdquo Soil Dy-namics and Earthquake Engineering vol 80 pp 25ndash39 2016

[11] JGJ138-2016 Code for Design of Composite Structures ChinaArchitecture amp Building Press Beijing China 2016

[12] R D Lequesne G J Parra-Montesinos and J K WightldquoSeismic behavior and detailing of high-performance fiber-reinforced concrete coupling beams and coupled wall sys-temsrdquo Journal of Structural Engineering vol 139 no 8pp 1362ndash1370 2012

[13] M Otieno H Beushausen and M Alexander ldquoTowardsincorporating the influence of cover cracking on steel cor-rosion in RC design codes the concept of performance-basedcrack width limitsrdquo Materials and Structures vol 45 no 12pp 1805ndash1816 2012

[14] SIMULIA Dassault Systems ABAQUS Analysis UserrsquosManual Version 616 SIMULIA Johnston RI USA 2016

[15] J C Goodnight M J Kowalsky and J M Nau ldquoEffect of loadhistory on performance limit states of circular bridge col-umnsrdquo Journal of Bridge Engineering vol 18 no 12pp 1383ndash1396 2013

[16] R T Ranf ldquoDamage accumulation in lightly confined rein-forced concrete bridge columnsrdquo PEER Report PacificEarthquake Engineering Research Center University ofCalifornia Berkeley CA USA 2006

[17] A Babazadeh R Burguentildeo and P F Silva ldquoUse of 3D finite-element models for predicting intermediate damage limitstates in RC bridge columnsrdquo Journal of Structural Engi-neering vol 141 no 10 article 04015012 2015

[18] J Moon CW Roeder andH-E Lee ldquoAnalytical modeling ofbending of circular concrete-filled steel tubesrdquo EngineeringStructures vol 42 no 12 pp 349ndash361 2012

[19] GB50010-2010 Code for Design of Concrete Structures ChinaArchitecture amp Building Press Beijing China 2010

[20] H Zhu M T Stephens and D E Lehman ldquoInelastic responseprediction of CFST columns and connections subjected tolateral loadingrdquo Journal of Constructional Steel Researchvol 132 pp 130ndash140 2017

[21] M J N Priestley ldquoPerformance based seismic designrdquo inProceedings of 12th World Conference on EarthquakeEngineering Auckland New Zealand January 2000

[22] Y Shi M Wang and Y Wang ldquoExperimental and consti-tutive model study of structural steel under cyclic loadingrdquoJournal of Constructional Steel Research vol 67 no 8pp 1185ndash1197 2011

[23] H Jiang X Lu and T Kubo ldquoDamage displacement esti-mation of flexure-dominant RC columnsrdquo Advances inStructural Engineering vol 13 no 2 pp 357ndash368 2010

[24] GB50011-2010 Code for Seismic Design of Buildings ChinaArchitecture amp Building Press Beijing China 2010

Advances in Civil Engineering 15

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of specimen Beam2 which means that the lateral loadcarrying capacity changes in inverse proportion with theaspect ratio and all specimens reached its exural strengthIn general the larger aspect ratio specimen tends to havesmaller lateral load carrying capacity at the individualdamage characteristic point Considering displacements ofthe individual damage state the initial damage states(concrete cracking steel tensile yielding and rebar tensileyielding) of specimen Beam3 with a aspect ratio of 5 tend tooccur later than those of specimen Beam1 with a aspect ratioof 2 which is consistent with the elastic chord rotationequation of the Timoshenko cantilever beam which is asfollows

θ ΔLML

3EI+M

GAL (6)

where M is the xed end section moment of the cantileverbeam L is the length of the cantilever beam E is the elasticmodulus I is the section moment inertia G is the shearmodulus and A is the eective shear section area When L islarger than

3EIGA

radicasymp 08h (h is the beam section height)

chord rotation θ increases with the increase of the beamlength under the same xed end moment e damage statessuch as steel web principle yielding concrete crushingconcrete spalling rebar buckling and rebar fracture of

specimen Beam3 tend to occur earlier than those of spec-imen Beam1 because specimen Beam3 has a relativelysmaller moment gradient at the plastic zone which causesexural damages of Beam3 to occur easily and smaller shearforce in Beam3 leads to smaller shear deformation also

For specimens Beam1 Beam4 and Beam5 with dierentange-web area ratios of encased steel specimen Beam4witha ange-web ratio of 05 has the largest lateral load carryingcapacity which is 11866 kN and is 33 larger than that ofspecimen Beam1 and 225 larger than that of specimenBeam5 which means that the specimen without the ange ofencased steel has a signicant smaller lateral load carryingcapacity e reason that specimen Beam4 with a smallerange-web ratio has slightly larger lateral load capacity thanspecimen Beam1 is that the encased steel consists of steelplates with dierent thicknesses and dierent yieldingstrengths and the average yielding strength of encased steelof specimen Beam4 is slightly larger than that of specimenBeam1 e calculated lateral load capacity (MnL) forspecimens Beam4 and Beam1 shown in Table 3 veried thisexplanation Considering the displacements of individualdamage states except the damage states like steel tensileyielding and rebar tensile yielding the other damage states ofspecimen Beam1 with a ange-web ratio of 1 tend to occurlater than those of specimen Beam5 with a ange-web ratio

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash60 ndash30 0 30 60

Lateral displacement (mm)

Concrete crackingSteel tensile yieldingRebar tensile yieldingSteel web yielding

Concrete crushingCover spalling Rebar buckling Rebar fracturing

ndash004 000 004 008ndash008Rotation (rad)

Late

ral l

oad

(kN

)

ndash1200

ndash800

ndash400

0

400

800

1200ndash60 ndash30 0 30 60

Lateral displacement (mm)

ndash004 000 004 008ndash008Rotation (rad)

(g)

Figure 6 Lateral load-chord rotation hysteretic curves and skeleton curves of specimens (a) Beam1 (b) Beam2 (c) Beam3 (d) Beam4(e) Beam5 (f ) Beam6 (g) Beam7

Table 4 Chord rotation of specimens at the individual damage characteristic point

Specimen number θc (rad) θsty (rad) θrty (rad) θswy (rad) θcc (rad) θcs (rad) θrb (rad) θrf (rad)Beam1 00012 00033 00072 00140 00238 00403 00502 00609Beam2 00013 00063 00065 00120 00192 00385 00451 00558Beam3 00014 00044 00091 00095 00139 00378 00478 00560Beam4 00009 00041 00072 00085 00233 00416 00485 00565Beam5 00008 00053 00078 00078 00179 00346 00444 00586Beam6 00010 00065 00065 00100 00237 00485 00522 00653Beam7 00013 00039 00105 00131 00201 00430 00511 00593Note θc θsty θrty θswy θcc θcs θrb and θrf represent the chord rotation of specimens at damage states of concrete cracking steel tensile yielding rebar tensileyielding steel web principle tensile yielding concrete crushing concrete spalling rebar buckling and rebar fracture respectively For Beam5 rebar tensileyielding and steel web principle tensile yielding occurred at the same time For Beam6 steel tensile yielding and rebar tensile yielding occurred at the sametime

Advances in Civil Engineering 9

of 0 is is because the flange steel enhances the com-pression behavior of the concrete and delays the concretecrushing and spalling In addition shear deformation ofspecimen Beam1 with smaller web steel is larger than that ofspecimen Beam5 at the same damage state

For specimens Beam2 Beam6 and Beam7 with theincrease of steel ratio from 5 to 83 the lateral loadcarrying capacity increases from 7503 kN to 9688 kN by292 which means that the lateral load carrying capacity ofSRC coupling beam was influenced largely by the steel ratioExcept initial damage states like concrete cracking rebartensile yielding and steel web principle tensile yielding theother damage states of specimen Beam6 with a steel ratio of67 tend to occur later than those of specimen Beam2 witha steel ratio of 5 and Beam7 with a steel ratio of 83

Concrete cover cracking influences the encased steelcorrosion initiation and the crack width influences thecorrosion propagation thus both influence the performanceof structures [13] e maximum residual crack width of allspecimens represented by Wmres was measured during thetest cycles before concrete cover crashed or spalled evariation of maximum residual crack width with the chordrotation is shown in Figure 7 Generally the maximumresidual crack width rises up with the increase of the chordrotation e maximum residual crack width of the speci-men at the same rotation tends to be smaller with the in-crease of the aspect ratio or steel ratio for the average value ofthat for both directions For specimens Beam1 Beam4 andBeam5 with different flange-web area ratios of encased steelBeam4 has the smallest maximum residual crack width whileBeam1 has the largest maximum residual crack width at thesame rotation

4 Numerical Analysis and Verification

41 Modeling ree-dimensional nonlinear finite elementmodels were developed to simulate the inelastic behavior oftested SRC coupling beam specimens using Abaqus [14] Notonly the global force-rotation behavior but also the localmaterial damage behavior during the test process includingconcrete (cracking crushing and spalling) steel yieldingand rebar (yielding buckling and fracture) was predictedthrough finite element analysis It has been reported [15ndash17]that material damage states ie spalling and yielding arenot dependent on the history of loading but are ratherclosely related to the maximum displacement that thestructure has experienced erefore a monotonic analysiswas sufficient for predicting damage deformation of flexure-yielding SRC coupling beams

Damaged plasticity model was used to simulate theconcrete inelastic behavior in SRC coupling beam specimensis model is applicable in the situation that the concrete is atlow confinement pressures (less than four to five times thelargest compressive stress that can be carried by the concretein uniaxial compression) which is suitable for SRC couplingbeams Moon et al [18] used this model to study the con-finement effect of steel tubes on the infilled concrete andBabazadeh et al [17] used this model to study the spalling ofthe concrete for RC bridge columnse uniaxial stress-strain

relationship for the concrete recommended in Chinese codeGB50010-2010 [19] was adopted here as shown in Figure 8(a)e compression strength of the concrete is 373MPa whichis the prismatic compression strength of concrete fck which iscalculated based on the conversion formula in Chinese code50010-2010 [19] and the tested cubic compression strength ofconcrete fcu is equal to 578MPa

Ductile damage plasticity model was used to simulate theencased steel and rebar inelastic behavior in SRC couplingbeam specimens is model offers a general capability forpredicting the onset of failure and a capability for modelingprogressive damage and failure of ductile metals Zhu et al[20] used this model to simulate the steel tearing of concrete-filled steel tube columns e strengthening stage of steeladopted a bilinear model hardening stiffness of which is 1of elastic stiffness and damage initiated at tensile strain anddamage evolution adopted a linear damage form Consid-ering the cyclic fatigue of longitudinal rebar under earth-quakes Priestley [21] suggested the tensile strain of thelongitudinal rebar to be reduced by 40 Shi et al [22]carried out the structural steel low cycle fatigue test andproved that the tensile strain of Q345B steel was reduced by203 and Q235B steel was reduced by 386 after cyclicloading e fracture strain was conservatively taken as twotimes tensile strain refer to the former test results euniaxial stress-strain relationship for the 12mm diameterrebar is shown in Figure 8(b)

Eight-node solid elements with reduced integration(C3D8R) were used for the concrete four-node shell ele-ments with reduced integration (S4R) were used for theencased steel and two-node linear displacement truss ele-ments were used for rebar A perfect bond was assumedbetween the steel rebar elements and the concrete parttherefore the truss elements and shell elements were em-bedded in the concrete instance using the lowastEMBEDDEDELEMENT option e bottom surface of the pedestal wasfixed against all degrees of freedom A reference point wasmodeled on the surface of the loading plate which wasconstrained with the surface of the loading plate using thelowastCOUPLING option available in the ABAQUS library

42 Analysis Results e global skeleton curves of all thespecimens obtained from the FEA are compared with theskeleton curves obtained from the test and two of them areshown in Figure 9 e FEA model gave a stiffer result in thepositive part and softer one in the negative part for specimenBeam1 compared to the experimental result which may bedue to the slippage of the pedestal or the gap between loadinghead and specimen in the test e local material damagesobtained from FEA are also compared with test results andconcrete spalling and rebar fracture are shown in Figure 10From the qualitative comparison good agreement isachieved between experimental and FEA results not only onthe global behavior but also on the local material damagebehavior

Concrete crushing and spalling were predicted throughthe compression strain of concrete Priestley [21] suggested avalue of 0004 for cover concrete edge compressive crushing

10 Advances in Civil Engineering

strain and Jiang et al [23] proposed an equation to calculatethe conned concrete edge compression spalling strainwhich is equal to 0005 for test specimense concrete crack

width was predicted through the tensile strain of rebarPriestley [21] suggested a value of 001 for longitudinal rebartensile strain to control the residual crack width within

Stre

ss (M

Pa)

ndash5

0

5

10

15

20

25

30

35

40

0002 0004 0006 0008 00100000Strain

(a)

Stre

ss (M

Pa)

0

100

200

300

400

500

600

004 008 012 016000Strain

(b)

Figure 8 Uniaxial constitutive relationships of materials (a) Concrete (b) Rebar 12mm

Wm

res (

mm

)

Beam1Beam2Beam3

00

05

10

15

20

ndash002 000 002 004ndash004Rotation (rad)

(a)W

mre

s (m

m)

Beam1Beam4Beam5

00

05

10

15

20

ndash002 000 002 004ndash004Rotation (rad)

(b)

Wm

res (

mm

)

Beam2Beam6Beam7

00

05

10

15

20

ndash002 000 002 004ndash004Rotation (rad)

(c)

Figure 7 Maximum residual crack width of specimens (a) Eect of aspect ratio (b) Eect of ange-web ratio (c) Eect of steel ratio

Late

ral l

oad

(kN

)

FEATest

ndash1200

ndash800

ndash400

0

400

800

1200

ndash006 ndash003 000 003 006 009ndash009Rotation (rad)

(a)

Late

ral l

oad

(kN

)

FEATest

ndash1200

ndash800

ndash400

0

400

800

1200

ndash006 ndash003 000 003 006 009ndash009Rotation (rad)

(b)

Figure 9 Comparison of experimental and numerical skeleton curves (a) Specimen Beam1 (b) Specimen Beam5

Advances in Civil Engineering 11

10mm e chord rotations corresponding to differentconcrete damage states obtained from finite element analysiswere compared with the test result as shown in Table 5From the quantitative comparison for concrete damagedeformation finite element analysis can only provide astatistically consistent simulation result not specifically ac-curate simulation result for each specimen e mean ro-tation ratios between FEA and the test for the concreteresidual crack width equal to 1mm concrete crushing and

concrete spalling are 099 083 and 074 respectively If thecover concrete edge compression crushing strain is revisedto 0005 and confined concrete edge compression spallingstrain is revised to 00075 the mean rotation ratios betweenFEA and the test for concrete crushing and concrete spallingare 104 and 103 respectively

Steel flange tensile yielding and web principle tensileyielding were predicted directly through steel yielding strainrecorded in Table 2 e chord rotations corresponding to

Rebar fracture

PE max principalSNEG(fraction = ndash10)(avg 75)

+1454e ndash 01+1333e ndash 01+1212e ndash 01+1090e ndash 01+9693e ndash 02+8481e ndash 02+7269e ndash 02+6058e ndash 02+4846e ndash 02+3635e ndash 02+2423e ndash 02+1212e ndash 02+0000e + 00

(a)

Concrete spalling

PEEQ(avg 75)

+4683e ndash 02+4292e ndash 02+3902e ndash 02+3512e ndash 02+3122e ndash 02+2731e ndash 02+2341e ndash 02+1951e ndash 02+1561e ndash 02+1171e ndash 02+7804e ndash 03+3902e ndash 03+0000e + 00

(b)

Figure 10 Comparison of experimental and numerical damages (a) Rebar fracture of specimen Beam1 (b) Concrete spalling of specimenBeam1

Table 5 Comparison of chord rotations of specimens for different concrete damage states

Specimen numberResidual crack width lt1mm Concrete crushing Concrete spallingTest FEA FEAtest Test FEA FEAtest Test FEA FEAtest

Beam1 00084 00157 187 00238 00231 097 00403 00442 110Beam2 00116 00141 122 00192 00137 071 00385 00244 063Beam3 00150 00155 103 00139 00143 103 00378 00256 068Beam4 00261 00145 056 00233 00185 079 00416 00288 069Beam5 00200 00149 075 00179 00196 109 00346 00363 105Beam6 00187 00140 075 00237 00133 056 00485 00233 048Beam7 00190 00141 074 00201 00130 065 00430 00225 052

12 Advances in Civil Engineering

different steel yielding states obtained from finite elementanalysis were compared with the test result as shown inTable 6 e finite element analysis can provide a statisticallyconsistent simulation result and the mean rotation ratiosbetween FEA and the test for steel flange tensile yielding andsteel web principle tensile yielding are 123 and 108respectively

Rebar tensile yielding and rebar fracture were pre-dicted directly through rebar yielding strain and tensilestrain recorded in Table 2 Rebar buckling was predictedthrough confined concrete ultimate compressive strainwhich is calculated using equation suggested by Priestley[21] e chord rotations corresponding to different rebardamage states obtained from finite element analysis werecompared with the test result as shown in Table 7 efinite element analysis can provide a statistically consis-tent simulation result and the mean rotation ratios be-tween FEA and the test for rebar tensile yielding rebarbuckling and rebar fracture are 074 103 and 090respectively

43 Performance Index Limit Analysis e seismic per-formance of SRC coupling beams is affected by the ma-terial damage which is related to the material strain Onthe other hand the degradation of the load carrying ca-pacity of SRC coupling beams affects its seismic perfor-mance also Based on the study on the material damagestrain limits [21 23] and component strength degradationlimits [24] four performance levels are defined as shownin Table 8 Since there is a lack of test records of speci-mensrsquo deformation at damage states of concrete strainequal to 0002 or crack width equal to 2mm the chordrotation of specimens at different performance levels canonly be obtained through FEA Table 9 shows the chord

rotations of SRC coupling beam specimens at differentperformance levels and then the mean values wereadopted as the performance index limits which were0005 rad 0014 rad 0024 rad and 0047 rad for the fourperformance levels

5 Summary and Conclusions

Seven half-scale flexural-yielding SRC coupling beamspecimens designed according to Chinese approach weretested under cyclic loade influence of design parameterssuch as aspect ratio flange-web area ratio of encased steeland steel ratio on damage development hysteretic be-havior strength and maximum residual crack width werediscussed Finite element analysis was conducted forspecimens both global skeleton curves and local materialdamage were simulated simultaneously rough quanti-tative comparison finite element analysis can provide astatistically consistent simulation result for materialdamages for each specimen Some conclusions are drawnfrom this research

(1) All specimens failed in flexural mode e damagedevelopment was roughly the same and the typicaldamage states were recorded through the wholeloading process which can be used in assessing theseismic performance level of SRC coupling beams

(2) With the increase of aspect ratio the lateral loadcarrying capacity drops down significantly and themaximum residual crack width tends to be smallerWith the increase of flange-web area ratio of encasedsteel the hysteretic curve gets fuller e specimenwith intermediate flange-web area ratio has thelargest lateral load carrying capacity but smallestmaximum residual crack width With the increase of

Table 6 Comparison of chord rotations of specimens for different steel damage states

Specimen numberSteel flange yielding Steel web yielding

Test FEA FEAtest Test FEA FEAtestBeam1 00033 00059 179 00140 00124 089Beam2 00063 00053 084 00120 00116 097Beam3 00044 00061 139 00095 00108 114Beam4 00041 00051 124 00085 00105 124Beam5 00053 00056 106 00078 00098 126Beam6 00065 00057 088 00100 00115 115Beam7 00039 00056 144 00131 00120 092

Table 7 Comparison of chord rotations of specimens for different rebar damage states

Specimen numberRebar yielding Rebar buckling Rebar fracture

Test FEA FEAtest Test FEA FEAtest Test FEA FEAtestBeam1 00072 00059 082 00502 00777 155 00609 00562 092Beam2 00065 00054 083 00451 00426 094 00558 00502 090Beam3 00091 00060 066 00478 00446 093 00560 00571 102Beam4 00072 00056 078 00485 00527 109 00565 00504 089Beam5 00078 00054 069 00444 00526 118 00586 00596 102Beam6 00065 00056 086 00522 00403 077 00653 00490 075Beam7 00105 00057 054 00511 00390 076 00593 00493 083

Advances in Civil Engineering 13

steel ratio the lateral load carrying capacity increasessignificantly while the maximum residual crackwidth drops down

(3) e finite element model was benchmarkedthrough comparison with test results for bothglobal load-deformation curves and local materialdamages Both qualitative and quantitative com-parisons testify the accuracy of finite elementmodels e cover concrete edge compressionstrain and confined concrete edge compressionstrain were recommended to be 0005 and 00075respectively for accurately modeling concretecrushing and spalling Based on the damagecharacters and strength degradation four perfor-mance levels were defined and correspondingchord rotation limits were obtained through theverified numerical analysis

Data Availability

All the data in this paper are obtained from tests and nu-merical analysis and no other data in the literature are usedto support this study

Conflicts of Interest

e authors declare that there are no potential conflicts ofinterest with respect to the research authorship and pub-lication of this article

Acknowledgments

e financial support from the Program of Shanghai Aca-demic Research Leader (grant number 18XD1403900) andthe National Key Research and Development Program ofChina (grant number 2017YFC1500701) is gratefullyacknowledged

References

[1] S El-Tawil K A Harries P J Fortney B M Shahrooz andY Kurama ldquoSeismic design of hybrid coupled wall systemsstate of the artrdquo Journal of structural engineering vol 136no 7 pp 755ndash769 2010

[2] C-C Hung and W-T Lu ldquoA performance-based designmethod for coupled wall structuresrdquo Journal of EarthquakeEngineering vol 21 no 4 pp 579ndash603 2016

[3] C J Motter D C Fields J D Hooper et al ldquoSteel-reinforcedconcrete coupling beams I testingrdquo Journal of StructuralEngineering vol 143 no 3 article 04016191 2016

[4] B Gong and B M Shahrooz ldquoConcrete-steel compositecoupling beams I component testingrdquo Journal of StructuralEngineering vol 127 no 6 pp 625ndash631 2001

[5] B Gong and B M Shahrooz ldquoConcrete-steel compositecoupling beams II subassembly testing and design verifi-cationrdquo Journal of Structural Engineering vol 127 no 6pp 632ndash638 2001

[6] R K L Su and W Y Lam ldquoA unified design approach forplate-reinforced composite coupling beamsrdquo Journal ofConstructional Steel Research vol 65 no 3 pp 675ndash6862009

Table 8 Method of defining performance levels for SRC coupling beams

Performance level Damage descriptionPerformance criterion

Rebar or steel strain Concretestrain Load carrying capacity

Being basically intact ere are fine cracks in concrete while steel or rebaris not yielding εy 0002 mdash

Slight damage Concrete cover is not crushing and residual crackwidth is less than 1mm 0015 0005 mdash

Moderate damage Concrete cover is not spalling and residual crackwidth is less than 2mm 003 00075 95 Pmax

Severe damage Concrete core is not crushing and rebar or steel isnot fracturing εsu εcu 85 Pmax

Note εy is the yielding strain of steel or rebar εsu is the tensile strain of steel or rebar εcu is the ultimate strain of the concrete Pmax is the lateral load carryingcapacity of specimens

Table 9 Chord rotations of SRC coupling beams at different performance levels (rad)

Specimen numberPerformance level

Being basically intact Slight damage Moderate damage Severe damageBeam1 00055 00157 00264 00562Beam2 00053 00137 00212 00426Beam3 00060 00143 00235 00446Beam4 00051 00145 00239 00504Beam5 00054 00149 00257 00526Beam6 00051 00133 00228 00403Beam7 00050 00130 00228 00390

14 Advances in Civil Engineering

[7] C J Motter D C Fields J D Hooper et al ldquoSteel-reinforcedconcrete coupling beams II Modelingrdquo Journal of StructuralEngineering vol 143 no 3 article 04016192 2016

[8] Q Z Liang and X L Han ldquoe behavior of stiffening beamsand lintel beams under cyclic loadingrdquo Journal of South ChinaUniversity of Technology vol 23 no 1 pp 27ndash33 1995 inChinese

[9] H Jiang B Wang and X Lu ldquoExperimental study on damagebehavior of reinforced concrete shear walls subjected to cyclicloadsrdquo Journal of Earthquake Engineering vol 17 no 7pp 958ndash971 2013

[10] J Yue J Qian and D E Beskos ldquoA generalized multi-levelseismic damage model for RC framed structuresrdquo Soil Dy-namics and Earthquake Engineering vol 80 pp 25ndash39 2016

[11] JGJ138-2016 Code for Design of Composite Structures ChinaArchitecture amp Building Press Beijing China 2016

[12] R D Lequesne G J Parra-Montesinos and J K WightldquoSeismic behavior and detailing of high-performance fiber-reinforced concrete coupling beams and coupled wall sys-temsrdquo Journal of Structural Engineering vol 139 no 8pp 1362ndash1370 2012

[13] M Otieno H Beushausen and M Alexander ldquoTowardsincorporating the influence of cover cracking on steel cor-rosion in RC design codes the concept of performance-basedcrack width limitsrdquo Materials and Structures vol 45 no 12pp 1805ndash1816 2012

[14] SIMULIA Dassault Systems ABAQUS Analysis UserrsquosManual Version 616 SIMULIA Johnston RI USA 2016

[15] J C Goodnight M J Kowalsky and J M Nau ldquoEffect of loadhistory on performance limit states of circular bridge col-umnsrdquo Journal of Bridge Engineering vol 18 no 12pp 1383ndash1396 2013

[16] R T Ranf ldquoDamage accumulation in lightly confined rein-forced concrete bridge columnsrdquo PEER Report PacificEarthquake Engineering Research Center University ofCalifornia Berkeley CA USA 2006

[17] A Babazadeh R Burguentildeo and P F Silva ldquoUse of 3D finite-element models for predicting intermediate damage limitstates in RC bridge columnsrdquo Journal of Structural Engi-neering vol 141 no 10 article 04015012 2015

[18] J Moon CW Roeder andH-E Lee ldquoAnalytical modeling ofbending of circular concrete-filled steel tubesrdquo EngineeringStructures vol 42 no 12 pp 349ndash361 2012

[19] GB50010-2010 Code for Design of Concrete Structures ChinaArchitecture amp Building Press Beijing China 2010

[20] H Zhu M T Stephens and D E Lehman ldquoInelastic responseprediction of CFST columns and connections subjected tolateral loadingrdquo Journal of Constructional Steel Researchvol 132 pp 130ndash140 2017

[21] M J N Priestley ldquoPerformance based seismic designrdquo inProceedings of 12th World Conference on EarthquakeEngineering Auckland New Zealand January 2000

[22] Y Shi M Wang and Y Wang ldquoExperimental and consti-tutive model study of structural steel under cyclic loadingrdquoJournal of Constructional Steel Research vol 67 no 8pp 1185ndash1197 2011

[23] H Jiang X Lu and T Kubo ldquoDamage displacement esti-mation of flexure-dominant RC columnsrdquo Advances inStructural Engineering vol 13 no 2 pp 357ndash368 2010

[24] GB50011-2010 Code for Seismic Design of Buildings ChinaArchitecture amp Building Press Beijing China 2010

Advances in Civil Engineering 15

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of 0 is is because the flange steel enhances the com-pression behavior of the concrete and delays the concretecrushing and spalling In addition shear deformation ofspecimen Beam1 with smaller web steel is larger than that ofspecimen Beam5 at the same damage state

For specimens Beam2 Beam6 and Beam7 with theincrease of steel ratio from 5 to 83 the lateral loadcarrying capacity increases from 7503 kN to 9688 kN by292 which means that the lateral load carrying capacity ofSRC coupling beam was influenced largely by the steel ratioExcept initial damage states like concrete cracking rebartensile yielding and steel web principle tensile yielding theother damage states of specimen Beam6 with a steel ratio of67 tend to occur later than those of specimen Beam2 witha steel ratio of 5 and Beam7 with a steel ratio of 83

Concrete cover cracking influences the encased steelcorrosion initiation and the crack width influences thecorrosion propagation thus both influence the performanceof structures [13] e maximum residual crack width of allspecimens represented by Wmres was measured during thetest cycles before concrete cover crashed or spalled evariation of maximum residual crack width with the chordrotation is shown in Figure 7 Generally the maximumresidual crack width rises up with the increase of the chordrotation e maximum residual crack width of the speci-men at the same rotation tends to be smaller with the in-crease of the aspect ratio or steel ratio for the average value ofthat for both directions For specimens Beam1 Beam4 andBeam5 with different flange-web area ratios of encased steelBeam4 has the smallest maximum residual crack width whileBeam1 has the largest maximum residual crack width at thesame rotation

4 Numerical Analysis and Verification

41 Modeling ree-dimensional nonlinear finite elementmodels were developed to simulate the inelastic behavior oftested SRC coupling beam specimens using Abaqus [14] Notonly the global force-rotation behavior but also the localmaterial damage behavior during the test process includingconcrete (cracking crushing and spalling) steel yieldingand rebar (yielding buckling and fracture) was predictedthrough finite element analysis It has been reported [15ndash17]that material damage states ie spalling and yielding arenot dependent on the history of loading but are ratherclosely related to the maximum displacement that thestructure has experienced erefore a monotonic analysiswas sufficient for predicting damage deformation of flexure-yielding SRC coupling beams

Damaged plasticity model was used to simulate theconcrete inelastic behavior in SRC coupling beam specimensis model is applicable in the situation that the concrete is atlow confinement pressures (less than four to five times thelargest compressive stress that can be carried by the concretein uniaxial compression) which is suitable for SRC couplingbeams Moon et al [18] used this model to study the con-finement effect of steel tubes on the infilled concrete andBabazadeh et al [17] used this model to study the spalling ofthe concrete for RC bridge columnse uniaxial stress-strain

relationship for the concrete recommended in Chinese codeGB50010-2010 [19] was adopted here as shown in Figure 8(a)e compression strength of the concrete is 373MPa whichis the prismatic compression strength of concrete fck which iscalculated based on the conversion formula in Chinese code50010-2010 [19] and the tested cubic compression strength ofconcrete fcu is equal to 578MPa

Ductile damage plasticity model was used to simulate theencased steel and rebar inelastic behavior in SRC couplingbeam specimens is model offers a general capability forpredicting the onset of failure and a capability for modelingprogressive damage and failure of ductile metals Zhu et al[20] used this model to simulate the steel tearing of concrete-filled steel tube columns e strengthening stage of steeladopted a bilinear model hardening stiffness of which is 1of elastic stiffness and damage initiated at tensile strain anddamage evolution adopted a linear damage form Consid-ering the cyclic fatigue of longitudinal rebar under earth-quakes Priestley [21] suggested the tensile strain of thelongitudinal rebar to be reduced by 40 Shi et al [22]carried out the structural steel low cycle fatigue test andproved that the tensile strain of Q345B steel was reduced by203 and Q235B steel was reduced by 386 after cyclicloading e fracture strain was conservatively taken as twotimes tensile strain refer to the former test results euniaxial stress-strain relationship for the 12mm diameterrebar is shown in Figure 8(b)

Eight-node solid elements with reduced integration(C3D8R) were used for the concrete four-node shell ele-ments with reduced integration (S4R) were used for theencased steel and two-node linear displacement truss ele-ments were used for rebar A perfect bond was assumedbetween the steel rebar elements and the concrete parttherefore the truss elements and shell elements were em-bedded in the concrete instance using the lowastEMBEDDEDELEMENT option e bottom surface of the pedestal wasfixed against all degrees of freedom A reference point wasmodeled on the surface of the loading plate which wasconstrained with the surface of the loading plate using thelowastCOUPLING option available in the ABAQUS library

42 Analysis Results e global skeleton curves of all thespecimens obtained from the FEA are compared with theskeleton curves obtained from the test and two of them areshown in Figure 9 e FEA model gave a stiffer result in thepositive part and softer one in the negative part for specimenBeam1 compared to the experimental result which may bedue to the slippage of the pedestal or the gap between loadinghead and specimen in the test e local material damagesobtained from FEA are also compared with test results andconcrete spalling and rebar fracture are shown in Figure 10From the qualitative comparison good agreement isachieved between experimental and FEA results not only onthe global behavior but also on the local material damagebehavior

Concrete crushing and spalling were predicted throughthe compression strain of concrete Priestley [21] suggested avalue of 0004 for cover concrete edge compressive crushing

10 Advances in Civil Engineering

strain and Jiang et al [23] proposed an equation to calculatethe conned concrete edge compression spalling strainwhich is equal to 0005 for test specimense concrete crack

width was predicted through the tensile strain of rebarPriestley [21] suggested a value of 001 for longitudinal rebartensile strain to control the residual crack width within

Stre

ss (M

Pa)

ndash5

0

5

10

15

20

25

30

35

40

0002 0004 0006 0008 00100000Strain

(a)

Stre

ss (M

Pa)

0

100

200

300

400

500

600

004 008 012 016000Strain

(b)

Figure 8 Uniaxial constitutive relationships of materials (a) Concrete (b) Rebar 12mm

Wm

res (

mm

)

Beam1Beam2Beam3

00

05

10

15

20

ndash002 000 002 004ndash004Rotation (rad)

(a)W

mre

s (m

m)

Beam1Beam4Beam5

00

05

10

15

20

ndash002 000 002 004ndash004Rotation (rad)

(b)

Wm

res (

mm

)

Beam2Beam6Beam7

00

05

10

15

20

ndash002 000 002 004ndash004Rotation (rad)

(c)

Figure 7 Maximum residual crack width of specimens (a) Eect of aspect ratio (b) Eect of ange-web ratio (c) Eect of steel ratio

Late

ral l

oad

(kN

)

FEATest

ndash1200

ndash800

ndash400

0

400

800

1200

ndash006 ndash003 000 003 006 009ndash009Rotation (rad)

(a)

Late

ral l

oad

(kN

)

FEATest

ndash1200

ndash800

ndash400

0

400

800

1200

ndash006 ndash003 000 003 006 009ndash009Rotation (rad)

(b)

Figure 9 Comparison of experimental and numerical skeleton curves (a) Specimen Beam1 (b) Specimen Beam5

Advances in Civil Engineering 11

10mm e chord rotations corresponding to differentconcrete damage states obtained from finite element analysiswere compared with the test result as shown in Table 5From the quantitative comparison for concrete damagedeformation finite element analysis can only provide astatistically consistent simulation result not specifically ac-curate simulation result for each specimen e mean ro-tation ratios between FEA and the test for the concreteresidual crack width equal to 1mm concrete crushing and

concrete spalling are 099 083 and 074 respectively If thecover concrete edge compression crushing strain is revisedto 0005 and confined concrete edge compression spallingstrain is revised to 00075 the mean rotation ratios betweenFEA and the test for concrete crushing and concrete spallingare 104 and 103 respectively

Steel flange tensile yielding and web principle tensileyielding were predicted directly through steel yielding strainrecorded in Table 2 e chord rotations corresponding to

Rebar fracture

PE max principalSNEG(fraction = ndash10)(avg 75)

+1454e ndash 01+1333e ndash 01+1212e ndash 01+1090e ndash 01+9693e ndash 02+8481e ndash 02+7269e ndash 02+6058e ndash 02+4846e ndash 02+3635e ndash 02+2423e ndash 02+1212e ndash 02+0000e + 00

(a)

Concrete spalling

PEEQ(avg 75)

+4683e ndash 02+4292e ndash 02+3902e ndash 02+3512e ndash 02+3122e ndash 02+2731e ndash 02+2341e ndash 02+1951e ndash 02+1561e ndash 02+1171e ndash 02+7804e ndash 03+3902e ndash 03+0000e + 00

(b)

Figure 10 Comparison of experimental and numerical damages (a) Rebar fracture of specimen Beam1 (b) Concrete spalling of specimenBeam1

Table 5 Comparison of chord rotations of specimens for different concrete damage states

Specimen numberResidual crack width lt1mm Concrete crushing Concrete spallingTest FEA FEAtest Test FEA FEAtest Test FEA FEAtest

Beam1 00084 00157 187 00238 00231 097 00403 00442 110Beam2 00116 00141 122 00192 00137 071 00385 00244 063Beam3 00150 00155 103 00139 00143 103 00378 00256 068Beam4 00261 00145 056 00233 00185 079 00416 00288 069Beam5 00200 00149 075 00179 00196 109 00346 00363 105Beam6 00187 00140 075 00237 00133 056 00485 00233 048Beam7 00190 00141 074 00201 00130 065 00430 00225 052

12 Advances in Civil Engineering

different steel yielding states obtained from finite elementanalysis were compared with the test result as shown inTable 6 e finite element analysis can provide a statisticallyconsistent simulation result and the mean rotation ratiosbetween FEA and the test for steel flange tensile yielding andsteel web principle tensile yielding are 123 and 108respectively

Rebar tensile yielding and rebar fracture were pre-dicted directly through rebar yielding strain and tensilestrain recorded in Table 2 Rebar buckling was predictedthrough confined concrete ultimate compressive strainwhich is calculated using equation suggested by Priestley[21] e chord rotations corresponding to different rebardamage states obtained from finite element analysis werecompared with the test result as shown in Table 7 efinite element analysis can provide a statistically consis-tent simulation result and the mean rotation ratios be-tween FEA and the test for rebar tensile yielding rebarbuckling and rebar fracture are 074 103 and 090respectively

43 Performance Index Limit Analysis e seismic per-formance of SRC coupling beams is affected by the ma-terial damage which is related to the material strain Onthe other hand the degradation of the load carrying ca-pacity of SRC coupling beams affects its seismic perfor-mance also Based on the study on the material damagestrain limits [21 23] and component strength degradationlimits [24] four performance levels are defined as shownin Table 8 Since there is a lack of test records of speci-mensrsquo deformation at damage states of concrete strainequal to 0002 or crack width equal to 2mm the chordrotation of specimens at different performance levels canonly be obtained through FEA Table 9 shows the chord

rotations of SRC coupling beam specimens at differentperformance levels and then the mean values wereadopted as the performance index limits which were0005 rad 0014 rad 0024 rad and 0047 rad for the fourperformance levels

5 Summary and Conclusions

Seven half-scale flexural-yielding SRC coupling beamspecimens designed according to Chinese approach weretested under cyclic loade influence of design parameterssuch as aspect ratio flange-web area ratio of encased steeland steel ratio on damage development hysteretic be-havior strength and maximum residual crack width werediscussed Finite element analysis was conducted forspecimens both global skeleton curves and local materialdamage were simulated simultaneously rough quanti-tative comparison finite element analysis can provide astatistically consistent simulation result for materialdamages for each specimen Some conclusions are drawnfrom this research

(1) All specimens failed in flexural mode e damagedevelopment was roughly the same and the typicaldamage states were recorded through the wholeloading process which can be used in assessing theseismic performance level of SRC coupling beams

(2) With the increase of aspect ratio the lateral loadcarrying capacity drops down significantly and themaximum residual crack width tends to be smallerWith the increase of flange-web area ratio of encasedsteel the hysteretic curve gets fuller e specimenwith intermediate flange-web area ratio has thelargest lateral load carrying capacity but smallestmaximum residual crack width With the increase of

Table 6 Comparison of chord rotations of specimens for different steel damage states

Specimen numberSteel flange yielding Steel web yielding

Test FEA FEAtest Test FEA FEAtestBeam1 00033 00059 179 00140 00124 089Beam2 00063 00053 084 00120 00116 097Beam3 00044 00061 139 00095 00108 114Beam4 00041 00051 124 00085 00105 124Beam5 00053 00056 106 00078 00098 126Beam6 00065 00057 088 00100 00115 115Beam7 00039 00056 144 00131 00120 092

Table 7 Comparison of chord rotations of specimens for different rebar damage states

Specimen numberRebar yielding Rebar buckling Rebar fracture

Test FEA FEAtest Test FEA FEAtest Test FEA FEAtestBeam1 00072 00059 082 00502 00777 155 00609 00562 092Beam2 00065 00054 083 00451 00426 094 00558 00502 090Beam3 00091 00060 066 00478 00446 093 00560 00571 102Beam4 00072 00056 078 00485 00527 109 00565 00504 089Beam5 00078 00054 069 00444 00526 118 00586 00596 102Beam6 00065 00056 086 00522 00403 077 00653 00490 075Beam7 00105 00057 054 00511 00390 076 00593 00493 083

Advances in Civil Engineering 13

steel ratio the lateral load carrying capacity increasessignificantly while the maximum residual crackwidth drops down

(3) e finite element model was benchmarkedthrough comparison with test results for bothglobal load-deformation curves and local materialdamages Both qualitative and quantitative com-parisons testify the accuracy of finite elementmodels e cover concrete edge compressionstrain and confined concrete edge compressionstrain were recommended to be 0005 and 00075respectively for accurately modeling concretecrushing and spalling Based on the damagecharacters and strength degradation four perfor-mance levels were defined and correspondingchord rotation limits were obtained through theverified numerical analysis

Data Availability

All the data in this paper are obtained from tests and nu-merical analysis and no other data in the literature are usedto support this study

Conflicts of Interest

e authors declare that there are no potential conflicts ofinterest with respect to the research authorship and pub-lication of this article

Acknowledgments

e financial support from the Program of Shanghai Aca-demic Research Leader (grant number 18XD1403900) andthe National Key Research and Development Program ofChina (grant number 2017YFC1500701) is gratefullyacknowledged

References

[1] S El-Tawil K A Harries P J Fortney B M Shahrooz andY Kurama ldquoSeismic design of hybrid coupled wall systemsstate of the artrdquo Journal of structural engineering vol 136no 7 pp 755ndash769 2010

[2] C-C Hung and W-T Lu ldquoA performance-based designmethod for coupled wall structuresrdquo Journal of EarthquakeEngineering vol 21 no 4 pp 579ndash603 2016

[3] C J Motter D C Fields J D Hooper et al ldquoSteel-reinforcedconcrete coupling beams I testingrdquo Journal of StructuralEngineering vol 143 no 3 article 04016191 2016

[4] B Gong and B M Shahrooz ldquoConcrete-steel compositecoupling beams I component testingrdquo Journal of StructuralEngineering vol 127 no 6 pp 625ndash631 2001

[5] B Gong and B M Shahrooz ldquoConcrete-steel compositecoupling beams II subassembly testing and design verifi-cationrdquo Journal of Structural Engineering vol 127 no 6pp 632ndash638 2001

[6] R K L Su and W Y Lam ldquoA unified design approach forplate-reinforced composite coupling beamsrdquo Journal ofConstructional Steel Research vol 65 no 3 pp 675ndash6862009

Table 8 Method of defining performance levels for SRC coupling beams

Performance level Damage descriptionPerformance criterion

Rebar or steel strain Concretestrain Load carrying capacity

Being basically intact ere are fine cracks in concrete while steel or rebaris not yielding εy 0002 mdash

Slight damage Concrete cover is not crushing and residual crackwidth is less than 1mm 0015 0005 mdash

Moderate damage Concrete cover is not spalling and residual crackwidth is less than 2mm 003 00075 95 Pmax

Severe damage Concrete core is not crushing and rebar or steel isnot fracturing εsu εcu 85 Pmax

Note εy is the yielding strain of steel or rebar εsu is the tensile strain of steel or rebar εcu is the ultimate strain of the concrete Pmax is the lateral load carryingcapacity of specimens

Table 9 Chord rotations of SRC coupling beams at different performance levels (rad)

Specimen numberPerformance level

Being basically intact Slight damage Moderate damage Severe damageBeam1 00055 00157 00264 00562Beam2 00053 00137 00212 00426Beam3 00060 00143 00235 00446Beam4 00051 00145 00239 00504Beam5 00054 00149 00257 00526Beam6 00051 00133 00228 00403Beam7 00050 00130 00228 00390

14 Advances in Civil Engineering

[7] C J Motter D C Fields J D Hooper et al ldquoSteel-reinforcedconcrete coupling beams II Modelingrdquo Journal of StructuralEngineering vol 143 no 3 article 04016192 2016

[8] Q Z Liang and X L Han ldquoe behavior of stiffening beamsand lintel beams under cyclic loadingrdquo Journal of South ChinaUniversity of Technology vol 23 no 1 pp 27ndash33 1995 inChinese

[9] H Jiang B Wang and X Lu ldquoExperimental study on damagebehavior of reinforced concrete shear walls subjected to cyclicloadsrdquo Journal of Earthquake Engineering vol 17 no 7pp 958ndash971 2013

[10] J Yue J Qian and D E Beskos ldquoA generalized multi-levelseismic damage model for RC framed structuresrdquo Soil Dy-namics and Earthquake Engineering vol 80 pp 25ndash39 2016

[11] JGJ138-2016 Code for Design of Composite Structures ChinaArchitecture amp Building Press Beijing China 2016

[12] R D Lequesne G J Parra-Montesinos and J K WightldquoSeismic behavior and detailing of high-performance fiber-reinforced concrete coupling beams and coupled wall sys-temsrdquo Journal of Structural Engineering vol 139 no 8pp 1362ndash1370 2012

[13] M Otieno H Beushausen and M Alexander ldquoTowardsincorporating the influence of cover cracking on steel cor-rosion in RC design codes the concept of performance-basedcrack width limitsrdquo Materials and Structures vol 45 no 12pp 1805ndash1816 2012

[14] SIMULIA Dassault Systems ABAQUS Analysis UserrsquosManual Version 616 SIMULIA Johnston RI USA 2016

[15] J C Goodnight M J Kowalsky and J M Nau ldquoEffect of loadhistory on performance limit states of circular bridge col-umnsrdquo Journal of Bridge Engineering vol 18 no 12pp 1383ndash1396 2013

[16] R T Ranf ldquoDamage accumulation in lightly confined rein-forced concrete bridge columnsrdquo PEER Report PacificEarthquake Engineering Research Center University ofCalifornia Berkeley CA USA 2006

[17] A Babazadeh R Burguentildeo and P F Silva ldquoUse of 3D finite-element models for predicting intermediate damage limitstates in RC bridge columnsrdquo Journal of Structural Engi-neering vol 141 no 10 article 04015012 2015

[18] J Moon CW Roeder andH-E Lee ldquoAnalytical modeling ofbending of circular concrete-filled steel tubesrdquo EngineeringStructures vol 42 no 12 pp 349ndash361 2012

[19] GB50010-2010 Code for Design of Concrete Structures ChinaArchitecture amp Building Press Beijing China 2010

[20] H Zhu M T Stephens and D E Lehman ldquoInelastic responseprediction of CFST columns and connections subjected tolateral loadingrdquo Journal of Constructional Steel Researchvol 132 pp 130ndash140 2017

[21] M J N Priestley ldquoPerformance based seismic designrdquo inProceedings of 12th World Conference on EarthquakeEngineering Auckland New Zealand January 2000

[22] Y Shi M Wang and Y Wang ldquoExperimental and consti-tutive model study of structural steel under cyclic loadingrdquoJournal of Constructional Steel Research vol 67 no 8pp 1185ndash1197 2011

[23] H Jiang X Lu and T Kubo ldquoDamage displacement esti-mation of flexure-dominant RC columnsrdquo Advances inStructural Engineering vol 13 no 2 pp 357ndash368 2010

[24] GB50011-2010 Code for Seismic Design of Buildings ChinaArchitecture amp Building Press Beijing China 2010

Advances in Civil Engineering 15

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

strain and Jiang et al [23] proposed an equation to calculatethe conned concrete edge compression spalling strainwhich is equal to 0005 for test specimense concrete crack

width was predicted through the tensile strain of rebarPriestley [21] suggested a value of 001 for longitudinal rebartensile strain to control the residual crack width within

Stre

ss (M

Pa)

ndash5

0

5

10

15

20

25

30

35

40

0002 0004 0006 0008 00100000Strain

(a)

Stre

ss (M

Pa)

0

100

200

300

400

500

600

004 008 012 016000Strain

(b)

Figure 8 Uniaxial constitutive relationships of materials (a) Concrete (b) Rebar 12mm

Wm

res (

mm

)

Beam1Beam2Beam3

00

05

10

15

20

ndash002 000 002 004ndash004Rotation (rad)

(a)W

mre

s (m

m)

Beam1Beam4Beam5

00

05

10

15

20

ndash002 000 002 004ndash004Rotation (rad)

(b)

Wm

res (

mm

)

Beam2Beam6Beam7

00

05

10

15

20

ndash002 000 002 004ndash004Rotation (rad)

(c)

Figure 7 Maximum residual crack width of specimens (a) Eect of aspect ratio (b) Eect of ange-web ratio (c) Eect of steel ratio

Late

ral l

oad

(kN

)

FEATest

ndash1200

ndash800

ndash400

0

400

800

1200

ndash006 ndash003 000 003 006 009ndash009Rotation (rad)

(a)

Late

ral l

oad

(kN

)

FEATest

ndash1200

ndash800

ndash400

0

400

800

1200

ndash006 ndash003 000 003 006 009ndash009Rotation (rad)

(b)

Figure 9 Comparison of experimental and numerical skeleton curves (a) Specimen Beam1 (b) Specimen Beam5

Advances in Civil Engineering 11

10mm e chord rotations corresponding to differentconcrete damage states obtained from finite element analysiswere compared with the test result as shown in Table 5From the quantitative comparison for concrete damagedeformation finite element analysis can only provide astatistically consistent simulation result not specifically ac-curate simulation result for each specimen e mean ro-tation ratios between FEA and the test for the concreteresidual crack width equal to 1mm concrete crushing and

concrete spalling are 099 083 and 074 respectively If thecover concrete edge compression crushing strain is revisedto 0005 and confined concrete edge compression spallingstrain is revised to 00075 the mean rotation ratios betweenFEA and the test for concrete crushing and concrete spallingare 104 and 103 respectively

Steel flange tensile yielding and web principle tensileyielding were predicted directly through steel yielding strainrecorded in Table 2 e chord rotations corresponding to

Rebar fracture

PE max principalSNEG(fraction = ndash10)(avg 75)

+1454e ndash 01+1333e ndash 01+1212e ndash 01+1090e ndash 01+9693e ndash 02+8481e ndash 02+7269e ndash 02+6058e ndash 02+4846e ndash 02+3635e ndash 02+2423e ndash 02+1212e ndash 02+0000e + 00

(a)

Concrete spalling

PEEQ(avg 75)

+4683e ndash 02+4292e ndash 02+3902e ndash 02+3512e ndash 02+3122e ndash 02+2731e ndash 02+2341e ndash 02+1951e ndash 02+1561e ndash 02+1171e ndash 02+7804e ndash 03+3902e ndash 03+0000e + 00

(b)

Figure 10 Comparison of experimental and numerical damages (a) Rebar fracture of specimen Beam1 (b) Concrete spalling of specimenBeam1

Table 5 Comparison of chord rotations of specimens for different concrete damage states

Specimen numberResidual crack width lt1mm Concrete crushing Concrete spallingTest FEA FEAtest Test FEA FEAtest Test FEA FEAtest

Beam1 00084 00157 187 00238 00231 097 00403 00442 110Beam2 00116 00141 122 00192 00137 071 00385 00244 063Beam3 00150 00155 103 00139 00143 103 00378 00256 068Beam4 00261 00145 056 00233 00185 079 00416 00288 069Beam5 00200 00149 075 00179 00196 109 00346 00363 105Beam6 00187 00140 075 00237 00133 056 00485 00233 048Beam7 00190 00141 074 00201 00130 065 00430 00225 052

12 Advances in Civil Engineering

different steel yielding states obtained from finite elementanalysis were compared with the test result as shown inTable 6 e finite element analysis can provide a statisticallyconsistent simulation result and the mean rotation ratiosbetween FEA and the test for steel flange tensile yielding andsteel web principle tensile yielding are 123 and 108respectively

Rebar tensile yielding and rebar fracture were pre-dicted directly through rebar yielding strain and tensilestrain recorded in Table 2 Rebar buckling was predictedthrough confined concrete ultimate compressive strainwhich is calculated using equation suggested by Priestley[21] e chord rotations corresponding to different rebardamage states obtained from finite element analysis werecompared with the test result as shown in Table 7 efinite element analysis can provide a statistically consis-tent simulation result and the mean rotation ratios be-tween FEA and the test for rebar tensile yielding rebarbuckling and rebar fracture are 074 103 and 090respectively

43 Performance Index Limit Analysis e seismic per-formance of SRC coupling beams is affected by the ma-terial damage which is related to the material strain Onthe other hand the degradation of the load carrying ca-pacity of SRC coupling beams affects its seismic perfor-mance also Based on the study on the material damagestrain limits [21 23] and component strength degradationlimits [24] four performance levels are defined as shownin Table 8 Since there is a lack of test records of speci-mensrsquo deformation at damage states of concrete strainequal to 0002 or crack width equal to 2mm the chordrotation of specimens at different performance levels canonly be obtained through FEA Table 9 shows the chord

rotations of SRC coupling beam specimens at differentperformance levels and then the mean values wereadopted as the performance index limits which were0005 rad 0014 rad 0024 rad and 0047 rad for the fourperformance levels

5 Summary and Conclusions

Seven half-scale flexural-yielding SRC coupling beamspecimens designed according to Chinese approach weretested under cyclic loade influence of design parameterssuch as aspect ratio flange-web area ratio of encased steeland steel ratio on damage development hysteretic be-havior strength and maximum residual crack width werediscussed Finite element analysis was conducted forspecimens both global skeleton curves and local materialdamage were simulated simultaneously rough quanti-tative comparison finite element analysis can provide astatistically consistent simulation result for materialdamages for each specimen Some conclusions are drawnfrom this research

(1) All specimens failed in flexural mode e damagedevelopment was roughly the same and the typicaldamage states were recorded through the wholeloading process which can be used in assessing theseismic performance level of SRC coupling beams

(2) With the increase of aspect ratio the lateral loadcarrying capacity drops down significantly and themaximum residual crack width tends to be smallerWith the increase of flange-web area ratio of encasedsteel the hysteretic curve gets fuller e specimenwith intermediate flange-web area ratio has thelargest lateral load carrying capacity but smallestmaximum residual crack width With the increase of

Table 6 Comparison of chord rotations of specimens for different steel damage states

Specimen numberSteel flange yielding Steel web yielding

Test FEA FEAtest Test FEA FEAtestBeam1 00033 00059 179 00140 00124 089Beam2 00063 00053 084 00120 00116 097Beam3 00044 00061 139 00095 00108 114Beam4 00041 00051 124 00085 00105 124Beam5 00053 00056 106 00078 00098 126Beam6 00065 00057 088 00100 00115 115Beam7 00039 00056 144 00131 00120 092

Table 7 Comparison of chord rotations of specimens for different rebar damage states

Specimen numberRebar yielding Rebar buckling Rebar fracture

Test FEA FEAtest Test FEA FEAtest Test FEA FEAtestBeam1 00072 00059 082 00502 00777 155 00609 00562 092Beam2 00065 00054 083 00451 00426 094 00558 00502 090Beam3 00091 00060 066 00478 00446 093 00560 00571 102Beam4 00072 00056 078 00485 00527 109 00565 00504 089Beam5 00078 00054 069 00444 00526 118 00586 00596 102Beam6 00065 00056 086 00522 00403 077 00653 00490 075Beam7 00105 00057 054 00511 00390 076 00593 00493 083

Advances in Civil Engineering 13

steel ratio the lateral load carrying capacity increasessignificantly while the maximum residual crackwidth drops down

(3) e finite element model was benchmarkedthrough comparison with test results for bothglobal load-deformation curves and local materialdamages Both qualitative and quantitative com-parisons testify the accuracy of finite elementmodels e cover concrete edge compressionstrain and confined concrete edge compressionstrain were recommended to be 0005 and 00075respectively for accurately modeling concretecrushing and spalling Based on the damagecharacters and strength degradation four perfor-mance levels were defined and correspondingchord rotation limits were obtained through theverified numerical analysis

Data Availability

All the data in this paper are obtained from tests and nu-merical analysis and no other data in the literature are usedto support this study

Conflicts of Interest

e authors declare that there are no potential conflicts ofinterest with respect to the research authorship and pub-lication of this article

Acknowledgments

e financial support from the Program of Shanghai Aca-demic Research Leader (grant number 18XD1403900) andthe National Key Research and Development Program ofChina (grant number 2017YFC1500701) is gratefullyacknowledged

References

[1] S El-Tawil K A Harries P J Fortney B M Shahrooz andY Kurama ldquoSeismic design of hybrid coupled wall systemsstate of the artrdquo Journal of structural engineering vol 136no 7 pp 755ndash769 2010

[2] C-C Hung and W-T Lu ldquoA performance-based designmethod for coupled wall structuresrdquo Journal of EarthquakeEngineering vol 21 no 4 pp 579ndash603 2016

[3] C J Motter D C Fields J D Hooper et al ldquoSteel-reinforcedconcrete coupling beams I testingrdquo Journal of StructuralEngineering vol 143 no 3 article 04016191 2016

[4] B Gong and B M Shahrooz ldquoConcrete-steel compositecoupling beams I component testingrdquo Journal of StructuralEngineering vol 127 no 6 pp 625ndash631 2001

[5] B Gong and B M Shahrooz ldquoConcrete-steel compositecoupling beams II subassembly testing and design verifi-cationrdquo Journal of Structural Engineering vol 127 no 6pp 632ndash638 2001

[6] R K L Su and W Y Lam ldquoA unified design approach forplate-reinforced composite coupling beamsrdquo Journal ofConstructional Steel Research vol 65 no 3 pp 675ndash6862009

Table 8 Method of defining performance levels for SRC coupling beams

Performance level Damage descriptionPerformance criterion

Rebar or steel strain Concretestrain Load carrying capacity

Being basically intact ere are fine cracks in concrete while steel or rebaris not yielding εy 0002 mdash

Slight damage Concrete cover is not crushing and residual crackwidth is less than 1mm 0015 0005 mdash

Moderate damage Concrete cover is not spalling and residual crackwidth is less than 2mm 003 00075 95 Pmax

Severe damage Concrete core is not crushing and rebar or steel isnot fracturing εsu εcu 85 Pmax

Note εy is the yielding strain of steel or rebar εsu is the tensile strain of steel or rebar εcu is the ultimate strain of the concrete Pmax is the lateral load carryingcapacity of specimens

Table 9 Chord rotations of SRC coupling beams at different performance levels (rad)

Specimen numberPerformance level

Being basically intact Slight damage Moderate damage Severe damageBeam1 00055 00157 00264 00562Beam2 00053 00137 00212 00426Beam3 00060 00143 00235 00446Beam4 00051 00145 00239 00504Beam5 00054 00149 00257 00526Beam6 00051 00133 00228 00403Beam7 00050 00130 00228 00390

14 Advances in Civil Engineering

[7] C J Motter D C Fields J D Hooper et al ldquoSteel-reinforcedconcrete coupling beams II Modelingrdquo Journal of StructuralEngineering vol 143 no 3 article 04016192 2016

[8] Q Z Liang and X L Han ldquoe behavior of stiffening beamsand lintel beams under cyclic loadingrdquo Journal of South ChinaUniversity of Technology vol 23 no 1 pp 27ndash33 1995 inChinese

[9] H Jiang B Wang and X Lu ldquoExperimental study on damagebehavior of reinforced concrete shear walls subjected to cyclicloadsrdquo Journal of Earthquake Engineering vol 17 no 7pp 958ndash971 2013

[10] J Yue J Qian and D E Beskos ldquoA generalized multi-levelseismic damage model for RC framed structuresrdquo Soil Dy-namics and Earthquake Engineering vol 80 pp 25ndash39 2016

[11] JGJ138-2016 Code for Design of Composite Structures ChinaArchitecture amp Building Press Beijing China 2016

[12] R D Lequesne G J Parra-Montesinos and J K WightldquoSeismic behavior and detailing of high-performance fiber-reinforced concrete coupling beams and coupled wall sys-temsrdquo Journal of Structural Engineering vol 139 no 8pp 1362ndash1370 2012

[13] M Otieno H Beushausen and M Alexander ldquoTowardsincorporating the influence of cover cracking on steel cor-rosion in RC design codes the concept of performance-basedcrack width limitsrdquo Materials and Structures vol 45 no 12pp 1805ndash1816 2012

[14] SIMULIA Dassault Systems ABAQUS Analysis UserrsquosManual Version 616 SIMULIA Johnston RI USA 2016

[15] J C Goodnight M J Kowalsky and J M Nau ldquoEffect of loadhistory on performance limit states of circular bridge col-umnsrdquo Journal of Bridge Engineering vol 18 no 12pp 1383ndash1396 2013

[16] R T Ranf ldquoDamage accumulation in lightly confined rein-forced concrete bridge columnsrdquo PEER Report PacificEarthquake Engineering Research Center University ofCalifornia Berkeley CA USA 2006

[17] A Babazadeh R Burguentildeo and P F Silva ldquoUse of 3D finite-element models for predicting intermediate damage limitstates in RC bridge columnsrdquo Journal of Structural Engi-neering vol 141 no 10 article 04015012 2015

[18] J Moon CW Roeder andH-E Lee ldquoAnalytical modeling ofbending of circular concrete-filled steel tubesrdquo EngineeringStructures vol 42 no 12 pp 349ndash361 2012

[19] GB50010-2010 Code for Design of Concrete Structures ChinaArchitecture amp Building Press Beijing China 2010

[20] H Zhu M T Stephens and D E Lehman ldquoInelastic responseprediction of CFST columns and connections subjected tolateral loadingrdquo Journal of Constructional Steel Researchvol 132 pp 130ndash140 2017

[21] M J N Priestley ldquoPerformance based seismic designrdquo inProceedings of 12th World Conference on EarthquakeEngineering Auckland New Zealand January 2000

[22] Y Shi M Wang and Y Wang ldquoExperimental and consti-tutive model study of structural steel under cyclic loadingrdquoJournal of Constructional Steel Research vol 67 no 8pp 1185ndash1197 2011

[23] H Jiang X Lu and T Kubo ldquoDamage displacement esti-mation of flexure-dominant RC columnsrdquo Advances inStructural Engineering vol 13 no 2 pp 357ndash368 2010

[24] GB50011-2010 Code for Seismic Design of Buildings ChinaArchitecture amp Building Press Beijing China 2010

Advances in Civil Engineering 15

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

10mm e chord rotations corresponding to differentconcrete damage states obtained from finite element analysiswere compared with the test result as shown in Table 5From the quantitative comparison for concrete damagedeformation finite element analysis can only provide astatistically consistent simulation result not specifically ac-curate simulation result for each specimen e mean ro-tation ratios between FEA and the test for the concreteresidual crack width equal to 1mm concrete crushing and

concrete spalling are 099 083 and 074 respectively If thecover concrete edge compression crushing strain is revisedto 0005 and confined concrete edge compression spallingstrain is revised to 00075 the mean rotation ratios betweenFEA and the test for concrete crushing and concrete spallingare 104 and 103 respectively

Steel flange tensile yielding and web principle tensileyielding were predicted directly through steel yielding strainrecorded in Table 2 e chord rotations corresponding to

Rebar fracture

PE max principalSNEG(fraction = ndash10)(avg 75)

+1454e ndash 01+1333e ndash 01+1212e ndash 01+1090e ndash 01+9693e ndash 02+8481e ndash 02+7269e ndash 02+6058e ndash 02+4846e ndash 02+3635e ndash 02+2423e ndash 02+1212e ndash 02+0000e + 00

(a)

Concrete spalling

PEEQ(avg 75)

+4683e ndash 02+4292e ndash 02+3902e ndash 02+3512e ndash 02+3122e ndash 02+2731e ndash 02+2341e ndash 02+1951e ndash 02+1561e ndash 02+1171e ndash 02+7804e ndash 03+3902e ndash 03+0000e + 00

(b)

Figure 10 Comparison of experimental and numerical damages (a) Rebar fracture of specimen Beam1 (b) Concrete spalling of specimenBeam1

Table 5 Comparison of chord rotations of specimens for different concrete damage states

Specimen numberResidual crack width lt1mm Concrete crushing Concrete spallingTest FEA FEAtest Test FEA FEAtest Test FEA FEAtest

Beam1 00084 00157 187 00238 00231 097 00403 00442 110Beam2 00116 00141 122 00192 00137 071 00385 00244 063Beam3 00150 00155 103 00139 00143 103 00378 00256 068Beam4 00261 00145 056 00233 00185 079 00416 00288 069Beam5 00200 00149 075 00179 00196 109 00346 00363 105Beam6 00187 00140 075 00237 00133 056 00485 00233 048Beam7 00190 00141 074 00201 00130 065 00430 00225 052

12 Advances in Civil Engineering

different steel yielding states obtained from finite elementanalysis were compared with the test result as shown inTable 6 e finite element analysis can provide a statisticallyconsistent simulation result and the mean rotation ratiosbetween FEA and the test for steel flange tensile yielding andsteel web principle tensile yielding are 123 and 108respectively

Rebar tensile yielding and rebar fracture were pre-dicted directly through rebar yielding strain and tensilestrain recorded in Table 2 Rebar buckling was predictedthrough confined concrete ultimate compressive strainwhich is calculated using equation suggested by Priestley[21] e chord rotations corresponding to different rebardamage states obtained from finite element analysis werecompared with the test result as shown in Table 7 efinite element analysis can provide a statistically consis-tent simulation result and the mean rotation ratios be-tween FEA and the test for rebar tensile yielding rebarbuckling and rebar fracture are 074 103 and 090respectively

43 Performance Index Limit Analysis e seismic per-formance of SRC coupling beams is affected by the ma-terial damage which is related to the material strain Onthe other hand the degradation of the load carrying ca-pacity of SRC coupling beams affects its seismic perfor-mance also Based on the study on the material damagestrain limits [21 23] and component strength degradationlimits [24] four performance levels are defined as shownin Table 8 Since there is a lack of test records of speci-mensrsquo deformation at damage states of concrete strainequal to 0002 or crack width equal to 2mm the chordrotation of specimens at different performance levels canonly be obtained through FEA Table 9 shows the chord

rotations of SRC coupling beam specimens at differentperformance levels and then the mean values wereadopted as the performance index limits which were0005 rad 0014 rad 0024 rad and 0047 rad for the fourperformance levels

5 Summary and Conclusions

Seven half-scale flexural-yielding SRC coupling beamspecimens designed according to Chinese approach weretested under cyclic loade influence of design parameterssuch as aspect ratio flange-web area ratio of encased steeland steel ratio on damage development hysteretic be-havior strength and maximum residual crack width werediscussed Finite element analysis was conducted forspecimens both global skeleton curves and local materialdamage were simulated simultaneously rough quanti-tative comparison finite element analysis can provide astatistically consistent simulation result for materialdamages for each specimen Some conclusions are drawnfrom this research

(1) All specimens failed in flexural mode e damagedevelopment was roughly the same and the typicaldamage states were recorded through the wholeloading process which can be used in assessing theseismic performance level of SRC coupling beams

(2) With the increase of aspect ratio the lateral loadcarrying capacity drops down significantly and themaximum residual crack width tends to be smallerWith the increase of flange-web area ratio of encasedsteel the hysteretic curve gets fuller e specimenwith intermediate flange-web area ratio has thelargest lateral load carrying capacity but smallestmaximum residual crack width With the increase of

Table 6 Comparison of chord rotations of specimens for different steel damage states

Specimen numberSteel flange yielding Steel web yielding

Test FEA FEAtest Test FEA FEAtestBeam1 00033 00059 179 00140 00124 089Beam2 00063 00053 084 00120 00116 097Beam3 00044 00061 139 00095 00108 114Beam4 00041 00051 124 00085 00105 124Beam5 00053 00056 106 00078 00098 126Beam6 00065 00057 088 00100 00115 115Beam7 00039 00056 144 00131 00120 092

Table 7 Comparison of chord rotations of specimens for different rebar damage states

Specimen numberRebar yielding Rebar buckling Rebar fracture

Test FEA FEAtest Test FEA FEAtest Test FEA FEAtestBeam1 00072 00059 082 00502 00777 155 00609 00562 092Beam2 00065 00054 083 00451 00426 094 00558 00502 090Beam3 00091 00060 066 00478 00446 093 00560 00571 102Beam4 00072 00056 078 00485 00527 109 00565 00504 089Beam5 00078 00054 069 00444 00526 118 00586 00596 102Beam6 00065 00056 086 00522 00403 077 00653 00490 075Beam7 00105 00057 054 00511 00390 076 00593 00493 083

Advances in Civil Engineering 13

steel ratio the lateral load carrying capacity increasessignificantly while the maximum residual crackwidth drops down

(3) e finite element model was benchmarkedthrough comparison with test results for bothglobal load-deformation curves and local materialdamages Both qualitative and quantitative com-parisons testify the accuracy of finite elementmodels e cover concrete edge compressionstrain and confined concrete edge compressionstrain were recommended to be 0005 and 00075respectively for accurately modeling concretecrushing and spalling Based on the damagecharacters and strength degradation four perfor-mance levels were defined and correspondingchord rotation limits were obtained through theverified numerical analysis

Data Availability

All the data in this paper are obtained from tests and nu-merical analysis and no other data in the literature are usedto support this study

Conflicts of Interest

e authors declare that there are no potential conflicts ofinterest with respect to the research authorship and pub-lication of this article

Acknowledgments

e financial support from the Program of Shanghai Aca-demic Research Leader (grant number 18XD1403900) andthe National Key Research and Development Program ofChina (grant number 2017YFC1500701) is gratefullyacknowledged

References

[1] S El-Tawil K A Harries P J Fortney B M Shahrooz andY Kurama ldquoSeismic design of hybrid coupled wall systemsstate of the artrdquo Journal of structural engineering vol 136no 7 pp 755ndash769 2010

[2] C-C Hung and W-T Lu ldquoA performance-based designmethod for coupled wall structuresrdquo Journal of EarthquakeEngineering vol 21 no 4 pp 579ndash603 2016

[3] C J Motter D C Fields J D Hooper et al ldquoSteel-reinforcedconcrete coupling beams I testingrdquo Journal of StructuralEngineering vol 143 no 3 article 04016191 2016

[4] B Gong and B M Shahrooz ldquoConcrete-steel compositecoupling beams I component testingrdquo Journal of StructuralEngineering vol 127 no 6 pp 625ndash631 2001

[5] B Gong and B M Shahrooz ldquoConcrete-steel compositecoupling beams II subassembly testing and design verifi-cationrdquo Journal of Structural Engineering vol 127 no 6pp 632ndash638 2001

[6] R K L Su and W Y Lam ldquoA unified design approach forplate-reinforced composite coupling beamsrdquo Journal ofConstructional Steel Research vol 65 no 3 pp 675ndash6862009

Table 8 Method of defining performance levels for SRC coupling beams

Performance level Damage descriptionPerformance criterion

Rebar or steel strain Concretestrain Load carrying capacity

Being basically intact ere are fine cracks in concrete while steel or rebaris not yielding εy 0002 mdash

Slight damage Concrete cover is not crushing and residual crackwidth is less than 1mm 0015 0005 mdash

Moderate damage Concrete cover is not spalling and residual crackwidth is less than 2mm 003 00075 95 Pmax

Severe damage Concrete core is not crushing and rebar or steel isnot fracturing εsu εcu 85 Pmax

Note εy is the yielding strain of steel or rebar εsu is the tensile strain of steel or rebar εcu is the ultimate strain of the concrete Pmax is the lateral load carryingcapacity of specimens

Table 9 Chord rotations of SRC coupling beams at different performance levels (rad)

Specimen numberPerformance level

Being basically intact Slight damage Moderate damage Severe damageBeam1 00055 00157 00264 00562Beam2 00053 00137 00212 00426Beam3 00060 00143 00235 00446Beam4 00051 00145 00239 00504Beam5 00054 00149 00257 00526Beam6 00051 00133 00228 00403Beam7 00050 00130 00228 00390

14 Advances in Civil Engineering

[7] C J Motter D C Fields J D Hooper et al ldquoSteel-reinforcedconcrete coupling beams II Modelingrdquo Journal of StructuralEngineering vol 143 no 3 article 04016192 2016

[8] Q Z Liang and X L Han ldquoe behavior of stiffening beamsand lintel beams under cyclic loadingrdquo Journal of South ChinaUniversity of Technology vol 23 no 1 pp 27ndash33 1995 inChinese

[9] H Jiang B Wang and X Lu ldquoExperimental study on damagebehavior of reinforced concrete shear walls subjected to cyclicloadsrdquo Journal of Earthquake Engineering vol 17 no 7pp 958ndash971 2013

[10] J Yue J Qian and D E Beskos ldquoA generalized multi-levelseismic damage model for RC framed structuresrdquo Soil Dy-namics and Earthquake Engineering vol 80 pp 25ndash39 2016

[11] JGJ138-2016 Code for Design of Composite Structures ChinaArchitecture amp Building Press Beijing China 2016

[12] R D Lequesne G J Parra-Montesinos and J K WightldquoSeismic behavior and detailing of high-performance fiber-reinforced concrete coupling beams and coupled wall sys-temsrdquo Journal of Structural Engineering vol 139 no 8pp 1362ndash1370 2012

[13] M Otieno H Beushausen and M Alexander ldquoTowardsincorporating the influence of cover cracking on steel cor-rosion in RC design codes the concept of performance-basedcrack width limitsrdquo Materials and Structures vol 45 no 12pp 1805ndash1816 2012

[14] SIMULIA Dassault Systems ABAQUS Analysis UserrsquosManual Version 616 SIMULIA Johnston RI USA 2016

[15] J C Goodnight M J Kowalsky and J M Nau ldquoEffect of loadhistory on performance limit states of circular bridge col-umnsrdquo Journal of Bridge Engineering vol 18 no 12pp 1383ndash1396 2013

[16] R T Ranf ldquoDamage accumulation in lightly confined rein-forced concrete bridge columnsrdquo PEER Report PacificEarthquake Engineering Research Center University ofCalifornia Berkeley CA USA 2006

[17] A Babazadeh R Burguentildeo and P F Silva ldquoUse of 3D finite-element models for predicting intermediate damage limitstates in RC bridge columnsrdquo Journal of Structural Engi-neering vol 141 no 10 article 04015012 2015

[18] J Moon CW Roeder andH-E Lee ldquoAnalytical modeling ofbending of circular concrete-filled steel tubesrdquo EngineeringStructures vol 42 no 12 pp 349ndash361 2012

[19] GB50010-2010 Code for Design of Concrete Structures ChinaArchitecture amp Building Press Beijing China 2010

[20] H Zhu M T Stephens and D E Lehman ldquoInelastic responseprediction of CFST columns and connections subjected tolateral loadingrdquo Journal of Constructional Steel Researchvol 132 pp 130ndash140 2017

[21] M J N Priestley ldquoPerformance based seismic designrdquo inProceedings of 12th World Conference on EarthquakeEngineering Auckland New Zealand January 2000

[22] Y Shi M Wang and Y Wang ldquoExperimental and consti-tutive model study of structural steel under cyclic loadingrdquoJournal of Constructional Steel Research vol 67 no 8pp 1185ndash1197 2011

[23] H Jiang X Lu and T Kubo ldquoDamage displacement esti-mation of flexure-dominant RC columnsrdquo Advances inStructural Engineering vol 13 no 2 pp 357ndash368 2010

[24] GB50011-2010 Code for Seismic Design of Buildings ChinaArchitecture amp Building Press Beijing China 2010

Advances in Civil Engineering 15

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

different steel yielding states obtained from finite elementanalysis were compared with the test result as shown inTable 6 e finite element analysis can provide a statisticallyconsistent simulation result and the mean rotation ratiosbetween FEA and the test for steel flange tensile yielding andsteel web principle tensile yielding are 123 and 108respectively

Rebar tensile yielding and rebar fracture were pre-dicted directly through rebar yielding strain and tensilestrain recorded in Table 2 Rebar buckling was predictedthrough confined concrete ultimate compressive strainwhich is calculated using equation suggested by Priestley[21] e chord rotations corresponding to different rebardamage states obtained from finite element analysis werecompared with the test result as shown in Table 7 efinite element analysis can provide a statistically consis-tent simulation result and the mean rotation ratios be-tween FEA and the test for rebar tensile yielding rebarbuckling and rebar fracture are 074 103 and 090respectively

43 Performance Index Limit Analysis e seismic per-formance of SRC coupling beams is affected by the ma-terial damage which is related to the material strain Onthe other hand the degradation of the load carrying ca-pacity of SRC coupling beams affects its seismic perfor-mance also Based on the study on the material damagestrain limits [21 23] and component strength degradationlimits [24] four performance levels are defined as shownin Table 8 Since there is a lack of test records of speci-mensrsquo deformation at damage states of concrete strainequal to 0002 or crack width equal to 2mm the chordrotation of specimens at different performance levels canonly be obtained through FEA Table 9 shows the chord

rotations of SRC coupling beam specimens at differentperformance levels and then the mean values wereadopted as the performance index limits which were0005 rad 0014 rad 0024 rad and 0047 rad for the fourperformance levels

5 Summary and Conclusions

Seven half-scale flexural-yielding SRC coupling beamspecimens designed according to Chinese approach weretested under cyclic loade influence of design parameterssuch as aspect ratio flange-web area ratio of encased steeland steel ratio on damage development hysteretic be-havior strength and maximum residual crack width werediscussed Finite element analysis was conducted forspecimens both global skeleton curves and local materialdamage were simulated simultaneously rough quanti-tative comparison finite element analysis can provide astatistically consistent simulation result for materialdamages for each specimen Some conclusions are drawnfrom this research

(1) All specimens failed in flexural mode e damagedevelopment was roughly the same and the typicaldamage states were recorded through the wholeloading process which can be used in assessing theseismic performance level of SRC coupling beams

(2) With the increase of aspect ratio the lateral loadcarrying capacity drops down significantly and themaximum residual crack width tends to be smallerWith the increase of flange-web area ratio of encasedsteel the hysteretic curve gets fuller e specimenwith intermediate flange-web area ratio has thelargest lateral load carrying capacity but smallestmaximum residual crack width With the increase of

Table 6 Comparison of chord rotations of specimens for different steel damage states

Specimen numberSteel flange yielding Steel web yielding

Test FEA FEAtest Test FEA FEAtestBeam1 00033 00059 179 00140 00124 089Beam2 00063 00053 084 00120 00116 097Beam3 00044 00061 139 00095 00108 114Beam4 00041 00051 124 00085 00105 124Beam5 00053 00056 106 00078 00098 126Beam6 00065 00057 088 00100 00115 115Beam7 00039 00056 144 00131 00120 092

Table 7 Comparison of chord rotations of specimens for different rebar damage states

Specimen numberRebar yielding Rebar buckling Rebar fracture

Test FEA FEAtest Test FEA FEAtest Test FEA FEAtestBeam1 00072 00059 082 00502 00777 155 00609 00562 092Beam2 00065 00054 083 00451 00426 094 00558 00502 090Beam3 00091 00060 066 00478 00446 093 00560 00571 102Beam4 00072 00056 078 00485 00527 109 00565 00504 089Beam5 00078 00054 069 00444 00526 118 00586 00596 102Beam6 00065 00056 086 00522 00403 077 00653 00490 075Beam7 00105 00057 054 00511 00390 076 00593 00493 083

Advances in Civil Engineering 13

steel ratio the lateral load carrying capacity increasessignificantly while the maximum residual crackwidth drops down

(3) e finite element model was benchmarkedthrough comparison with test results for bothglobal load-deformation curves and local materialdamages Both qualitative and quantitative com-parisons testify the accuracy of finite elementmodels e cover concrete edge compressionstrain and confined concrete edge compressionstrain were recommended to be 0005 and 00075respectively for accurately modeling concretecrushing and spalling Based on the damagecharacters and strength degradation four perfor-mance levels were defined and correspondingchord rotation limits were obtained through theverified numerical analysis

Data Availability

All the data in this paper are obtained from tests and nu-merical analysis and no other data in the literature are usedto support this study

Conflicts of Interest

e authors declare that there are no potential conflicts ofinterest with respect to the research authorship and pub-lication of this article

Acknowledgments

e financial support from the Program of Shanghai Aca-demic Research Leader (grant number 18XD1403900) andthe National Key Research and Development Program ofChina (grant number 2017YFC1500701) is gratefullyacknowledged

References

[1] S El-Tawil K A Harries P J Fortney B M Shahrooz andY Kurama ldquoSeismic design of hybrid coupled wall systemsstate of the artrdquo Journal of structural engineering vol 136no 7 pp 755ndash769 2010

[2] C-C Hung and W-T Lu ldquoA performance-based designmethod for coupled wall structuresrdquo Journal of EarthquakeEngineering vol 21 no 4 pp 579ndash603 2016

[3] C J Motter D C Fields J D Hooper et al ldquoSteel-reinforcedconcrete coupling beams I testingrdquo Journal of StructuralEngineering vol 143 no 3 article 04016191 2016

[4] B Gong and B M Shahrooz ldquoConcrete-steel compositecoupling beams I component testingrdquo Journal of StructuralEngineering vol 127 no 6 pp 625ndash631 2001

[5] B Gong and B M Shahrooz ldquoConcrete-steel compositecoupling beams II subassembly testing and design verifi-cationrdquo Journal of Structural Engineering vol 127 no 6pp 632ndash638 2001

[6] R K L Su and W Y Lam ldquoA unified design approach forplate-reinforced composite coupling beamsrdquo Journal ofConstructional Steel Research vol 65 no 3 pp 675ndash6862009

Table 8 Method of defining performance levels for SRC coupling beams

Performance level Damage descriptionPerformance criterion

Rebar or steel strain Concretestrain Load carrying capacity

Being basically intact ere are fine cracks in concrete while steel or rebaris not yielding εy 0002 mdash

Slight damage Concrete cover is not crushing and residual crackwidth is less than 1mm 0015 0005 mdash

Moderate damage Concrete cover is not spalling and residual crackwidth is less than 2mm 003 00075 95 Pmax

Severe damage Concrete core is not crushing and rebar or steel isnot fracturing εsu εcu 85 Pmax

Note εy is the yielding strain of steel or rebar εsu is the tensile strain of steel or rebar εcu is the ultimate strain of the concrete Pmax is the lateral load carryingcapacity of specimens

Table 9 Chord rotations of SRC coupling beams at different performance levels (rad)

Specimen numberPerformance level

Being basically intact Slight damage Moderate damage Severe damageBeam1 00055 00157 00264 00562Beam2 00053 00137 00212 00426Beam3 00060 00143 00235 00446Beam4 00051 00145 00239 00504Beam5 00054 00149 00257 00526Beam6 00051 00133 00228 00403Beam7 00050 00130 00228 00390

14 Advances in Civil Engineering

[7] C J Motter D C Fields J D Hooper et al ldquoSteel-reinforcedconcrete coupling beams II Modelingrdquo Journal of StructuralEngineering vol 143 no 3 article 04016192 2016

[8] Q Z Liang and X L Han ldquoe behavior of stiffening beamsand lintel beams under cyclic loadingrdquo Journal of South ChinaUniversity of Technology vol 23 no 1 pp 27ndash33 1995 inChinese

[9] H Jiang B Wang and X Lu ldquoExperimental study on damagebehavior of reinforced concrete shear walls subjected to cyclicloadsrdquo Journal of Earthquake Engineering vol 17 no 7pp 958ndash971 2013

[10] J Yue J Qian and D E Beskos ldquoA generalized multi-levelseismic damage model for RC framed structuresrdquo Soil Dy-namics and Earthquake Engineering vol 80 pp 25ndash39 2016

[11] JGJ138-2016 Code for Design of Composite Structures ChinaArchitecture amp Building Press Beijing China 2016

[12] R D Lequesne G J Parra-Montesinos and J K WightldquoSeismic behavior and detailing of high-performance fiber-reinforced concrete coupling beams and coupled wall sys-temsrdquo Journal of Structural Engineering vol 139 no 8pp 1362ndash1370 2012

[13] M Otieno H Beushausen and M Alexander ldquoTowardsincorporating the influence of cover cracking on steel cor-rosion in RC design codes the concept of performance-basedcrack width limitsrdquo Materials and Structures vol 45 no 12pp 1805ndash1816 2012

[14] SIMULIA Dassault Systems ABAQUS Analysis UserrsquosManual Version 616 SIMULIA Johnston RI USA 2016

[15] J C Goodnight M J Kowalsky and J M Nau ldquoEffect of loadhistory on performance limit states of circular bridge col-umnsrdquo Journal of Bridge Engineering vol 18 no 12pp 1383ndash1396 2013

[16] R T Ranf ldquoDamage accumulation in lightly confined rein-forced concrete bridge columnsrdquo PEER Report PacificEarthquake Engineering Research Center University ofCalifornia Berkeley CA USA 2006

[17] A Babazadeh R Burguentildeo and P F Silva ldquoUse of 3D finite-element models for predicting intermediate damage limitstates in RC bridge columnsrdquo Journal of Structural Engi-neering vol 141 no 10 article 04015012 2015

[18] J Moon CW Roeder andH-E Lee ldquoAnalytical modeling ofbending of circular concrete-filled steel tubesrdquo EngineeringStructures vol 42 no 12 pp 349ndash361 2012

[19] GB50010-2010 Code for Design of Concrete Structures ChinaArchitecture amp Building Press Beijing China 2010

[20] H Zhu M T Stephens and D E Lehman ldquoInelastic responseprediction of CFST columns and connections subjected tolateral loadingrdquo Journal of Constructional Steel Researchvol 132 pp 130ndash140 2017

[21] M J N Priestley ldquoPerformance based seismic designrdquo inProceedings of 12th World Conference on EarthquakeEngineering Auckland New Zealand January 2000

[22] Y Shi M Wang and Y Wang ldquoExperimental and consti-tutive model study of structural steel under cyclic loadingrdquoJournal of Constructional Steel Research vol 67 no 8pp 1185ndash1197 2011

[23] H Jiang X Lu and T Kubo ldquoDamage displacement esti-mation of flexure-dominant RC columnsrdquo Advances inStructural Engineering vol 13 no 2 pp 357ndash368 2010

[24] GB50011-2010 Code for Seismic Design of Buildings ChinaArchitecture amp Building Press Beijing China 2010

Advances in Civil Engineering 15

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

steel ratio the lateral load carrying capacity increasessignificantly while the maximum residual crackwidth drops down

(3) e finite element model was benchmarkedthrough comparison with test results for bothglobal load-deformation curves and local materialdamages Both qualitative and quantitative com-parisons testify the accuracy of finite elementmodels e cover concrete edge compressionstrain and confined concrete edge compressionstrain were recommended to be 0005 and 00075respectively for accurately modeling concretecrushing and spalling Based on the damagecharacters and strength degradation four perfor-mance levels were defined and correspondingchord rotation limits were obtained through theverified numerical analysis

Data Availability

All the data in this paper are obtained from tests and nu-merical analysis and no other data in the literature are usedto support this study

Conflicts of Interest

e authors declare that there are no potential conflicts ofinterest with respect to the research authorship and pub-lication of this article

Acknowledgments

e financial support from the Program of Shanghai Aca-demic Research Leader (grant number 18XD1403900) andthe National Key Research and Development Program ofChina (grant number 2017YFC1500701) is gratefullyacknowledged

References

[1] S El-Tawil K A Harries P J Fortney B M Shahrooz andY Kurama ldquoSeismic design of hybrid coupled wall systemsstate of the artrdquo Journal of structural engineering vol 136no 7 pp 755ndash769 2010

[2] C-C Hung and W-T Lu ldquoA performance-based designmethod for coupled wall structuresrdquo Journal of EarthquakeEngineering vol 21 no 4 pp 579ndash603 2016

[3] C J Motter D C Fields J D Hooper et al ldquoSteel-reinforcedconcrete coupling beams I testingrdquo Journal of StructuralEngineering vol 143 no 3 article 04016191 2016

[4] B Gong and B M Shahrooz ldquoConcrete-steel compositecoupling beams I component testingrdquo Journal of StructuralEngineering vol 127 no 6 pp 625ndash631 2001

[5] B Gong and B M Shahrooz ldquoConcrete-steel compositecoupling beams II subassembly testing and design verifi-cationrdquo Journal of Structural Engineering vol 127 no 6pp 632ndash638 2001

[6] R K L Su and W Y Lam ldquoA unified design approach forplate-reinforced composite coupling beamsrdquo Journal ofConstructional Steel Research vol 65 no 3 pp 675ndash6862009

Table 8 Method of defining performance levels for SRC coupling beams

Performance level Damage descriptionPerformance criterion

Rebar or steel strain Concretestrain Load carrying capacity

Being basically intact ere are fine cracks in concrete while steel or rebaris not yielding εy 0002 mdash

Slight damage Concrete cover is not crushing and residual crackwidth is less than 1mm 0015 0005 mdash

Moderate damage Concrete cover is not spalling and residual crackwidth is less than 2mm 003 00075 95 Pmax

Severe damage Concrete core is not crushing and rebar or steel isnot fracturing εsu εcu 85 Pmax

Note εy is the yielding strain of steel or rebar εsu is the tensile strain of steel or rebar εcu is the ultimate strain of the concrete Pmax is the lateral load carryingcapacity of specimens

Table 9 Chord rotations of SRC coupling beams at different performance levels (rad)

Specimen numberPerformance level

Being basically intact Slight damage Moderate damage Severe damageBeam1 00055 00157 00264 00562Beam2 00053 00137 00212 00426Beam3 00060 00143 00235 00446Beam4 00051 00145 00239 00504Beam5 00054 00149 00257 00526Beam6 00051 00133 00228 00403Beam7 00050 00130 00228 00390

14 Advances in Civil Engineering

[7] C J Motter D C Fields J D Hooper et al ldquoSteel-reinforcedconcrete coupling beams II Modelingrdquo Journal of StructuralEngineering vol 143 no 3 article 04016192 2016

[8] Q Z Liang and X L Han ldquoe behavior of stiffening beamsand lintel beams under cyclic loadingrdquo Journal of South ChinaUniversity of Technology vol 23 no 1 pp 27ndash33 1995 inChinese

[9] H Jiang B Wang and X Lu ldquoExperimental study on damagebehavior of reinforced concrete shear walls subjected to cyclicloadsrdquo Journal of Earthquake Engineering vol 17 no 7pp 958ndash971 2013

[10] J Yue J Qian and D E Beskos ldquoA generalized multi-levelseismic damage model for RC framed structuresrdquo Soil Dy-namics and Earthquake Engineering vol 80 pp 25ndash39 2016

[11] JGJ138-2016 Code for Design of Composite Structures ChinaArchitecture amp Building Press Beijing China 2016

[12] R D Lequesne G J Parra-Montesinos and J K WightldquoSeismic behavior and detailing of high-performance fiber-reinforced concrete coupling beams and coupled wall sys-temsrdquo Journal of Structural Engineering vol 139 no 8pp 1362ndash1370 2012

[13] M Otieno H Beushausen and M Alexander ldquoTowardsincorporating the influence of cover cracking on steel cor-rosion in RC design codes the concept of performance-basedcrack width limitsrdquo Materials and Structures vol 45 no 12pp 1805ndash1816 2012

[14] SIMULIA Dassault Systems ABAQUS Analysis UserrsquosManual Version 616 SIMULIA Johnston RI USA 2016

[15] J C Goodnight M J Kowalsky and J M Nau ldquoEffect of loadhistory on performance limit states of circular bridge col-umnsrdquo Journal of Bridge Engineering vol 18 no 12pp 1383ndash1396 2013

[16] R T Ranf ldquoDamage accumulation in lightly confined rein-forced concrete bridge columnsrdquo PEER Report PacificEarthquake Engineering Research Center University ofCalifornia Berkeley CA USA 2006

[17] A Babazadeh R Burguentildeo and P F Silva ldquoUse of 3D finite-element models for predicting intermediate damage limitstates in RC bridge columnsrdquo Journal of Structural Engi-neering vol 141 no 10 article 04015012 2015

[18] J Moon CW Roeder andH-E Lee ldquoAnalytical modeling ofbending of circular concrete-filled steel tubesrdquo EngineeringStructures vol 42 no 12 pp 349ndash361 2012

[19] GB50010-2010 Code for Design of Concrete Structures ChinaArchitecture amp Building Press Beijing China 2010

[20] H Zhu M T Stephens and D E Lehman ldquoInelastic responseprediction of CFST columns and connections subjected tolateral loadingrdquo Journal of Constructional Steel Researchvol 132 pp 130ndash140 2017

[21] M J N Priestley ldquoPerformance based seismic designrdquo inProceedings of 12th World Conference on EarthquakeEngineering Auckland New Zealand January 2000

[22] Y Shi M Wang and Y Wang ldquoExperimental and consti-tutive model study of structural steel under cyclic loadingrdquoJournal of Constructional Steel Research vol 67 no 8pp 1185ndash1197 2011

[23] H Jiang X Lu and T Kubo ldquoDamage displacement esti-mation of flexure-dominant RC columnsrdquo Advances inStructural Engineering vol 13 no 2 pp 357ndash368 2010

[24] GB50011-2010 Code for Seismic Design of Buildings ChinaArchitecture amp Building Press Beijing China 2010

Advances in Civil Engineering 15

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

[7] C J Motter D C Fields J D Hooper et al ldquoSteel-reinforcedconcrete coupling beams II Modelingrdquo Journal of StructuralEngineering vol 143 no 3 article 04016192 2016

[8] Q Z Liang and X L Han ldquoe behavior of stiffening beamsand lintel beams under cyclic loadingrdquo Journal of South ChinaUniversity of Technology vol 23 no 1 pp 27ndash33 1995 inChinese

[9] H Jiang B Wang and X Lu ldquoExperimental study on damagebehavior of reinforced concrete shear walls subjected to cyclicloadsrdquo Journal of Earthquake Engineering vol 17 no 7pp 958ndash971 2013

[10] J Yue J Qian and D E Beskos ldquoA generalized multi-levelseismic damage model for RC framed structuresrdquo Soil Dy-namics and Earthquake Engineering vol 80 pp 25ndash39 2016

[11] JGJ138-2016 Code for Design of Composite Structures ChinaArchitecture amp Building Press Beijing China 2016

[12] R D Lequesne G J Parra-Montesinos and J K WightldquoSeismic behavior and detailing of high-performance fiber-reinforced concrete coupling beams and coupled wall sys-temsrdquo Journal of Structural Engineering vol 139 no 8pp 1362ndash1370 2012

[13] M Otieno H Beushausen and M Alexander ldquoTowardsincorporating the influence of cover cracking on steel cor-rosion in RC design codes the concept of performance-basedcrack width limitsrdquo Materials and Structures vol 45 no 12pp 1805ndash1816 2012

[14] SIMULIA Dassault Systems ABAQUS Analysis UserrsquosManual Version 616 SIMULIA Johnston RI USA 2016

[15] J C Goodnight M J Kowalsky and J M Nau ldquoEffect of loadhistory on performance limit states of circular bridge col-umnsrdquo Journal of Bridge Engineering vol 18 no 12pp 1383ndash1396 2013

[16] R T Ranf ldquoDamage accumulation in lightly confined rein-forced concrete bridge columnsrdquo PEER Report PacificEarthquake Engineering Research Center University ofCalifornia Berkeley CA USA 2006

[17] A Babazadeh R Burguentildeo and P F Silva ldquoUse of 3D finite-element models for predicting intermediate damage limitstates in RC bridge columnsrdquo Journal of Structural Engi-neering vol 141 no 10 article 04015012 2015

[18] J Moon CW Roeder andH-E Lee ldquoAnalytical modeling ofbending of circular concrete-filled steel tubesrdquo EngineeringStructures vol 42 no 12 pp 349ndash361 2012

[19] GB50010-2010 Code for Design of Concrete Structures ChinaArchitecture amp Building Press Beijing China 2010

[20] H Zhu M T Stephens and D E Lehman ldquoInelastic responseprediction of CFST columns and connections subjected tolateral loadingrdquo Journal of Constructional Steel Researchvol 132 pp 130ndash140 2017

[21] M J N Priestley ldquoPerformance based seismic designrdquo inProceedings of 12th World Conference on EarthquakeEngineering Auckland New Zealand January 2000

[22] Y Shi M Wang and Y Wang ldquoExperimental and consti-tutive model study of structural steel under cyclic loadingrdquoJournal of Constructional Steel Research vol 67 no 8pp 1185ndash1197 2011

[23] H Jiang X Lu and T Kubo ldquoDamage displacement esti-mation of flexure-dominant RC columnsrdquo Advances inStructural Engineering vol 13 no 2 pp 357ndash368 2010

[24] GB50011-2010 Code for Seismic Design of Buildings ChinaArchitecture amp Building Press Beijing China 2010

Advances in Civil Engineering 15

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom