Research ArticleSeismic Behavior and Finite Element Analysis of ReinforcedConcrete Short Columns Impacted by Oblique Earthquakes

Chunyang Liu 12 Guixin Yu1 Xisen Fan12 Changqun Guo1 and Fei Li1

1Department of Civil Engineering Shandong Jianzhu University Jinan 250101 China2Key Laboratory of Building Structural Retrofitting and Underground Space Engineering (Shandong Jianzhu University)Ministry of Education Jinan 250101 China

Correspondence should be addressed to Chunyang Liu liucy2011sdjzueducn

Received 19 January 2020 Revised 24 June 2020 Accepted 12 September 2020 Published 30 September 2020

Academic Editor Antonio Formisano

Copyright copy 2020 Chunyang Liu 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

(is study evaluates the seismic behavior of reinforced concrete (RC) short columns with a high axial compression ratio underoblique earthquake conditions (e studied parameters include the loading angle axial compression ratio the high-strengthstirrups with small spacing and the carbon-fiber-reinforced polymer (CFRP) wrapped column end or outer steel plate mesh at theend of the column Low-cycle repeated loading tests were used to analyze the specimensrsquo seismic performance indices of hystereticbehavior strength stiffness deformation capacity and energy dissipation capacity Results suggest that the OpenSees finiteelement program can sufficiently simulate the nonlinear response of the specimen Oblique loading led to the increase of damageto the specimens and the deterioration of stiffness of the specimens which was especially seen with the increase of the axialcompression ratio Accordingly arranging high-strength stirrups with small spacing and the column end outer steel plate meshboth transform the failure mode from shear failure to bending shear failure Additionally wrapping the CFRP at the end ofcolumns improves their strength but does not improve their deformation capacity(e demonstrated success of these strategies inimproving the seismic performance of RC short columns under diagonal loads with high axial compression ratios can informpractical engineering applications

1 Introduction

Seismic damage investigations have shown that reinforcedconcrete (RC) short columns are prone to shear damageunder strong ground motions which can cause severedamage or even collapse of the RC frame structure [12] Oneof the reasons for this tendency for severe earthquakedamage is that the direction of strong ground motion on theRC short columns is arbitrary [34] RC short columns aresubjected to horizontal earthquakes transmitted accordingto the two horizontal adjacent components effect this effectcauses the component ie the columns to withstand greaterforces than a single horizontal direction and thus typicallycauses greater damage Researchers have examined theperformance of RC short columns under a variety of seismicconditions For example Woodward and Jirsa [5] andMaruyama et al [6] studied the effect of load direction on the

shear performance and stiffness of RC short columns theyshowed that the cumulative damage caused by the loading ofthe specimens in different directions reduces the stiffness ofthe concrete column but has little effect on the shear capacityof the specimens Rodrigues et al [7] studied the seismicperformance of reinforced concrete columns under bidi-rectional cyclic loading (e results showed that the bidi-rectional cyclic loading led to a decrease in the stiffness andstrength of the column and affected the ductility and energydissipation capacity of the column When RC short columnsare used in high-rise buildings and super high-rise buildingsthey experience high vertical loads resulting in a generallyhigh axial compression ratio when the column section size isconstant Previous research demonstrated that when anearthquake occurred the RC column was affected by boththe axial force and the vertical ground motion [89] (estrong vertical ground motion increased the axial force of

HindawiAdvances in Civil EngineeringVolume 2020 Article ID 9260203 15 pageshttpsdoiorg10115520209260203

the RC short column resulting in the axial compressionratio of the short column approaching or exceeding thedesign limits and contributing to the componentrsquos beingseverely damaged in the earthquake (ese results indicatethat the seismic performance of RC short columns in theoblique or nonspindle direction under high axial com-pression ratio needs further study Zhou and Liu [10] ex-amined the behavior of RC short columns with axialcompression ratios ranging from 035 to 055 Ma et al [11]examined the behavior of RC short columns with axialcompression ratios ranging from 03 to 09 However theseismic performance of these RC short columns under highaxial pressures during oblique earthquake action is currentlynot adequately characterized

Researchers have conducted research on various ap-proaches to effectively improve the problem of shear failureof RC short columns under strong ground motion Con-sidering the characteristics of high-strength steel bars withhigh yield strength and good toughness the application ofsuch research to concrete structures is conducive to im-proving the seismic performance of various structures withRC short columns Sokoli and Ghannoum [12] studied theapplicability of high-strength longitudinal reinforcements inRC columns the results showed that high-strength longi-tudinal reinforcement could achieve shear force transmis-sion mechanisms that enable RC columns to meet seismicrequirements Ding et al [13] studied the seismic perfor-mance of high-strength stirrup restraining high-strengthconcrete short columns results showed that the restrainingeffect of high-strength stirrup on the concrete improved thestrength and seismic performance of the specimen FurtherShin et al [14] also proved that high-strength stirrups withgood restraint can provide effective restraint for longitudinalreinforcement and improve the strength ductility andenergy consumption of the column While the addition ofhigh-strength steel stirrups to RC short columns can im-prove characteristics of these components researchers havealso considered reinforcement with carbon-fiber-reinforcedpolymer (CFRP) For example Shehata et al [15] studied theductile properties of CFRP-wrapped RC short columnsresults show that the ultimate deformation of the specimendepends on the lateral restraint strength Colomb et al [16]studied the effect of CFRP on the failure mode of RC shortcolumns results showed that the reinforcement mode ofCFRP changed the failure mode of RC short columns suchthat the specimens changed from shear brittle failure toductile bending shear failure Galal et al [17] conductedresearch on the seismic performance of RC short columnsrestrained by CFRP results showed that the RC short col-umns restrained by CFRP can effectively improve the shearcapacity and energy dissipation capacity of the specimen Asan alternative to CFRP researchers also consider using steelplate mesh to strengthen reinforced concrete columns Forexample Morshed and Kazemi [18] studied the seismicperformance of concrete short columns confined by a steelmesh results showed that the steel plate mesh constraintssignificantly improved the shear resistance and deformationability of RC columns Li et al [19] subjected high-strengthRC columns containing steel plate mesh restraints to low-

cycle repeated loading tests results showed that the hys-teresis curve of the outsourced expanded steel mesh con-strained specimen was full the strength and ductility of thespecimen significantly improved and the stiffness degra-dation slowed(e collective results of research on the effectsof arranging dense high-strength stirrups CFRP and steelplate mesh on the performance of RC short columns showthat these reinforcements improve the seismic performanceof RC short columns in the main axis direction (ereforeunder oblique earthquake action these reinforcements havedemonstrated a significant ability to improve the seismicperformance of RC short columns with high axial com-pression ratios

Here six short concrete columns with high-strengthlongitudinal reinforcement were designed and subjected torepeated low-cycle loading tests (e effects of the loadingangle axial compression ratio dense high-strength stirrupscolumn-end wound carbon fiber cloth and column-endcoated steel mesh on the hysteretic characteristics strengthstiffness deformation capacity and energy dissipation ca-pacity of the test pieces were analyzed Test results were thencompared to those obtained by OpenSees simulation (isstudy is intended to provide a reference for improving theseismic performance of RC short columns under diagonalloads with high axial compression ratios

2 Experimental Program

21 Specimen Design (is study used six RC short columnspecimens (Table 1) referred to as SC-1 through SC-6 SC-1was a comparative specimen with a 0deg horizontal loadingSC-2 through SC-6 were loaded at a 45deg oblique loading SC-4 included dense high-strength stirrups that is a specimenconfigured with small spacing high-strength stirrup whereasSC-5 and SC-6 were partially strengthened with eithercolumn-end winding CFRP (A Table 1) or column-endouter steel mesh (B Table 1) All specimens had300mmtimes 300mm cross sections and C40 concrete designstrength with a 20mm thick protective layer (e longitu-dinal reinforcement in the columnwasmade of 12 HTRB630high-strength steel bars with a 16mm diameter (ese barswere evenly distributed along the section to achieve a re-inforcement ratio of 268 In the experiments the stirrupgrade was varied as either HRB400 or HTRB630 both ofwhich had diameters of 8mm (Table 1) All stirrups were inthe form of well-typed composite stirrups with varied stirrupspacing and volume stirrup ratios (Table 1) (e distancebetween the horizontal loading point of the specimen andthe bottom of the column was 600mm and the shear spanratio was 2 (e dimensions of the specimen and the re-inforcement of the section were varied among specimentypes (Figure 1) Considering the influence of differentloading directions on the seismic performance of thespecimen two typical directions of load loading 0deg and 45degwere selected for this test Considering that the axialcompression ratio of RC short columns in actual engineeringmeets or even exceeds the design upper limit the designaxial compression ratio (n) of this test was selected to be 08and 10 Considering that the common stirrups under high

2 Advances in Civil Engineering

Table 1 Design parameters of specimens

Specimen α (deg) n Strengthening measuresStirrup

Stirrup grade Diameter spacing (mm) ρv ()

SC-1 0 08 mdash HRB400 880 190SC-2 45 08 mdash HRB400 880 190SC-3 45 10 mdash HRB400 880 190SC-4 45 10 mdash HTRB630 850 305SC-5 45 10 A HTRB630 850 305SC-6 45 10 B HTRB630 850 305Note SC short column α loading direction nNfcbh where N is the design value of axial pressure fc is the design value of concrete strength b is thecolumn section width and h is the column section height ρv is the rebar ratio

1-1

1 1

300

14001400550 300 550

450450

450

450

500

600

1325

225

500

600

1325

225

300

Pedestal

Speci-men

Load endblock

C 880

C 880

C 880

4DH16

otimesotimes

(a)

1-1

500

600

1325

225

300

300

1400488 488424

450

450

Pedestal

Specimen

Load endblock

1 11

1400

450

450

500

600

1325

225

4DH16

C 880

C 880

C 880

otimesotimes

(b)

1-1

500

600

1325

225

300

300

1400488 488424

450

450

Pedestal

Specimen

Load endblock

11

1400

450

450

500

600

1325

225

4DH 16

DH 850

DH 850

DH 850

otimesotimes

(c)

Figure 1 Schematics of prepared specimens ie short column-1 (SC-1) through SC-6 including arrangement of reinforcing barsDH HTRB630 steel bar and CHRB400 steel bar otimes horizontal load loading point (a) SC-1 (b) SC-2 SC-3 (c) SC-4 SC-5 and SC-6

Advances in Civil Engineering 3

axial compression ratio have the challenge of prematureyielding and short-column brittle failure HRB400 andHTRB630 rebars were selected for this test (e mechanicalproperties of the concrete used in this study (outlined inTable 2) were held constant whereas the mechanicalproperties of the three types of steel bars (outlined in Table 3)and the two types of reinforcing materials (outlined inTable 4) were previously characterized

Production of the specimens SC-1 through SC-4 in-volved first ligating the longitudinal reinforcements and thestirrups to form a steel cage Formwork and concretepouring were then completed To facilitate test loadingobliquely loaded column sections were placed at a 45deg to thebase Specimen SC-5 involved wrapping the end of thecolumn with CFRP which had a single layer thickness of011mm and a total of three layers totaling 200mm in totalheight At the time of construction the steel bars were firsttied to form a steel cage the concrete was then poured andcured To avoid tearing of the CFRP the chamfer radius ofthe corner was 25mm(is method was used to improve therestraint effect of the column-end concrete as well as toimprove the seismic performance of the specimen

SC-6 involved reinforcement with a column-end outersteel plate mesh (e steel plate mesh adopted a round holesteel plate mesh with a wrapping height of 300mm athickness of 3mm a circular hole diameter of 5mm and ahole pitch of 5mm which was processed into a squarepattern (Figure 2(a)) First the U-shaped snap fastener wasplaced on the longitudinal bar and fixed at the joint of thelongitudinal reinforcement and the stirrup passing throughthe screw and tightening the nut (Figures 2(b) and 2(c))(en the steel plate mesh was placed on the outer side of thesteel skeleton to make the inner surface of the steel platemesh tightly attached to the outer side of the U-shaped snapfastener (Figure 2(d)) To ensure that the steel plate mesh didnot participate in the force of the column end a 5mm gapwas left between the end portion and the column base Afterplacement the steel plate mesh was fixed with local windingwires After construction of the steel skeleton the concretewas poured resulting in the surface of the column beingflush with the surface of the steel plate mesh (is methodwas used to improve the restraining effect on the column-end concrete and to improve the seismic performance of thespecimen

22 Load Method Vertical loads were applied in the axialdirection using a 200 ton vertical actuator and held con-stant at the designated axial compression ratios(e actuatorused was made in China (e horizontal load tests wereconducted by adopting the low-cycle repeated loadingmode(e tests were performed by conducting displacement-controlled loading with the displacement cycle loaded twiceper stage until the load dropped to either 85 of the peakload or to the point at which the specimen was not suitablefor carrying the load (Figure 3) It was assumed that positiveforce and displacement were produced by the thrust of theactuator and that negative force and displacement wereproduced by the pull force caused by the actuator (e

loading displacement of the column-end load point wasimplemented by an MTS 100 ton horizontal actuator (isactuator was made in the United States and incorporates anassociated data acquisition system that collects the load anddisplacement data (Figure 4) Collected data were used togenerate a hysteresis curve Cracks on the specimen werevisually observed and manually mapped

3 Experimental Results and Analysis

31 Failure Modes Application of loads resulted in variablestates of damage to all specimens tested in this study basedon visual observations (e definition of the observationsurface of each specimen is shown in Figure 5 (e finalfailure mode of each specimen is shown in Figure 6

For specimen SC-1 small horizontal cracks appearedwithin a range of 300mm from the column bottom when thehorizontal displacement of the column top was loaded to15mm as the loading continued the number of cracksincreased At 182mm the concrete at the bottom corner ofthe column fell off and some longitudinal reinforcementsand stirrups were exposed When specimen was broken thelongitudinal reinforcements in the southwest corner brokeAccordingly specimen SC-1 has obvious shear failurecharacteristics (Figure 6(a)) Regarding specimen SC-2 at15mm small horizontal cracks appeared within a range of150mm from the column bottom as the loading continuedhorizontal cracks developed into oblique cracks and thenumber of cracks increased At 182mm the concrete in thecorner of the column fell off and some longitudinal rein-forcements and stirrups were exposed When the specimenwas broken the corner concrete severely fell off and thelongitudinal reinforcement in the corners in the east andwest directions broke Accordingly specimen SC-2 hasobvious shear failure characteristics (Figure 6(b)) Regarding

Table 2 Mechanical properties of the concrete

Concrete grade fcuk (MPa) fck (MPa) Ec (MPa)C40 604 453 360times104

Note fcuk is the compressive strength of concrete cubes fck is the com-pressive strength of concrete prism Ec is the elastic modulus of concrete

Table 3 Mechanical properties of reinforced bars

Steel bartype

Diameter(mm)

fy(MPa)

fu(MPa) δ () Es (MPa)

HRB400 8 488 640 2625 202times105

HTRB630 8 601 855 238 229times105

HTRB630 16 668 845 230 245times105

Note fy is the rebar yield strength fu is the rebar ultimate strength δ is therebar elongation after breaking and Es is the rebar modulus of elasticity

Table 4 Mechanical properties of strengthening material

Material type (ickness(mm) fy (MPa) fu (MPa) Es (MPa)

Steel plate mesh 3 208 313 168times105

CFRP 0167 ndash 3471 231times 105

4 Advances in Civil Engineering

specimen SC-3 at 15mm small horizontal cracks appearedwithin a range of 200mm from the columnrsquos bottom whenthe loading continued the number of cracks increased andpenetration cracks appeared At 15mm the concrete fell offand some longitudinal reinforcements and stirrups wereexposedWhen the specimen was broken the concrete in thecore area had been crushed and some longitudinal rein-forcements were broken Accordingly specimen SC-3 hasobvious shear failure characteristics (Figure 6(c))

Regarding specimen SC-4 at 15mm small horizontalcracks appeared within a range of 150mm from the columnbottom as the loading continued the number of cracksincreased At 32mm the northwest concrete began to fall offand the longitudinal tendons broke When the specimen wasdamaged the concrete at the bottom corner of the column inthe east and west directions was crushed and the

longitudinal tendons broke Accordingly the bending andshear failure characteristics of specimen SC-4 can be seen(Figure 6(d)) Regarding specimen SC-5 at 15mm cracksappeared on the edge of the CFRP when the loadingcontinued the number of cracks increased and penetratingcracks appeared At 182mm the concrete started to fall offand the carbon fiber cloth cracked When specimen wasbroken the concrete at the bottom corner of the column inthe east and west directions was crushed (Figure 6(e)) Afterthe test the carbon fiber cloth was peeled off it was foundthat the column-angle concrete had been significantlybroken diagonally and the longitudinal tendons and stirrupshad become exposed Accordingly specimen SC-5 has shearfailure characteristics (Figure 6(f )) Regarding specimen SC-6 at 3mm cracks appeared on the edge of the steel platemesh as loading continued the number of cracks increased

(a)

90degbending part

Longitudinalreinforcement

Stirrups

NutScrew

Longitudinal reinforcement

U-shaped snap fastener

Steel plate mesh Limit switch

(b)

Longitudinalreinforcement

Stirrups

U-shaped snap

(c)

Steelskeleton

Steel planemesh

(d)

Figure 2 Details of steel skeleton production (a) Steel plate mesh (b) limit device floor plan (c) steel skeleton with U-shaped snap fastenerand (d) steel skeleton with steel plate mesh

Advances in Civil Engineering 5

Disp

lace

men

t (m

m)

Loading cycle

1 24 486

12182 22

28 3238

4350

ndash15 ndash3 ndash6ndash10

ndash15 ndash20ndash25

ndash30ndash35

ndash40ndash45

ndash60

Figure 3 Loading protocol (e tests performed via displacement-controlled loading

Reaction frame

Lifting jackConnector

Steel backing plate

MTSScrew

Steel plate

Electronic displacement meter

Spec

imen

Pedestal

Anchor boltStatic platform

Reac

tion

wal

l

Figure 4 Experimental test set-up MTS actuator with data acquisition system collects load and displacement data

S

N

WE

Specimen

y

x

Pull Push

(a)

Specimen

y xS

N

E W

Pull Push

(b)

Figure 5 Definition of specimen observation surface (a) Spindle loading (b) 45deg loading

6 Advances in Civil Engineering

At 40mm the longitudinal reinforcement was brokenWhen the specimen was broken the steel plate mesh at thebottom of the column was convex (Figure 6(g)) After thetest the steel plate mesh was peeled off it was found that theconcrete at the bottom of the column was broken and thelongitudinal steel bars were convex and partially brokenAccordingly the bending and shear failure characteristics ofspecimen SC-6 can be seen (Figure 6(h))

Overall compared with the horizontally loaded testspecimens the concrete at the corners of the diagonallyloaded test specimens fell off severely which reduced theworkability of the test specimens In particular the increasein the axial pressure ratio makes this damage more seriousCompared to the unreinforced test specimens high-strengthstirrups with small spacing column-end wrapped CFRPand column-end outer steel plate mesh enhanced the re-straint effect on concrete limited concrete falling off andimproved the seismic performance of the specimens underoblique loads

32 Hysteresis Curves (e load-displacement hysteresiscurves of each specimen demonstrate the performance ofeach specimen during the duration of the tests (Figure 7) Pis the measured horizontal load Δ is the measured hori-zontal displacement of the loading point As can be seenfrom Figure 7 compared to specimen SC-1 specimen SC-2undergoes accelerated strength degradation at a later stage ofloading and the residual deformation is larger(is could beattributed to the oblique loading that leads to the corner

concrete of the specimen being subjected to loads in twodirections resulting in serious damage to the corner con-crete (Figures 7(a) and 7(b)) In contrast to specimen SC-2specimen SC-3 has a significantly lower load at the later stageof loading this is due to the severe fall of the concrete at thelater stage of loading (Figures 7(b) and 7(c)) (ere were twosignificant drops in the hysteresis curves of SC-4 and SC-6likely due to the fracture of the high-strength longitudinalbars which led to a significant decline in the strength ofthese specimens (Figures 7(d) and 7(f)) However the high-strength stirrups with small spacing included in thesetreatments provided a strong constraint effect for high-strength longitudinal bars that enabled the specimens toretain a strong strength Compared to the hysteresis curve ofspecimen SC-4 that of specimen SC-5 is less full (is isbecause the CFRP is prone to tear and damage at the columnangle under a high axial pressure ratio (Figures 7(d) and7(e)) which causes the strength of the specimen to dropsharply In contrast to specimen SC-4 the load of specimenSC-6 decreases slowly at the later stage of loading and thehysteresis curve was relatively plump (Figures 7(d) and 7(f ))(is is because the steel plate net at the end of the columncan effectively slow the fall of concrete and exert a strongerenergy consumption

33 Skeleton Curves In the hysteretic curve under thecondition of low-cycle reciprocating loading the outerwinding line of the peak loading point of each stage is calleda skeleton curve which characterizes the characteristics of

Ordinary comparison

specimen

(a)

α = 45deg

n = 08

(b)

α = 45deg

n = 10

(c)

Dense high-strength stirrups

α = 45deg

n = 10

(d)

CFRP constraint

α = 45deg

n = 10

(e)

Remove CFRP

α = 45deg

n = 10

(f )

α = 45deg

n = 10

Steel plate mesh constraint

(g)

Remove steel plate mesh

α = 45deg

n = 10

(h)

Figure 6 Visual observations of the ultimate failure modes of short column (SC) specimens (a) SC-1 (b) SC-2 (c) SC-3 (d) SC-4 (e) SC-5(f ) SC-5 after removal of CFRP (g) SC-6 and (h) SC-6 after removal of steel plate mesh

Advances in Civil Engineering 7

stress and deformation during the loading of the specimen(e skeleton curve of each specimen is shown in Figure 8 Ascan be seen from the figure the development of the skeleton

curves of each specimen can be roughly divided into threestages (1) In the elastic stage the load changes linearly withthe displacement the specimen has yet to crack and no

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(a)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(b)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

(c)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(d)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

(e)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(f )

Figure 7 Hysteretic curves of short column (SC) specimens 1ndash6 (a) SC-1 (b) SC-2 (c) SC-3 (d) SC-4 (e) SC-5 and (f) SC-6

8 Advances in Civil Engineering

residual deformation is observed (2) During the develop-ment stage of a multicrack many cracks appear in thespecimen When residual deformation begins to appearmultiple tiny cracks appear on the surface of the specimenand the horizontal load of the specimen slowly increasesWith the accumulation of damage the specimen reaches thepeak load (3) In the load drop stage for specimens SC-1SC-2 and SC-3 the skeleton curve decreases significantly inthe later stage of loading (is is because the ordinarystirrups with large spacing cannot provide effective lateralrestraints for the specimens under a high axial compressionratio thus making the strength of the specimens dropdramatically Compared to specimen SC-3 the skeletoncurves of specimens SC-4 SC-5 and SC-6 decrease slowlyand show good deformation ability In particular the de-formation capacity of specimens SC-4 and SC-6 after thepeak point significantly improves this is conducive toimproving the seismic energy dissipation capability ofspecimens

34 Bearing Capacity and Ductility Each sample wascharacterized by the yield load point the peak load pointand the failure load point within a load-displacement curveAs shown in Figure 9 the yield point D was determined bythe equivalent elastic-plastic energy method that is wherethe area SOAB SBCD and the ultimate load was simplydefined as 85 of the peak load [20] Because the strength ofSC-1 SC-2 and SC-3 declined rapidly after reaching thepeak load and the ultimate load did not reach 85 of thepeak load the failure displacements of these were taken asthe ultimate displacement Here the ultimate displacementangle (θμ) was used to characterize the deformation ability ofthe specimen and was calculated as θμ Δul0 where l0 is thecolumnrsquos height For each specimen the characteristic loadand displacement calculation results are shown in Table 5

(e relative value is the ratio of the average of the positiveand negative corresponding coefficients of SC-2 through SC-6 and the average of the positive and negative correspondingcoefficients of SC-1

As can be seen in Table 5 compared to specimen SC-1the yield load peak load and ultimate load of specimen SC-2are reduced and the ultimate displacement angle is un-changed(is is because the concrete in the corner of the testspecimen is severely damaged under the diagonal horizontalloading making the strength of the specimen decreasehowever this has no effect on the deformation ability of thespecimen A comparison of SC-2 and SC-3 reveals thatunder the oblique load as the axial pressure ratio increasesthe strength of the specimen increases but the deformationcapacity decreases In contrast to specimen SC-4 the yieldload peak load and ultimate load of SC-5 improvedwhereas the ultimate displacement angle decreased by 1(is result indicates that although the strength of thespecimen under high axial pressure ratio improved thedeformation capacity of the specimen under high axialpressure ratio did not improve Compared to specimen SC-4 the yield load peak load and ultimate load of specimenSC-6 improved and the ultimate displacement angle in-creased by 52(is result was likely due to the column-endouter steel plate mesh providing a strong restraining effecton the column-end concrete which then increased thespecimenrsquos strength deformation capacity and seismicperformance

In comparison to SC-3 the yield load peak load andultimate load of SC-4 SC-5 and SC-6 were all greatlyimproved as were the ultimate displacement angles (isindicates that the high-strength stirrups with small spacingcolumn-end wound CFRP and column-end outer steel platemesh may improve the strength and the deformation abilityof the RC columns therefore this should be consideredwhen accounting for seismic loads in RC columns

35 Stiffness Degradation Stiffness degradation of a speci-men under cyclic loading is usually attributable to the ac-cumulation of specimen damage which has great influence

SC-1SC-2SC-3

SC-4SC-5SC-6

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

Figure 8 Skeleton curves of specimens Skeleton curves representthe outer winding line of the peak loading point of each stage

Δ (mm)

AB

D

P (k

N)

Pmax

Py085Pmax

Δy Δm Δu

C

O

Figure 9 Calculation of characteristic points for each specimen Pyis the yield load Pmax is the peak load

Advances in Civil Engineering 9

on the seismic performance of the specimens Here thesecant stiffness (Ki) was used to represent the stiffnessdegradation of the specimens (e secant stiffness Ki wascalculated as

Ki P

+i

11138681113868111386811138681113868111386811138681113868 + P

minusi

11138681113868111386811138681113868111386811138681113868

Δ+i

11138681113868111386811138681113868111386811138681113868 + Δminus

i

11138681113868111386811138681113868111386811138681113868 (1)

where Pi+ and Pminusi are the i-th positive and reverse peak loads

respectively and Δi+ and Δminusi are the i-th positive and reverse

peak displacements(e stiffness degradation curve of each test piece is

shown in Figure 10 As loading displacement increased thestiffness of each specimen gradually decreased (e stiffnessdegraded rapidly in the early stage and slowly in the laterstage (is could be due to the continuous cracking ofconcrete in the early stage of loading whereas no new crackswere generated in the late loading stages thus when thecumulative damage of the specimen reached a certain de-gree the slope of the stiffness degradation curve of thespecimen decreased Compared to specimen SC-1 thestiffness of specimen SC-2 degraded faster (is is becausethe oblique horizontal loading caused damage in the cornerof the specimen affecting each other In contrast to speci-men SC-2 the stiffness of specimen SC-3 decreased sharplyin the later stage of loading (is is due to the higher axialcompression ratio of the specimen which caused the con-crete to fall severely the stirrups to protrude and thelongitudinal bars to yield(e stiffness degradation curves ofSC-4 SC-5 and SC-6 had a slower downward trend and alonger curve extension compared to those of SC-3 (isindicates that the high-strength stirrups with small spacingthe column-end wound CFRP and the column-end outersteel plate mesh may have alleviated the damage degree ofthe specimen and thus slowed the degradation stiffnessdegradation of these specimens

36 Energy Dissipation (e energy dissipation capacity ofspecimens under earthquake action is an important indexfor evaluating their seismic performance Here the equiv-alent viscous damping coefficient (he) and cumulative energy

consumption (Ep) were used to characterize the energydissipation performance of the experimental specimens (eequivalent viscous damping coefficient characterizes theenergy dissipation performance of specimens at differentloading stages the cumulative energy consumption char-acterizes the overall energy dissipation capacity of specimensduring the whole loading process

As shown in Figure 11 the area of each hysteresis loop inthe hysteresis curve represents the energy-consuming ca-pacity of the specimens under this cycle When otherconditions are the same the larger the area of the hysteresisloop the better the energy consumption capability of thespecimen (e equivalent viscous damping coefficient he ofspecimens is calculated as

he 12π

timesSABC + SCDA

SODG + SOBH

(2)

Table 5 Experimentally derived characteristic loads and displacements for specimens SC-1 through SC-6

Specimen Loading direction Py (kN) Δy (mm) Pm (kN) Δm (mm) Pu (kN) Δu (mm) θμ () Relative value

SC-1 + 41650 986 49250 1820 46794 2500 417 1minus 40045 1205 47286 1819 46973 2500 417

SC-2 + 39470 938 46600 1817 41363 2500 417 1minus 38188 1066 45985 1820 44323 2500 417

SC-3 + 40820 850 47005 1820 44397 2000 333 080minus 41037 868 48192 1500 40963 2000 333

SC-4 + 43773 696 50493 1500 42919 3184 531 135minus 40828 972 48311 2500 41064 3595 599

SC-5 + 50121 917 57802 1820 49132 3223 761 134minus 43456 1113 51965 2800 48294 3500 798

SC-6 + 46587 1151 53813 2499 45741 4563 537 187minus 48357 1443 56164 3200 47739 4790 583

Note Py is the yield load Δy is the yield displacement Pm is the peak load Δm is the peak displacement Pu is the ultimate load Δu is the ultimate displacementand θμ is the deformation ability

100

80

60

40

20

0

Ki (k

Nm

m)

ndash10 0 10 20 30 40 50 60 70∆ (mm)

SC-1SC-2SC-3

SC-4SC-5SC-6

Figure 10 Stiffness degradation curves of specimens Stiffnessdegradation of the specimens is represented by secant stiffness Ki

10 Advances in Civil Engineering

As shown in Figure 12 the equivalent viscous dampingcoefficient (he) of the specimen and the displacement (Δ)curve of the column end were calculated for each specimenAt the initial stage of loading the energy consumption of thespecimen increased as the loading displacement increasedWhen the specimen was cracked stress redistribution oc-curred inside the specimen thereby impacting the stress anddeformation of the specimen and decreasing the energyconsumption As the loading displacement continued toincrease the crack continued opening and closing thusincreasing the energy consumption of the specimen Whenthe specimen yielded the internal longitudinal reinforce-ment of the specimen yielded and the stress redistributionoccurred again inside the specimen thus decreasing theenergy consumption of the specimen With continuousloading cracks of the specimen kept opening and closingand energy consumption continued increasing until thespecimen was destroyed (e equivalent viscous dampingcoefficient of each specimen increased as a whole whichindicated that the damage of the specimen increased as thehorizontal deformation increased during the loading pro-cess thereby increasing the energy consumption of thespecimen (Figure 12)

Cumulative energy consumption refers to the sum of allhysteresis loop areas generated from the beginning of theload application to the ultimate displacement point (elarger the value the stronger the energy dissipation capacityof the specimen and the better the seismic performance Asshown in Table 6 the cumulative energy dissipation wascalculated for each specimen

In contrast to SC-1 the cumulative energy consumptionof SC-2 increased by 37 indicating that the obliquehorizontal loading led to more serious cumulative damageand the consumption of more energy Compared to SC-2the accumulated energy consumption value of SC-3 de-creased by approximately 16 possibly due to the pre-mature failure of specimen and the increase of the axialpressure ratio which reduces the cumulative energy con-sumption capacity of specimen In contrast to specimen SC-3 the cumulative energy consumption values of specimensSC-4 SC-5 and SC-6 all improved with increase rates of222 278 and 412 respectively (is is because high-

strength stirrups with small spacing wound CFRP at the endof the column and steel plate mesh at the end of the columnlimit the shedding of concrete and thus increase the work ofthe concrete

37 OpenSees Finite Element Simulation (e open-sourcefinite element program OpenSees (Open System forEarthquake Engineering Simulation) was used as a platformto numerically simulate the experimental specimens (emodel used displacement-based nonlinear beam-columnelements (ree nodes along the height of the column wereused to form two units wherein the top node was free endand the bottom node was embedded (e P-Delta effectcaused by the vertical load was considered by the P-Del-taCrdTransf command (e fiber model was used to definethe relationship of the cross section restoring force at theunit integration point (e longitudinal reinforcement wasmodeled using the Reinforcing Steel uniaxial materialprovided in OpenSees which was based on the Chang-Mander uniaxial material model [21] and simulated theisotropic hardening behavior of steel bars (e concrete wassimulated by Concrete 02 provided by OpenSees (e ma-terial was based on the Kent-Scott-Park uniaxial material

A OG

D

B

C H Δ

P

Figure 11 PminusΔ hysteretic curve representing the energy-con-suming capacity of the specimen

Table 6 Accumulated dissipated energy (Ep) of all specimens

Specimen Ep (kNmiddotmm) Relative valueSC-1 49770 1SC-2 68307 137SC-3 41784 084SC-4 160490 322SC-5 187933 378SC-6 254794 512

SC-1SC-2SC-3

SC-4SC-5SC-6

004

006

008

010

012

014

016

018

020

022

024

he

0 10 20 30 40 50 60 70ndash10∆ (mm)

Figure 12 Viscous damping coefficient curves of each specimen(e equivalent viscous damping coefficient (he) of the specimenand the displacement (Δ) curve of the column end were calculatedfor each specimen

Advances in Civil Engineering 11

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

(a)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

(b)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

(c)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

(d)

Figure 13 Continued

12 Advances in Civil Engineering

model [22] (e model included the tensile mechanicalproperties of the concrete the stiffness degradation and theenergy dissipation behavior of the concrete during recip-rocating loading For the concrete in the core area theMander model [2324] was used to consider the restrainingeffect of stirrups on concrete Here the stress-strain rela-tionship of CFRP-constrained concrete was establishedusing the Concrete 02 material (e stress and strain at thepeak point were the same as the peak-point stress and strainof the concrete bound by the stirrup (e stress and strain atthe limit point were calculated using the peak-point stressand strain of the Lam-Teng model [2526] (ere was littleresearch on concrete columns reinforced by steel plate meshand no specific theoretical models Based on the existingsteel mesh reinforced concrete column the Concrete 02material in this study was used to establish the stress-strainrelationship of the steel plate mesh to the concrete equations(3) and (4) were used to calculate the peak concrete stress fccafter confinement [19] (e peak strain was 4 times that ofthe peak stress of unconstrained concrete the limit pointstress was twice that of the ultimate stress of unconstrainedconcrete the calculations of the remaining characteristicparameters were consistent with the calculation results of theunconstrained concrete

fcc 1 + 077λv( 1113857fck (3)

λv ρvfyv

fck

(4)

where fck is the axial compressive strength of the concrete λv isthe eigenvalue of the stirrup fyv is the yield strength of the steelplate mesh and ρv is the volumetric ratio of the steel plate mesh

(e vertical load was applied incrementally in 10 stepsusing the gravity loading module provided by OpenSees and

was held constant after the vertical load was completed (ehorizontal load was applied in time series and the loadingsystem was consistent with the experimental proceduresused in this study

(e hysteresis curves for SC-1 through SC-6 generatedby the OpenSees finite element analysis were compared tothe experimentally generated hysteresis curves as shown inFigure 13 (e curves generated by OpenSees are in goodagreement with the experimental results

4 Conclusion

Here six short concrete columns with high-strength lon-gitudinal reinforcements were subjected to low-cycle re-peated loading tests By comparing and analyzing the testresults based on observed test phenomena the followingconclusions are drawn

(1) Compared to the horizontally loaded test specimensthe strength of the diagonally loaded specimensdecreased and the stiffness degradation trendaccelerated this indicates that the effect of obliqueloading is unfavorable to the strength and stiffness ofthe specimens

(2) Under the action of oblique load as the axialcompression ratio increases the strength of thespecimen increases however the deformation ca-pacity becomes worse the stiffness becomes severelydegraded and the specimen is prone to shear brittlefailure

(3) Under the action of oblique load the reinforcementmeasures of the CFRP at the end of the columnimprove the strength and energy consumption of thespecimen however the higher axial compression

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(e)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(f)

Figure 13 OpenSees finite element simulations compared with the experimentally derived hysteresis curve for each specimen Resultscomparison of (a) SC-1 (b) SC-2 (c) SC-3 (d) SC-4 (e) SC-5 and (f) SC-6

Advances in Civil Engineering 13

ratio makes the CFRP more prone to damage anddoes not improve the deformation performance ofthe specimen However the local reinforcementmeasures of the steel plate mesh on the end of thecolumn not only increase the strength and energyconsumption of the specimen but also improve thedeformation ability of the specimen and the seismicperformance of the specimen

(4) In contrast to the unreinforced specimens theaddition of the high-strength stirrups with smallspacing column-end wound CFRP and column-end outer steel plate mesh all improve the strengthdeformation capacity and energy consumptioncapacity of the specimens (e addition of the high-strength stirrups with small spacing and the col-umn-end outer steel plate mesh both altered thefailure mode of the specimen transforming it fromshear failure to bending shear failure (is showsthat the above measures can effectively improve theseismic performance of the test specimen under theaction of oblique loads with a high axial com-pression ratio

(5) Under the action of a high axial pressure ratiooblique load by selecting the appropriate fiber unitand material constitutive relationship the OpenSeesprogram can obtain a simulation result that is ingood agreement with the test hysteresis curve (isverifies the validity of the numerical simulation andprovides a certain basis for subsequent and extendednumerical simulation analyses

Data Availability

All data or models used to support the findings of this studyare included within the article Some data or models thatsupport the findings of this study are available from thecorresponding author upon reasonable request

Conflicts of Interest

(e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

(is work was supported by the Natural Science Foundationof Shandong Province under Grant nos ZR2015EQ017 andZR2018MEE044 and Off-Campus Development Project ofKey Laboratory of Beijing University of Technology underGrant no 2020B03 (e authors are grateful to the KeyLaboratory of Building Structural Retrofitting and Under-ground Space Engineering (Shandong Jianzhu University)Ministry of Education for accommodating the use of theequipment and facilities Professor Xingquan Zhao forproviding computer equipment for numerical simulation ofthe experiment and Editage (httpwwweditagecn) forEnglish language editing

References

[1] A Ghobarah and K Galal ldquoSeismic rehabilitation of shortrectangular RC columnsrdquo Journal of Earthquake Engineeringvol 8 no 1 pp 45ndash68 2004

[2] Y A Li T Y Huang and S J Hwang ldquoSeismic response ofreinforced concrete short columns failed in shearrdquo ACIStructural Journal vol 111 no 4 pp 945ndash954 2014

[3] H Takizawa and H Aoyama ldquoBiaxial effects in modellingearthquake response of RC structuresrdquo Earthquake Engi-neering amp Structural Dynamics vol 4 no 6 pp 523ndash5521976

[4] H Umehara and J O Jirsa ldquoShort rectangular RC columnsunder bidirectional loadingsrdquo Journal of Structural Engi-neering vol 110 no 3 pp 605ndash618 1984

[5] K A Woodward and J O Jirsa ldquoInfluence of reinforcementon RC short column lateral resistancerdquo Journal of StructuralEngineering vol 110 no 1 pp 90ndash104 1984

[6] K Maruyama H Ramirez and J O Jirsa ldquoShort RC columnsunder bilateral load historiesrdquo Journal of Structural Engi-neering vol 110 no 1 pp 120ndash137 1984

[7] H Rodrigues H Varum A Arede and A G CostaldquoBehaviour of reinforced concrete column under biaxial cyclicloadingmdashstate of the artrdquo International Journal of AdvancedStructural Engineering vol 5 no 1 pp 1ndash12 2013

[8] D Wang L Huang T Yu and Z Wang ldquoSeismic perfor-mance of CFRP-retrofitted large-scale square RC columnswith high axial compression ratiosrdquo Journal of Composites forConstruction vol 21 no 5 Article ID 04017031 2017

[9] J Yang and J Wang ldquoSeismic performance of shear-con-trolled CFRP-strengthened high-strength concrete squarecolumns under simulated seismic loadrdquo Journal of Compositesfor Construction vol 22 no 6 Article ID 04018061 2018

[10] X Zhou and J Liu ldquoSeismic behavior and shear strength oftubed RC short columnsrdquo Journal of Constructional SteelResearch vol 66 no 3 pp 385ndash397 2010

[11] H Ma J Xue Y Liu and X Zhang ldquoCyclic loading tests andshear strength of steel reinforced recycled concrete shortcolumnsrdquo Engineering Structures vol 92 pp 55ndash68 2015

[12] D Sokoli and W M Ghannoum ldquoHigh-strength reinforce-ment in columns under high shear stressesrdquo ACI StructuralJournal vol 113 no 3 pp 605ndash614 2016

[13] H Ding Y Liu C Han and Y Guo ldquoSeismic performance ofhigh-strength short concrete column with high-strengthstirrups constraintsrdquo Transactions of Tianjin Universityvol 23 no 4 pp 360ndash369 2017

[14] H O Shin Y S Yoon W D Cook and D Mitchell ldquoAxialload response of ultra-high-strength concrete columns andhigh-strength reinforcementrdquo Transactions of Tianjin Uni-versity vol 113 no 2 pp 325ndash336 216

[15] L A E Shehata M L A V Carneiro and L C D ShehataldquoStrength of short concrete columns confined with CFRPsheetsrdquo Materials and Structures vol 35 pp 50ndash58 2002

[16] F Colomb H Tobbi E Ferrier and P Hamelin ldquoSeismicretrofit of reinforced concrete short columns by CFRPmaterialsfit of reinforced concrete short columns by CFRPmaterialsrdquo Composite Structures vol 82 no 4 pp 475ndash4872008

[17] K Galal A Arafa and A Ghobarah ldquoRetrofit of RC squareshort columnsrdquo Engineering Structures vol 27 no 5pp 801ndash813 2005

[18] R Morshed and M T Kazemi ldquoSeismic shear strengtheningof RC beams and columns with expanded steel meshesrdquo

14 Advances in Civil Engineering

Table 1 Design parameters of specimens

Specimen α (deg) n Strengthening measuresStirrup

Stirrup grade Diameter spacing (mm) ρv ()

SC-1 0 08 mdash HRB400 880 190SC-2 45 08 mdash HRB400 880 190SC-3 45 10 mdash HRB400 880 190SC-4 45 10 mdash HTRB630 850 305SC-5 45 10 A HTRB630 850 305SC-6 45 10 B HTRB630 850 305Note SC short column α loading direction nNfcbh where N is the design value of axial pressure fc is the design value of concrete strength b is thecolumn section width and h is the column section height ρv is the rebar ratio

1-1

1 1

300

14001400550 300 550

450450

450

450

500

600

1325

225

500

600

1325

225

300

Pedestal

Speci-men

Load endblock

C 880

C 880

C 880

4DH16

otimesotimes

(a)

1-1

500

600

1325

225

300

300

1400488 488424

450

450

Pedestal

Specimen

Load endblock

1 11

1400

450

450

500

600

1325

225

4DH16

C 880

C 880

C 880

otimesotimes

(b)

1-1

500

600

1325

225

300

300

1400488 488424

450

450

Pedestal

Specimen

Load endblock

11

1400

450

450

500

600

1325

225

4DH 16

DH 850

DH 850

DH 850

otimesotimes

(c)

Figure 1 Schematics of prepared specimens ie short column-1 (SC-1) through SC-6 including arrangement of reinforcing barsDH HTRB630 steel bar and CHRB400 steel bar otimes horizontal load loading point (a) SC-1 (b) SC-2 SC-3 (c) SC-4 SC-5 and SC-6

Advances in Civil Engineering 3

axial compression ratio have the challenge of prematureyielding and short-column brittle failure HRB400 andHTRB630 rebars were selected for this test (e mechanicalproperties of the concrete used in this study (outlined inTable 2) were held constant whereas the mechanicalproperties of the three types of steel bars (outlined in Table 3)and the two types of reinforcing materials (outlined inTable 4) were previously characterized

Production of the specimens SC-1 through SC-4 in-volved first ligating the longitudinal reinforcements and thestirrups to form a steel cage Formwork and concretepouring were then completed To facilitate test loadingobliquely loaded column sections were placed at a 45deg to thebase Specimen SC-5 involved wrapping the end of thecolumn with CFRP which had a single layer thickness of011mm and a total of three layers totaling 200mm in totalheight At the time of construction the steel bars were firsttied to form a steel cage the concrete was then poured andcured To avoid tearing of the CFRP the chamfer radius ofthe corner was 25mm(is method was used to improve therestraint effect of the column-end concrete as well as toimprove the seismic performance of the specimen

SC-6 involved reinforcement with a column-end outersteel plate mesh (e steel plate mesh adopted a round holesteel plate mesh with a wrapping height of 300mm athickness of 3mm a circular hole diameter of 5mm and ahole pitch of 5mm which was processed into a squarepattern (Figure 2(a)) First the U-shaped snap fastener wasplaced on the longitudinal bar and fixed at the joint of thelongitudinal reinforcement and the stirrup passing throughthe screw and tightening the nut (Figures 2(b) and 2(c))(en the steel plate mesh was placed on the outer side of thesteel skeleton to make the inner surface of the steel platemesh tightly attached to the outer side of the U-shaped snapfastener (Figure 2(d)) To ensure that the steel plate mesh didnot participate in the force of the column end a 5mm gapwas left between the end portion and the column base Afterplacement the steel plate mesh was fixed with local windingwires After construction of the steel skeleton the concretewas poured resulting in the surface of the column beingflush with the surface of the steel plate mesh (is methodwas used to improve the restraining effect on the column-end concrete and to improve the seismic performance of thespecimen

22 Load Method Vertical loads were applied in the axialdirection using a 200 ton vertical actuator and held con-stant at the designated axial compression ratios(e actuatorused was made in China (e horizontal load tests wereconducted by adopting the low-cycle repeated loadingmode(e tests were performed by conducting displacement-controlled loading with the displacement cycle loaded twiceper stage until the load dropped to either 85 of the peakload or to the point at which the specimen was not suitablefor carrying the load (Figure 3) It was assumed that positiveforce and displacement were produced by the thrust of theactuator and that negative force and displacement wereproduced by the pull force caused by the actuator (e

loading displacement of the column-end load point wasimplemented by an MTS 100 ton horizontal actuator (isactuator was made in the United States and incorporates anassociated data acquisition system that collects the load anddisplacement data (Figure 4) Collected data were used togenerate a hysteresis curve Cracks on the specimen werevisually observed and manually mapped

3 Experimental Results and Analysis

31 Failure Modes Application of loads resulted in variablestates of damage to all specimens tested in this study basedon visual observations (e definition of the observationsurface of each specimen is shown in Figure 5 (e finalfailure mode of each specimen is shown in Figure 6

For specimen SC-1 small horizontal cracks appearedwithin a range of 300mm from the column bottom when thehorizontal displacement of the column top was loaded to15mm as the loading continued the number of cracksincreased At 182mm the concrete at the bottom corner ofthe column fell off and some longitudinal reinforcementsand stirrups were exposed When specimen was broken thelongitudinal reinforcements in the southwest corner brokeAccordingly specimen SC-1 has obvious shear failurecharacteristics (Figure 6(a)) Regarding specimen SC-2 at15mm small horizontal cracks appeared within a range of150mm from the column bottom as the loading continuedhorizontal cracks developed into oblique cracks and thenumber of cracks increased At 182mm the concrete in thecorner of the column fell off and some longitudinal rein-forcements and stirrups were exposed When the specimenwas broken the corner concrete severely fell off and thelongitudinal reinforcement in the corners in the east andwest directions broke Accordingly specimen SC-2 hasobvious shear failure characteristics (Figure 6(b)) Regarding

Table 2 Mechanical properties of the concrete

Concrete grade fcuk (MPa) fck (MPa) Ec (MPa)C40 604 453 360times104

Note fcuk is the compressive strength of concrete cubes fck is the com-pressive strength of concrete prism Ec is the elastic modulus of concrete

Table 3 Mechanical properties of reinforced bars

Steel bartype

Diameter(mm)

fy(MPa)

fu(MPa) δ () Es (MPa)

HRB400 8 488 640 2625 202times105

HTRB630 8 601 855 238 229times105

HTRB630 16 668 845 230 245times105

Note fy is the rebar yield strength fu is the rebar ultimate strength δ is therebar elongation after breaking and Es is the rebar modulus of elasticity

Table 4 Mechanical properties of strengthening material

Material type (ickness(mm) fy (MPa) fu (MPa) Es (MPa)

Steel plate mesh 3 208 313 168times105

CFRP 0167 ndash 3471 231times 105

4 Advances in Civil Engineering

specimen SC-3 at 15mm small horizontal cracks appearedwithin a range of 200mm from the columnrsquos bottom whenthe loading continued the number of cracks increased andpenetration cracks appeared At 15mm the concrete fell offand some longitudinal reinforcements and stirrups wereexposedWhen the specimen was broken the concrete in thecore area had been crushed and some longitudinal rein-forcements were broken Accordingly specimen SC-3 hasobvious shear failure characteristics (Figure 6(c))

Regarding specimen SC-4 at 15mm small horizontalcracks appeared within a range of 150mm from the columnbottom as the loading continued the number of cracksincreased At 32mm the northwest concrete began to fall offand the longitudinal tendons broke When the specimen wasdamaged the concrete at the bottom corner of the column inthe east and west directions was crushed and the

longitudinal tendons broke Accordingly the bending andshear failure characteristics of specimen SC-4 can be seen(Figure 6(d)) Regarding specimen SC-5 at 15mm cracksappeared on the edge of the CFRP when the loadingcontinued the number of cracks increased and penetratingcracks appeared At 182mm the concrete started to fall offand the carbon fiber cloth cracked When specimen wasbroken the concrete at the bottom corner of the column inthe east and west directions was crushed (Figure 6(e)) Afterthe test the carbon fiber cloth was peeled off it was foundthat the column-angle concrete had been significantlybroken diagonally and the longitudinal tendons and stirrupshad become exposed Accordingly specimen SC-5 has shearfailure characteristics (Figure 6(f )) Regarding specimen SC-6 at 3mm cracks appeared on the edge of the steel platemesh as loading continued the number of cracks increased

(a)

90degbending part

Longitudinalreinforcement

Stirrups

NutScrew

Longitudinal reinforcement

U-shaped snap fastener

Steel plate mesh Limit switch

(b)

Longitudinalreinforcement

Stirrups

U-shaped snap

(c)

Steelskeleton

Steel planemesh

(d)

Figure 2 Details of steel skeleton production (a) Steel plate mesh (b) limit device floor plan (c) steel skeleton with U-shaped snap fastenerand (d) steel skeleton with steel plate mesh

Advances in Civil Engineering 5

Disp

lace

men

t (m

m)

Loading cycle

1 24 486

12182 22

28 3238

4350

ndash15 ndash3 ndash6ndash10

ndash15 ndash20ndash25

ndash30ndash35

ndash40ndash45

ndash60

Figure 3 Loading protocol (e tests performed via displacement-controlled loading

Reaction frame

Lifting jackConnector

Steel backing plate

MTSScrew

Steel plate

Electronic displacement meter

Spec

imen

Pedestal

Anchor boltStatic platform

Reac

tion

wal

l

Figure 4 Experimental test set-up MTS actuator with data acquisition system collects load and displacement data

S

N

WE

Specimen

y

x

Pull Push

(a)

Specimen

y xS

N

E W

Pull Push

(b)

Figure 5 Definition of specimen observation surface (a) Spindle loading (b) 45deg loading

6 Advances in Civil Engineering

At 40mm the longitudinal reinforcement was brokenWhen the specimen was broken the steel plate mesh at thebottom of the column was convex (Figure 6(g)) After thetest the steel plate mesh was peeled off it was found that theconcrete at the bottom of the column was broken and thelongitudinal steel bars were convex and partially brokenAccordingly the bending and shear failure characteristics ofspecimen SC-6 can be seen (Figure 6(h))

Overall compared with the horizontally loaded testspecimens the concrete at the corners of the diagonallyloaded test specimens fell off severely which reduced theworkability of the test specimens In particular the increasein the axial pressure ratio makes this damage more seriousCompared to the unreinforced test specimens high-strengthstirrups with small spacing column-end wrapped CFRPand column-end outer steel plate mesh enhanced the re-straint effect on concrete limited concrete falling off andimproved the seismic performance of the specimens underoblique loads

32 Hysteresis Curves (e load-displacement hysteresiscurves of each specimen demonstrate the performance ofeach specimen during the duration of the tests (Figure 7) Pis the measured horizontal load Δ is the measured hori-zontal displacement of the loading point As can be seenfrom Figure 7 compared to specimen SC-1 specimen SC-2undergoes accelerated strength degradation at a later stage ofloading and the residual deformation is larger(is could beattributed to the oblique loading that leads to the corner

concrete of the specimen being subjected to loads in twodirections resulting in serious damage to the corner con-crete (Figures 7(a) and 7(b)) In contrast to specimen SC-2specimen SC-3 has a significantly lower load at the later stageof loading this is due to the severe fall of the concrete at thelater stage of loading (Figures 7(b) and 7(c)) (ere were twosignificant drops in the hysteresis curves of SC-4 and SC-6likely due to the fracture of the high-strength longitudinalbars which led to a significant decline in the strength ofthese specimens (Figures 7(d) and 7(f)) However the high-strength stirrups with small spacing included in thesetreatments provided a strong constraint effect for high-strength longitudinal bars that enabled the specimens toretain a strong strength Compared to the hysteresis curve ofspecimen SC-4 that of specimen SC-5 is less full (is isbecause the CFRP is prone to tear and damage at the columnangle under a high axial pressure ratio (Figures 7(d) and7(e)) which causes the strength of the specimen to dropsharply In contrast to specimen SC-4 the load of specimenSC-6 decreases slowly at the later stage of loading and thehysteresis curve was relatively plump (Figures 7(d) and 7(f ))(is is because the steel plate net at the end of the columncan effectively slow the fall of concrete and exert a strongerenergy consumption

33 Skeleton Curves In the hysteretic curve under thecondition of low-cycle reciprocating loading the outerwinding line of the peak loading point of each stage is calleda skeleton curve which characterizes the characteristics of

Ordinary comparison

specimen

(a)

α = 45deg

n = 08

(b)

α = 45deg

n = 10

(c)

Dense high-strength stirrups

α = 45deg

n = 10

(d)

CFRP constraint

α = 45deg

n = 10

(e)

Remove CFRP

α = 45deg

n = 10

(f )

α = 45deg

n = 10

Steel plate mesh constraint

(g)

Remove steel plate mesh

α = 45deg

n = 10

(h)

Figure 6 Visual observations of the ultimate failure modes of short column (SC) specimens (a) SC-1 (b) SC-2 (c) SC-3 (d) SC-4 (e) SC-5(f ) SC-5 after removal of CFRP (g) SC-6 and (h) SC-6 after removal of steel plate mesh

Advances in Civil Engineering 7

stress and deformation during the loading of the specimen(e skeleton curve of each specimen is shown in Figure 8 Ascan be seen from the figure the development of the skeleton

curves of each specimen can be roughly divided into threestages (1) In the elastic stage the load changes linearly withthe displacement the specimen has yet to crack and no

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(a)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(b)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

(c)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(d)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

(e)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(f )

Figure 7 Hysteretic curves of short column (SC) specimens 1ndash6 (a) SC-1 (b) SC-2 (c) SC-3 (d) SC-4 (e) SC-5 and (f) SC-6

8 Advances in Civil Engineering

residual deformation is observed (2) During the develop-ment stage of a multicrack many cracks appear in thespecimen When residual deformation begins to appearmultiple tiny cracks appear on the surface of the specimenand the horizontal load of the specimen slowly increasesWith the accumulation of damage the specimen reaches thepeak load (3) In the load drop stage for specimens SC-1SC-2 and SC-3 the skeleton curve decreases significantly inthe later stage of loading (is is because the ordinarystirrups with large spacing cannot provide effective lateralrestraints for the specimens under a high axial compressionratio thus making the strength of the specimens dropdramatically Compared to specimen SC-3 the skeletoncurves of specimens SC-4 SC-5 and SC-6 decrease slowlyand show good deformation ability In particular the de-formation capacity of specimens SC-4 and SC-6 after thepeak point significantly improves this is conducive toimproving the seismic energy dissipation capability ofspecimens

34 Bearing Capacity and Ductility Each sample wascharacterized by the yield load point the peak load pointand the failure load point within a load-displacement curveAs shown in Figure 9 the yield point D was determined bythe equivalent elastic-plastic energy method that is wherethe area SOAB SBCD and the ultimate load was simplydefined as 85 of the peak load [20] Because the strength ofSC-1 SC-2 and SC-3 declined rapidly after reaching thepeak load and the ultimate load did not reach 85 of thepeak load the failure displacements of these were taken asthe ultimate displacement Here the ultimate displacementangle (θμ) was used to characterize the deformation ability ofthe specimen and was calculated as θμ Δul0 where l0 is thecolumnrsquos height For each specimen the characteristic loadand displacement calculation results are shown in Table 5

(e relative value is the ratio of the average of the positiveand negative corresponding coefficients of SC-2 through SC-6 and the average of the positive and negative correspondingcoefficients of SC-1

As can be seen in Table 5 compared to specimen SC-1the yield load peak load and ultimate load of specimen SC-2are reduced and the ultimate displacement angle is un-changed(is is because the concrete in the corner of the testspecimen is severely damaged under the diagonal horizontalloading making the strength of the specimen decreasehowever this has no effect on the deformation ability of thespecimen A comparison of SC-2 and SC-3 reveals thatunder the oblique load as the axial pressure ratio increasesthe strength of the specimen increases but the deformationcapacity decreases In contrast to specimen SC-4 the yieldload peak load and ultimate load of SC-5 improvedwhereas the ultimate displacement angle decreased by 1(is result indicates that although the strength of thespecimen under high axial pressure ratio improved thedeformation capacity of the specimen under high axialpressure ratio did not improve Compared to specimen SC-4 the yield load peak load and ultimate load of specimenSC-6 improved and the ultimate displacement angle in-creased by 52(is result was likely due to the column-endouter steel plate mesh providing a strong restraining effecton the column-end concrete which then increased thespecimenrsquos strength deformation capacity and seismicperformance

In comparison to SC-3 the yield load peak load andultimate load of SC-4 SC-5 and SC-6 were all greatlyimproved as were the ultimate displacement angles (isindicates that the high-strength stirrups with small spacingcolumn-end wound CFRP and column-end outer steel platemesh may improve the strength and the deformation abilityof the RC columns therefore this should be consideredwhen accounting for seismic loads in RC columns

35 Stiffness Degradation Stiffness degradation of a speci-men under cyclic loading is usually attributable to the ac-cumulation of specimen damage which has great influence

SC-1SC-2SC-3

SC-4SC-5SC-6

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

Figure 8 Skeleton curves of specimens Skeleton curves representthe outer winding line of the peak loading point of each stage

Δ (mm)

AB

D

P (k

N)

Pmax

Py085Pmax

Δy Δm Δu

C

O

Figure 9 Calculation of characteristic points for each specimen Pyis the yield load Pmax is the peak load

Advances in Civil Engineering 9

on the seismic performance of the specimens Here thesecant stiffness (Ki) was used to represent the stiffnessdegradation of the specimens (e secant stiffness Ki wascalculated as

Ki P

+i

11138681113868111386811138681113868111386811138681113868 + P

minusi

11138681113868111386811138681113868111386811138681113868

Δ+i

11138681113868111386811138681113868111386811138681113868 + Δminus

i

11138681113868111386811138681113868111386811138681113868 (1)

where Pi+ and Pminusi are the i-th positive and reverse peak loads

respectively and Δi+ and Δminusi are the i-th positive and reverse

peak displacements(e stiffness degradation curve of each test piece is

shown in Figure 10 As loading displacement increased thestiffness of each specimen gradually decreased (e stiffnessdegraded rapidly in the early stage and slowly in the laterstage (is could be due to the continuous cracking ofconcrete in the early stage of loading whereas no new crackswere generated in the late loading stages thus when thecumulative damage of the specimen reached a certain de-gree the slope of the stiffness degradation curve of thespecimen decreased Compared to specimen SC-1 thestiffness of specimen SC-2 degraded faster (is is becausethe oblique horizontal loading caused damage in the cornerof the specimen affecting each other In contrast to speci-men SC-2 the stiffness of specimen SC-3 decreased sharplyin the later stage of loading (is is due to the higher axialcompression ratio of the specimen which caused the con-crete to fall severely the stirrups to protrude and thelongitudinal bars to yield(e stiffness degradation curves ofSC-4 SC-5 and SC-6 had a slower downward trend and alonger curve extension compared to those of SC-3 (isindicates that the high-strength stirrups with small spacingthe column-end wound CFRP and the column-end outersteel plate mesh may have alleviated the damage degree ofthe specimen and thus slowed the degradation stiffnessdegradation of these specimens

36 Energy Dissipation (e energy dissipation capacity ofspecimens under earthquake action is an important indexfor evaluating their seismic performance Here the equiv-alent viscous damping coefficient (he) and cumulative energy

consumption (Ep) were used to characterize the energydissipation performance of the experimental specimens (eequivalent viscous damping coefficient characterizes theenergy dissipation performance of specimens at differentloading stages the cumulative energy consumption char-acterizes the overall energy dissipation capacity of specimensduring the whole loading process

As shown in Figure 11 the area of each hysteresis loop inthe hysteresis curve represents the energy-consuming ca-pacity of the specimens under this cycle When otherconditions are the same the larger the area of the hysteresisloop the better the energy consumption capability of thespecimen (e equivalent viscous damping coefficient he ofspecimens is calculated as

he 12π

timesSABC + SCDA

SODG + SOBH

(2)

Table 5 Experimentally derived characteristic loads and displacements for specimens SC-1 through SC-6

Specimen Loading direction Py (kN) Δy (mm) Pm (kN) Δm (mm) Pu (kN) Δu (mm) θμ () Relative value

SC-1 + 41650 986 49250 1820 46794 2500 417 1minus 40045 1205 47286 1819 46973 2500 417

SC-2 + 39470 938 46600 1817 41363 2500 417 1minus 38188 1066 45985 1820 44323 2500 417

SC-3 + 40820 850 47005 1820 44397 2000 333 080minus 41037 868 48192 1500 40963 2000 333

SC-4 + 43773 696 50493 1500 42919 3184 531 135minus 40828 972 48311 2500 41064 3595 599

SC-5 + 50121 917 57802 1820 49132 3223 761 134minus 43456 1113 51965 2800 48294 3500 798

SC-6 + 46587 1151 53813 2499 45741 4563 537 187minus 48357 1443 56164 3200 47739 4790 583

Note Py is the yield load Δy is the yield displacement Pm is the peak load Δm is the peak displacement Pu is the ultimate load Δu is the ultimate displacementand θμ is the deformation ability

100

80

60

40

20

0

Ki (k

Nm

m)

ndash10 0 10 20 30 40 50 60 70∆ (mm)

SC-1SC-2SC-3

SC-4SC-5SC-6

Figure 10 Stiffness degradation curves of specimens Stiffnessdegradation of the specimens is represented by secant stiffness Ki

10 Advances in Civil Engineering

As shown in Figure 12 the equivalent viscous dampingcoefficient (he) of the specimen and the displacement (Δ)curve of the column end were calculated for each specimenAt the initial stage of loading the energy consumption of thespecimen increased as the loading displacement increasedWhen the specimen was cracked stress redistribution oc-curred inside the specimen thereby impacting the stress anddeformation of the specimen and decreasing the energyconsumption As the loading displacement continued toincrease the crack continued opening and closing thusincreasing the energy consumption of the specimen Whenthe specimen yielded the internal longitudinal reinforce-ment of the specimen yielded and the stress redistributionoccurred again inside the specimen thus decreasing theenergy consumption of the specimen With continuousloading cracks of the specimen kept opening and closingand energy consumption continued increasing until thespecimen was destroyed (e equivalent viscous dampingcoefficient of each specimen increased as a whole whichindicated that the damage of the specimen increased as thehorizontal deformation increased during the loading pro-cess thereby increasing the energy consumption of thespecimen (Figure 12)

Cumulative energy consumption refers to the sum of allhysteresis loop areas generated from the beginning of theload application to the ultimate displacement point (elarger the value the stronger the energy dissipation capacityof the specimen and the better the seismic performance Asshown in Table 6 the cumulative energy dissipation wascalculated for each specimen

In contrast to SC-1 the cumulative energy consumptionof SC-2 increased by 37 indicating that the obliquehorizontal loading led to more serious cumulative damageand the consumption of more energy Compared to SC-2the accumulated energy consumption value of SC-3 de-creased by approximately 16 possibly due to the pre-mature failure of specimen and the increase of the axialpressure ratio which reduces the cumulative energy con-sumption capacity of specimen In contrast to specimen SC-3 the cumulative energy consumption values of specimensSC-4 SC-5 and SC-6 all improved with increase rates of222 278 and 412 respectively (is is because high-

strength stirrups with small spacing wound CFRP at the endof the column and steel plate mesh at the end of the columnlimit the shedding of concrete and thus increase the work ofthe concrete

37 OpenSees Finite Element Simulation (e open-sourcefinite element program OpenSees (Open System forEarthquake Engineering Simulation) was used as a platformto numerically simulate the experimental specimens (emodel used displacement-based nonlinear beam-columnelements (ree nodes along the height of the column wereused to form two units wherein the top node was free endand the bottom node was embedded (e P-Delta effectcaused by the vertical load was considered by the P-Del-taCrdTransf command (e fiber model was used to definethe relationship of the cross section restoring force at theunit integration point (e longitudinal reinforcement wasmodeled using the Reinforcing Steel uniaxial materialprovided in OpenSees which was based on the Chang-Mander uniaxial material model [21] and simulated theisotropic hardening behavior of steel bars (e concrete wassimulated by Concrete 02 provided by OpenSees (e ma-terial was based on the Kent-Scott-Park uniaxial material

A OG

D

B

C H Δ

P

Figure 11 PminusΔ hysteretic curve representing the energy-con-suming capacity of the specimen

Table 6 Accumulated dissipated energy (Ep) of all specimens

Specimen Ep (kNmiddotmm) Relative valueSC-1 49770 1SC-2 68307 137SC-3 41784 084SC-4 160490 322SC-5 187933 378SC-6 254794 512

SC-1SC-2SC-3

SC-4SC-5SC-6

004

006

008

010

012

014

016

018

020

022

024

he

0 10 20 30 40 50 60 70ndash10∆ (mm)

Figure 12 Viscous damping coefficient curves of each specimen(e equivalent viscous damping coefficient (he) of the specimenand the displacement (Δ) curve of the column end were calculatedfor each specimen

Advances in Civil Engineering 11

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

(a)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

(b)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

(c)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

(d)

Figure 13 Continued

12 Advances in Civil Engineering

model [22] (e model included the tensile mechanicalproperties of the concrete the stiffness degradation and theenergy dissipation behavior of the concrete during recip-rocating loading For the concrete in the core area theMander model [2324] was used to consider the restrainingeffect of stirrups on concrete Here the stress-strain rela-tionship of CFRP-constrained concrete was establishedusing the Concrete 02 material (e stress and strain at thepeak point were the same as the peak-point stress and strainof the concrete bound by the stirrup (e stress and strain atthe limit point were calculated using the peak-point stressand strain of the Lam-Teng model [2526] (ere was littleresearch on concrete columns reinforced by steel plate meshand no specific theoretical models Based on the existingsteel mesh reinforced concrete column the Concrete 02material in this study was used to establish the stress-strainrelationship of the steel plate mesh to the concrete equations(3) and (4) were used to calculate the peak concrete stress fccafter confinement [19] (e peak strain was 4 times that ofthe peak stress of unconstrained concrete the limit pointstress was twice that of the ultimate stress of unconstrainedconcrete the calculations of the remaining characteristicparameters were consistent with the calculation results of theunconstrained concrete

fcc 1 + 077λv( 1113857fck (3)

λv ρvfyv

fck

(4)

where fck is the axial compressive strength of the concrete λv isthe eigenvalue of the stirrup fyv is the yield strength of the steelplate mesh and ρv is the volumetric ratio of the steel plate mesh

(e vertical load was applied incrementally in 10 stepsusing the gravity loading module provided by OpenSees and

was held constant after the vertical load was completed (ehorizontal load was applied in time series and the loadingsystem was consistent with the experimental proceduresused in this study

(e hysteresis curves for SC-1 through SC-6 generatedby the OpenSees finite element analysis were compared tothe experimentally generated hysteresis curves as shown inFigure 13 (e curves generated by OpenSees are in goodagreement with the experimental results

4 Conclusion

Here six short concrete columns with high-strength lon-gitudinal reinforcements were subjected to low-cycle re-peated loading tests By comparing and analyzing the testresults based on observed test phenomena the followingconclusions are drawn

(1) Compared to the horizontally loaded test specimensthe strength of the diagonally loaded specimensdecreased and the stiffness degradation trendaccelerated this indicates that the effect of obliqueloading is unfavorable to the strength and stiffness ofthe specimens

(2) Under the action of oblique load as the axialcompression ratio increases the strength of thespecimen increases however the deformation ca-pacity becomes worse the stiffness becomes severelydegraded and the specimen is prone to shear brittlefailure

(3) Under the action of oblique load the reinforcementmeasures of the CFRP at the end of the columnimprove the strength and energy consumption of thespecimen however the higher axial compression

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(e)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(f)

Figure 13 OpenSees finite element simulations compared with the experimentally derived hysteresis curve for each specimen Resultscomparison of (a) SC-1 (b) SC-2 (c) SC-3 (d) SC-4 (e) SC-5 and (f) SC-6

Advances in Civil Engineering 13

ratio makes the CFRP more prone to damage anddoes not improve the deformation performance ofthe specimen However the local reinforcementmeasures of the steel plate mesh on the end of thecolumn not only increase the strength and energyconsumption of the specimen but also improve thedeformation ability of the specimen and the seismicperformance of the specimen

(4) In contrast to the unreinforced specimens theaddition of the high-strength stirrups with smallspacing column-end wound CFRP and column-end outer steel plate mesh all improve the strengthdeformation capacity and energy consumptioncapacity of the specimens (e addition of the high-strength stirrups with small spacing and the col-umn-end outer steel plate mesh both altered thefailure mode of the specimen transforming it fromshear failure to bending shear failure (is showsthat the above measures can effectively improve theseismic performance of the test specimen under theaction of oblique loads with a high axial com-pression ratio

(5) Under the action of a high axial pressure ratiooblique load by selecting the appropriate fiber unitand material constitutive relationship the OpenSeesprogram can obtain a simulation result that is ingood agreement with the test hysteresis curve (isverifies the validity of the numerical simulation andprovides a certain basis for subsequent and extendednumerical simulation analyses

Data Availability

All data or models used to support the findings of this studyare included within the article Some data or models thatsupport the findings of this study are available from thecorresponding author upon reasonable request

Conflicts of Interest

(e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

(is work was supported by the Natural Science Foundationof Shandong Province under Grant nos ZR2015EQ017 andZR2018MEE044 and Off-Campus Development Project ofKey Laboratory of Beijing University of Technology underGrant no 2020B03 (e authors are grateful to the KeyLaboratory of Building Structural Retrofitting and Under-ground Space Engineering (Shandong Jianzhu University)Ministry of Education for accommodating the use of theequipment and facilities Professor Xingquan Zhao forproviding computer equipment for numerical simulation ofthe experiment and Editage (httpwwweditagecn) forEnglish language editing

References

[1] A Ghobarah and K Galal ldquoSeismic rehabilitation of shortrectangular RC columnsrdquo Journal of Earthquake Engineeringvol 8 no 1 pp 45ndash68 2004

[2] Y A Li T Y Huang and S J Hwang ldquoSeismic response ofreinforced concrete short columns failed in shearrdquo ACIStructural Journal vol 111 no 4 pp 945ndash954 2014

[3] H Takizawa and H Aoyama ldquoBiaxial effects in modellingearthquake response of RC structuresrdquo Earthquake Engi-neering amp Structural Dynamics vol 4 no 6 pp 523ndash5521976

[4] H Umehara and J O Jirsa ldquoShort rectangular RC columnsunder bidirectional loadingsrdquo Journal of Structural Engi-neering vol 110 no 3 pp 605ndash618 1984

[5] K A Woodward and J O Jirsa ldquoInfluence of reinforcementon RC short column lateral resistancerdquo Journal of StructuralEngineering vol 110 no 1 pp 90ndash104 1984

[6] K Maruyama H Ramirez and J O Jirsa ldquoShort RC columnsunder bilateral load historiesrdquo Journal of Structural Engi-neering vol 110 no 1 pp 120ndash137 1984

[7] H Rodrigues H Varum A Arede and A G CostaldquoBehaviour of reinforced concrete column under biaxial cyclicloadingmdashstate of the artrdquo International Journal of AdvancedStructural Engineering vol 5 no 1 pp 1ndash12 2013

[8] D Wang L Huang T Yu and Z Wang ldquoSeismic perfor-mance of CFRP-retrofitted large-scale square RC columnswith high axial compression ratiosrdquo Journal of Composites forConstruction vol 21 no 5 Article ID 04017031 2017

[9] J Yang and J Wang ldquoSeismic performance of shear-con-trolled CFRP-strengthened high-strength concrete squarecolumns under simulated seismic loadrdquo Journal of Compositesfor Construction vol 22 no 6 Article ID 04018061 2018

[10] X Zhou and J Liu ldquoSeismic behavior and shear strength oftubed RC short columnsrdquo Journal of Constructional SteelResearch vol 66 no 3 pp 385ndash397 2010

[11] H Ma J Xue Y Liu and X Zhang ldquoCyclic loading tests andshear strength of steel reinforced recycled concrete shortcolumnsrdquo Engineering Structures vol 92 pp 55ndash68 2015

[12] D Sokoli and W M Ghannoum ldquoHigh-strength reinforce-ment in columns under high shear stressesrdquo ACI StructuralJournal vol 113 no 3 pp 605ndash614 2016

[13] H Ding Y Liu C Han and Y Guo ldquoSeismic performance ofhigh-strength short concrete column with high-strengthstirrups constraintsrdquo Transactions of Tianjin Universityvol 23 no 4 pp 360ndash369 2017

[14] H O Shin Y S Yoon W D Cook and D Mitchell ldquoAxialload response of ultra-high-strength concrete columns andhigh-strength reinforcementrdquo Transactions of Tianjin Uni-versity vol 113 no 2 pp 325ndash336 216

[15] L A E Shehata M L A V Carneiro and L C D ShehataldquoStrength of short concrete columns confined with CFRPsheetsrdquo Materials and Structures vol 35 pp 50ndash58 2002

[16] F Colomb H Tobbi E Ferrier and P Hamelin ldquoSeismicretrofit of reinforced concrete short columns by CFRPmaterialsfit of reinforced concrete short columns by CFRPmaterialsrdquo Composite Structures vol 82 no 4 pp 475ndash4872008

[17] K Galal A Arafa and A Ghobarah ldquoRetrofit of RC squareshort columnsrdquo Engineering Structures vol 27 no 5pp 801ndash813 2005

[18] R Morshed and M T Kazemi ldquoSeismic shear strengtheningof RC beams and columns with expanded steel meshesrdquo

14 Advances in Civil Engineering

axial compression ratio have the challenge of prematureyielding and short-column brittle failure HRB400 andHTRB630 rebars were selected for this test (e mechanicalproperties of the concrete used in this study (outlined inTable 2) were held constant whereas the mechanicalproperties of the three types of steel bars (outlined in Table 3)and the two types of reinforcing materials (outlined inTable 4) were previously characterized

Production of the specimens SC-1 through SC-4 in-volved first ligating the longitudinal reinforcements and thestirrups to form a steel cage Formwork and concretepouring were then completed To facilitate test loadingobliquely loaded column sections were placed at a 45deg to thebase Specimen SC-5 involved wrapping the end of thecolumn with CFRP which had a single layer thickness of011mm and a total of three layers totaling 200mm in totalheight At the time of construction the steel bars were firsttied to form a steel cage the concrete was then poured andcured To avoid tearing of the CFRP the chamfer radius ofthe corner was 25mm(is method was used to improve therestraint effect of the column-end concrete as well as toimprove the seismic performance of the specimen

SC-6 involved reinforcement with a column-end outersteel plate mesh (e steel plate mesh adopted a round holesteel plate mesh with a wrapping height of 300mm athickness of 3mm a circular hole diameter of 5mm and ahole pitch of 5mm which was processed into a squarepattern (Figure 2(a)) First the U-shaped snap fastener wasplaced on the longitudinal bar and fixed at the joint of thelongitudinal reinforcement and the stirrup passing throughthe screw and tightening the nut (Figures 2(b) and 2(c))(en the steel plate mesh was placed on the outer side of thesteel skeleton to make the inner surface of the steel platemesh tightly attached to the outer side of the U-shaped snapfastener (Figure 2(d)) To ensure that the steel plate mesh didnot participate in the force of the column end a 5mm gapwas left between the end portion and the column base Afterplacement the steel plate mesh was fixed with local windingwires After construction of the steel skeleton the concretewas poured resulting in the surface of the column beingflush with the surface of the steel plate mesh (is methodwas used to improve the restraining effect on the column-end concrete and to improve the seismic performance of thespecimen

22 Load Method Vertical loads were applied in the axialdirection using a 200 ton vertical actuator and held con-stant at the designated axial compression ratios(e actuatorused was made in China (e horizontal load tests wereconducted by adopting the low-cycle repeated loadingmode(e tests were performed by conducting displacement-controlled loading with the displacement cycle loaded twiceper stage until the load dropped to either 85 of the peakload or to the point at which the specimen was not suitablefor carrying the load (Figure 3) It was assumed that positiveforce and displacement were produced by the thrust of theactuator and that negative force and displacement wereproduced by the pull force caused by the actuator (e

loading displacement of the column-end load point wasimplemented by an MTS 100 ton horizontal actuator (isactuator was made in the United States and incorporates anassociated data acquisition system that collects the load anddisplacement data (Figure 4) Collected data were used togenerate a hysteresis curve Cracks on the specimen werevisually observed and manually mapped

3 Experimental Results and Analysis

31 Failure Modes Application of loads resulted in variablestates of damage to all specimens tested in this study basedon visual observations (e definition of the observationsurface of each specimen is shown in Figure 5 (e finalfailure mode of each specimen is shown in Figure 6

For specimen SC-1 small horizontal cracks appearedwithin a range of 300mm from the column bottom when thehorizontal displacement of the column top was loaded to15mm as the loading continued the number of cracksincreased At 182mm the concrete at the bottom corner ofthe column fell off and some longitudinal reinforcementsand stirrups were exposed When specimen was broken thelongitudinal reinforcements in the southwest corner brokeAccordingly specimen SC-1 has obvious shear failurecharacteristics (Figure 6(a)) Regarding specimen SC-2 at15mm small horizontal cracks appeared within a range of150mm from the column bottom as the loading continuedhorizontal cracks developed into oblique cracks and thenumber of cracks increased At 182mm the concrete in thecorner of the column fell off and some longitudinal rein-forcements and stirrups were exposed When the specimenwas broken the corner concrete severely fell off and thelongitudinal reinforcement in the corners in the east andwest directions broke Accordingly specimen SC-2 hasobvious shear failure characteristics (Figure 6(b)) Regarding

Table 2 Mechanical properties of the concrete

Concrete grade fcuk (MPa) fck (MPa) Ec (MPa)C40 604 453 360times104

Note fcuk is the compressive strength of concrete cubes fck is the com-pressive strength of concrete prism Ec is the elastic modulus of concrete

Table 3 Mechanical properties of reinforced bars

Steel bartype

Diameter(mm)

fy(MPa)

fu(MPa) δ () Es (MPa)

HRB400 8 488 640 2625 202times105

HTRB630 8 601 855 238 229times105

HTRB630 16 668 845 230 245times105

Note fy is the rebar yield strength fu is the rebar ultimate strength δ is therebar elongation after breaking and Es is the rebar modulus of elasticity

Table 4 Mechanical properties of strengthening material

Material type (ickness(mm) fy (MPa) fu (MPa) Es (MPa)

Steel plate mesh 3 208 313 168times105

CFRP 0167 ndash 3471 231times 105

4 Advances in Civil Engineering

specimen SC-3 at 15mm small horizontal cracks appearedwithin a range of 200mm from the columnrsquos bottom whenthe loading continued the number of cracks increased andpenetration cracks appeared At 15mm the concrete fell offand some longitudinal reinforcements and stirrups wereexposedWhen the specimen was broken the concrete in thecore area had been crushed and some longitudinal rein-forcements were broken Accordingly specimen SC-3 hasobvious shear failure characteristics (Figure 6(c))

Regarding specimen SC-4 at 15mm small horizontalcracks appeared within a range of 150mm from the columnbottom as the loading continued the number of cracksincreased At 32mm the northwest concrete began to fall offand the longitudinal tendons broke When the specimen wasdamaged the concrete at the bottom corner of the column inthe east and west directions was crushed and the

longitudinal tendons broke Accordingly the bending andshear failure characteristics of specimen SC-4 can be seen(Figure 6(d)) Regarding specimen SC-5 at 15mm cracksappeared on the edge of the CFRP when the loadingcontinued the number of cracks increased and penetratingcracks appeared At 182mm the concrete started to fall offand the carbon fiber cloth cracked When specimen wasbroken the concrete at the bottom corner of the column inthe east and west directions was crushed (Figure 6(e)) Afterthe test the carbon fiber cloth was peeled off it was foundthat the column-angle concrete had been significantlybroken diagonally and the longitudinal tendons and stirrupshad become exposed Accordingly specimen SC-5 has shearfailure characteristics (Figure 6(f )) Regarding specimen SC-6 at 3mm cracks appeared on the edge of the steel platemesh as loading continued the number of cracks increased

(a)

90degbending part

Longitudinalreinforcement

Stirrups

NutScrew

Longitudinal reinforcement

U-shaped snap fastener

Steel plate mesh Limit switch

(b)

Longitudinalreinforcement

Stirrups

U-shaped snap

(c)

Steelskeleton

Steel planemesh

(d)

Figure 2 Details of steel skeleton production (a) Steel plate mesh (b) limit device floor plan (c) steel skeleton with U-shaped snap fastenerand (d) steel skeleton with steel plate mesh

Advances in Civil Engineering 5

Disp

lace

men

t (m

m)

Loading cycle

1 24 486

12182 22

28 3238

4350

ndash15 ndash3 ndash6ndash10

ndash15 ndash20ndash25

ndash30ndash35

ndash40ndash45

ndash60

Figure 3 Loading protocol (e tests performed via displacement-controlled loading

Reaction frame

Lifting jackConnector

Steel backing plate

MTSScrew

Steel plate

Electronic displacement meter

Spec

imen

Pedestal

Anchor boltStatic platform

Reac

tion

wal

l

Figure 4 Experimental test set-up MTS actuator with data acquisition system collects load and displacement data

S

N

WE

Specimen

y

x

Pull Push

(a)

Specimen

y xS

N

E W

Pull Push

(b)

Figure 5 Definition of specimen observation surface (a) Spindle loading (b) 45deg loading

6 Advances in Civil Engineering

At 40mm the longitudinal reinforcement was brokenWhen the specimen was broken the steel plate mesh at thebottom of the column was convex (Figure 6(g)) After thetest the steel plate mesh was peeled off it was found that theconcrete at the bottom of the column was broken and thelongitudinal steel bars were convex and partially brokenAccordingly the bending and shear failure characteristics ofspecimen SC-6 can be seen (Figure 6(h))

Overall compared with the horizontally loaded testspecimens the concrete at the corners of the diagonallyloaded test specimens fell off severely which reduced theworkability of the test specimens In particular the increasein the axial pressure ratio makes this damage more seriousCompared to the unreinforced test specimens high-strengthstirrups with small spacing column-end wrapped CFRPand column-end outer steel plate mesh enhanced the re-straint effect on concrete limited concrete falling off andimproved the seismic performance of the specimens underoblique loads

32 Hysteresis Curves (e load-displacement hysteresiscurves of each specimen demonstrate the performance ofeach specimen during the duration of the tests (Figure 7) Pis the measured horizontal load Δ is the measured hori-zontal displacement of the loading point As can be seenfrom Figure 7 compared to specimen SC-1 specimen SC-2undergoes accelerated strength degradation at a later stage ofloading and the residual deformation is larger(is could beattributed to the oblique loading that leads to the corner

concrete of the specimen being subjected to loads in twodirections resulting in serious damage to the corner con-crete (Figures 7(a) and 7(b)) In contrast to specimen SC-2specimen SC-3 has a significantly lower load at the later stageof loading this is due to the severe fall of the concrete at thelater stage of loading (Figures 7(b) and 7(c)) (ere were twosignificant drops in the hysteresis curves of SC-4 and SC-6likely due to the fracture of the high-strength longitudinalbars which led to a significant decline in the strength ofthese specimens (Figures 7(d) and 7(f)) However the high-strength stirrups with small spacing included in thesetreatments provided a strong constraint effect for high-strength longitudinal bars that enabled the specimens toretain a strong strength Compared to the hysteresis curve ofspecimen SC-4 that of specimen SC-5 is less full (is isbecause the CFRP is prone to tear and damage at the columnangle under a high axial pressure ratio (Figures 7(d) and7(e)) which causes the strength of the specimen to dropsharply In contrast to specimen SC-4 the load of specimenSC-6 decreases slowly at the later stage of loading and thehysteresis curve was relatively plump (Figures 7(d) and 7(f ))(is is because the steel plate net at the end of the columncan effectively slow the fall of concrete and exert a strongerenergy consumption

33 Skeleton Curves In the hysteretic curve under thecondition of low-cycle reciprocating loading the outerwinding line of the peak loading point of each stage is calleda skeleton curve which characterizes the characteristics of

Ordinary comparison

specimen

(a)

α = 45deg

n = 08

(b)

α = 45deg

n = 10

(c)

Dense high-strength stirrups

α = 45deg

n = 10

(d)

CFRP constraint

α = 45deg

n = 10

(e)

Remove CFRP

α = 45deg

n = 10

(f )

α = 45deg

n = 10

Steel plate mesh constraint

(g)

Remove steel plate mesh

α = 45deg

n = 10

(h)

Figure 6 Visual observations of the ultimate failure modes of short column (SC) specimens (a) SC-1 (b) SC-2 (c) SC-3 (d) SC-4 (e) SC-5(f ) SC-5 after removal of CFRP (g) SC-6 and (h) SC-6 after removal of steel plate mesh

Advances in Civil Engineering 7

stress and deformation during the loading of the specimen(e skeleton curve of each specimen is shown in Figure 8 Ascan be seen from the figure the development of the skeleton

curves of each specimen can be roughly divided into threestages (1) In the elastic stage the load changes linearly withthe displacement the specimen has yet to crack and no

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(a)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(b)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

(c)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(d)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

(e)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(f )

Figure 7 Hysteretic curves of short column (SC) specimens 1ndash6 (a) SC-1 (b) SC-2 (c) SC-3 (d) SC-4 (e) SC-5 and (f) SC-6

8 Advances in Civil Engineering

residual deformation is observed (2) During the develop-ment stage of a multicrack many cracks appear in thespecimen When residual deformation begins to appearmultiple tiny cracks appear on the surface of the specimenand the horizontal load of the specimen slowly increasesWith the accumulation of damage the specimen reaches thepeak load (3) In the load drop stage for specimens SC-1SC-2 and SC-3 the skeleton curve decreases significantly inthe later stage of loading (is is because the ordinarystirrups with large spacing cannot provide effective lateralrestraints for the specimens under a high axial compressionratio thus making the strength of the specimens dropdramatically Compared to specimen SC-3 the skeletoncurves of specimens SC-4 SC-5 and SC-6 decrease slowlyand show good deformation ability In particular the de-formation capacity of specimens SC-4 and SC-6 after thepeak point significantly improves this is conducive toimproving the seismic energy dissipation capability ofspecimens

34 Bearing Capacity and Ductility Each sample wascharacterized by the yield load point the peak load pointand the failure load point within a load-displacement curveAs shown in Figure 9 the yield point D was determined bythe equivalent elastic-plastic energy method that is wherethe area SOAB SBCD and the ultimate load was simplydefined as 85 of the peak load [20] Because the strength ofSC-1 SC-2 and SC-3 declined rapidly after reaching thepeak load and the ultimate load did not reach 85 of thepeak load the failure displacements of these were taken asthe ultimate displacement Here the ultimate displacementangle (θμ) was used to characterize the deformation ability ofthe specimen and was calculated as θμ Δul0 where l0 is thecolumnrsquos height For each specimen the characteristic loadand displacement calculation results are shown in Table 5

(e relative value is the ratio of the average of the positiveand negative corresponding coefficients of SC-2 through SC-6 and the average of the positive and negative correspondingcoefficients of SC-1

As can be seen in Table 5 compared to specimen SC-1the yield load peak load and ultimate load of specimen SC-2are reduced and the ultimate displacement angle is un-changed(is is because the concrete in the corner of the testspecimen is severely damaged under the diagonal horizontalloading making the strength of the specimen decreasehowever this has no effect on the deformation ability of thespecimen A comparison of SC-2 and SC-3 reveals thatunder the oblique load as the axial pressure ratio increasesthe strength of the specimen increases but the deformationcapacity decreases In contrast to specimen SC-4 the yieldload peak load and ultimate load of SC-5 improvedwhereas the ultimate displacement angle decreased by 1(is result indicates that although the strength of thespecimen under high axial pressure ratio improved thedeformation capacity of the specimen under high axialpressure ratio did not improve Compared to specimen SC-4 the yield load peak load and ultimate load of specimenSC-6 improved and the ultimate displacement angle in-creased by 52(is result was likely due to the column-endouter steel plate mesh providing a strong restraining effecton the column-end concrete which then increased thespecimenrsquos strength deformation capacity and seismicperformance

In comparison to SC-3 the yield load peak load andultimate load of SC-4 SC-5 and SC-6 were all greatlyimproved as were the ultimate displacement angles (isindicates that the high-strength stirrups with small spacingcolumn-end wound CFRP and column-end outer steel platemesh may improve the strength and the deformation abilityof the RC columns therefore this should be consideredwhen accounting for seismic loads in RC columns

35 Stiffness Degradation Stiffness degradation of a speci-men under cyclic loading is usually attributable to the ac-cumulation of specimen damage which has great influence

SC-1SC-2SC-3

SC-4SC-5SC-6

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

Figure 8 Skeleton curves of specimens Skeleton curves representthe outer winding line of the peak loading point of each stage

Δ (mm)

AB

D

P (k

N)

Pmax

Py085Pmax

Δy Δm Δu

C

O

Figure 9 Calculation of characteristic points for each specimen Pyis the yield load Pmax is the peak load

Advances in Civil Engineering 9

on the seismic performance of the specimens Here thesecant stiffness (Ki) was used to represent the stiffnessdegradation of the specimens (e secant stiffness Ki wascalculated as

Ki P

+i

11138681113868111386811138681113868111386811138681113868 + P

minusi

11138681113868111386811138681113868111386811138681113868

Δ+i

11138681113868111386811138681113868111386811138681113868 + Δminus

i

11138681113868111386811138681113868111386811138681113868 (1)

where Pi+ and Pminusi are the i-th positive and reverse peak loads

respectively and Δi+ and Δminusi are the i-th positive and reverse

peak displacements(e stiffness degradation curve of each test piece is

shown in Figure 10 As loading displacement increased thestiffness of each specimen gradually decreased (e stiffnessdegraded rapidly in the early stage and slowly in the laterstage (is could be due to the continuous cracking ofconcrete in the early stage of loading whereas no new crackswere generated in the late loading stages thus when thecumulative damage of the specimen reached a certain de-gree the slope of the stiffness degradation curve of thespecimen decreased Compared to specimen SC-1 thestiffness of specimen SC-2 degraded faster (is is becausethe oblique horizontal loading caused damage in the cornerof the specimen affecting each other In contrast to speci-men SC-2 the stiffness of specimen SC-3 decreased sharplyin the later stage of loading (is is due to the higher axialcompression ratio of the specimen which caused the con-crete to fall severely the stirrups to protrude and thelongitudinal bars to yield(e stiffness degradation curves ofSC-4 SC-5 and SC-6 had a slower downward trend and alonger curve extension compared to those of SC-3 (isindicates that the high-strength stirrups with small spacingthe column-end wound CFRP and the column-end outersteel plate mesh may have alleviated the damage degree ofthe specimen and thus slowed the degradation stiffnessdegradation of these specimens

36 Energy Dissipation (e energy dissipation capacity ofspecimens under earthquake action is an important indexfor evaluating their seismic performance Here the equiv-alent viscous damping coefficient (he) and cumulative energy

consumption (Ep) were used to characterize the energydissipation performance of the experimental specimens (eequivalent viscous damping coefficient characterizes theenergy dissipation performance of specimens at differentloading stages the cumulative energy consumption char-acterizes the overall energy dissipation capacity of specimensduring the whole loading process

As shown in Figure 11 the area of each hysteresis loop inthe hysteresis curve represents the energy-consuming ca-pacity of the specimens under this cycle When otherconditions are the same the larger the area of the hysteresisloop the better the energy consumption capability of thespecimen (e equivalent viscous damping coefficient he ofspecimens is calculated as

he 12π

timesSABC + SCDA

SODG + SOBH

(2)

Table 5 Experimentally derived characteristic loads and displacements for specimens SC-1 through SC-6

Specimen Loading direction Py (kN) Δy (mm) Pm (kN) Δm (mm) Pu (kN) Δu (mm) θμ () Relative value

SC-1 + 41650 986 49250 1820 46794 2500 417 1minus 40045 1205 47286 1819 46973 2500 417

SC-2 + 39470 938 46600 1817 41363 2500 417 1minus 38188 1066 45985 1820 44323 2500 417

SC-3 + 40820 850 47005 1820 44397 2000 333 080minus 41037 868 48192 1500 40963 2000 333

SC-4 + 43773 696 50493 1500 42919 3184 531 135minus 40828 972 48311 2500 41064 3595 599

SC-5 + 50121 917 57802 1820 49132 3223 761 134minus 43456 1113 51965 2800 48294 3500 798

SC-6 + 46587 1151 53813 2499 45741 4563 537 187minus 48357 1443 56164 3200 47739 4790 583

Note Py is the yield load Δy is the yield displacement Pm is the peak load Δm is the peak displacement Pu is the ultimate load Δu is the ultimate displacementand θμ is the deformation ability

100

80

60

40

20

0

Ki (k

Nm

m)

ndash10 0 10 20 30 40 50 60 70∆ (mm)

SC-1SC-2SC-3

SC-4SC-5SC-6

Figure 10 Stiffness degradation curves of specimens Stiffnessdegradation of the specimens is represented by secant stiffness Ki

10 Advances in Civil Engineering

As shown in Figure 12 the equivalent viscous dampingcoefficient (he) of the specimen and the displacement (Δ)curve of the column end were calculated for each specimenAt the initial stage of loading the energy consumption of thespecimen increased as the loading displacement increasedWhen the specimen was cracked stress redistribution oc-curred inside the specimen thereby impacting the stress anddeformation of the specimen and decreasing the energyconsumption As the loading displacement continued toincrease the crack continued opening and closing thusincreasing the energy consumption of the specimen Whenthe specimen yielded the internal longitudinal reinforce-ment of the specimen yielded and the stress redistributionoccurred again inside the specimen thus decreasing theenergy consumption of the specimen With continuousloading cracks of the specimen kept opening and closingand energy consumption continued increasing until thespecimen was destroyed (e equivalent viscous dampingcoefficient of each specimen increased as a whole whichindicated that the damage of the specimen increased as thehorizontal deformation increased during the loading pro-cess thereby increasing the energy consumption of thespecimen (Figure 12)

Cumulative energy consumption refers to the sum of allhysteresis loop areas generated from the beginning of theload application to the ultimate displacement point (elarger the value the stronger the energy dissipation capacityof the specimen and the better the seismic performance Asshown in Table 6 the cumulative energy dissipation wascalculated for each specimen

In contrast to SC-1 the cumulative energy consumptionof SC-2 increased by 37 indicating that the obliquehorizontal loading led to more serious cumulative damageand the consumption of more energy Compared to SC-2the accumulated energy consumption value of SC-3 de-creased by approximately 16 possibly due to the pre-mature failure of specimen and the increase of the axialpressure ratio which reduces the cumulative energy con-sumption capacity of specimen In contrast to specimen SC-3 the cumulative energy consumption values of specimensSC-4 SC-5 and SC-6 all improved with increase rates of222 278 and 412 respectively (is is because high-

strength stirrups with small spacing wound CFRP at the endof the column and steel plate mesh at the end of the columnlimit the shedding of concrete and thus increase the work ofthe concrete

37 OpenSees Finite Element Simulation (e open-sourcefinite element program OpenSees (Open System forEarthquake Engineering Simulation) was used as a platformto numerically simulate the experimental specimens (emodel used displacement-based nonlinear beam-columnelements (ree nodes along the height of the column wereused to form two units wherein the top node was free endand the bottom node was embedded (e P-Delta effectcaused by the vertical load was considered by the P-Del-taCrdTransf command (e fiber model was used to definethe relationship of the cross section restoring force at theunit integration point (e longitudinal reinforcement wasmodeled using the Reinforcing Steel uniaxial materialprovided in OpenSees which was based on the Chang-Mander uniaxial material model [21] and simulated theisotropic hardening behavior of steel bars (e concrete wassimulated by Concrete 02 provided by OpenSees (e ma-terial was based on the Kent-Scott-Park uniaxial material

A OG

D

B

C H Δ

P

Figure 11 PminusΔ hysteretic curve representing the energy-con-suming capacity of the specimen

Table 6 Accumulated dissipated energy (Ep) of all specimens

Specimen Ep (kNmiddotmm) Relative valueSC-1 49770 1SC-2 68307 137SC-3 41784 084SC-4 160490 322SC-5 187933 378SC-6 254794 512

SC-1SC-2SC-3

SC-4SC-5SC-6

004

006

008

010

012

014

016

018

020

022

024

he

0 10 20 30 40 50 60 70ndash10∆ (mm)

Figure 12 Viscous damping coefficient curves of each specimen(e equivalent viscous damping coefficient (he) of the specimenand the displacement (Δ) curve of the column end were calculatedfor each specimen

Advances in Civil Engineering 11

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

(a)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

(b)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

(c)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

(d)

Figure 13 Continued

12 Advances in Civil Engineering

model [22] (e model included the tensile mechanicalproperties of the concrete the stiffness degradation and theenergy dissipation behavior of the concrete during recip-rocating loading For the concrete in the core area theMander model [2324] was used to consider the restrainingeffect of stirrups on concrete Here the stress-strain rela-tionship of CFRP-constrained concrete was establishedusing the Concrete 02 material (e stress and strain at thepeak point were the same as the peak-point stress and strainof the concrete bound by the stirrup (e stress and strain atthe limit point were calculated using the peak-point stressand strain of the Lam-Teng model [2526] (ere was littleresearch on concrete columns reinforced by steel plate meshand no specific theoretical models Based on the existingsteel mesh reinforced concrete column the Concrete 02material in this study was used to establish the stress-strainrelationship of the steel plate mesh to the concrete equations(3) and (4) were used to calculate the peak concrete stress fccafter confinement [19] (e peak strain was 4 times that ofthe peak stress of unconstrained concrete the limit pointstress was twice that of the ultimate stress of unconstrainedconcrete the calculations of the remaining characteristicparameters were consistent with the calculation results of theunconstrained concrete

fcc 1 + 077λv( 1113857fck (3)

λv ρvfyv

fck

(4)

where fck is the axial compressive strength of the concrete λv isthe eigenvalue of the stirrup fyv is the yield strength of the steelplate mesh and ρv is the volumetric ratio of the steel plate mesh

(e vertical load was applied incrementally in 10 stepsusing the gravity loading module provided by OpenSees and

was held constant after the vertical load was completed (ehorizontal load was applied in time series and the loadingsystem was consistent with the experimental proceduresused in this study

(e hysteresis curves for SC-1 through SC-6 generatedby the OpenSees finite element analysis were compared tothe experimentally generated hysteresis curves as shown inFigure 13 (e curves generated by OpenSees are in goodagreement with the experimental results

4 Conclusion

Here six short concrete columns with high-strength lon-gitudinal reinforcements were subjected to low-cycle re-peated loading tests By comparing and analyzing the testresults based on observed test phenomena the followingconclusions are drawn

(1) Compared to the horizontally loaded test specimensthe strength of the diagonally loaded specimensdecreased and the stiffness degradation trendaccelerated this indicates that the effect of obliqueloading is unfavorable to the strength and stiffness ofthe specimens

(2) Under the action of oblique load as the axialcompression ratio increases the strength of thespecimen increases however the deformation ca-pacity becomes worse the stiffness becomes severelydegraded and the specimen is prone to shear brittlefailure

(3) Under the action of oblique load the reinforcementmeasures of the CFRP at the end of the columnimprove the strength and energy consumption of thespecimen however the higher axial compression

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(e)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(f)

Figure 13 OpenSees finite element simulations compared with the experimentally derived hysteresis curve for each specimen Resultscomparison of (a) SC-1 (b) SC-2 (c) SC-3 (d) SC-4 (e) SC-5 and (f) SC-6

Advances in Civil Engineering 13

ratio makes the CFRP more prone to damage anddoes not improve the deformation performance ofthe specimen However the local reinforcementmeasures of the steel plate mesh on the end of thecolumn not only increase the strength and energyconsumption of the specimen but also improve thedeformation ability of the specimen and the seismicperformance of the specimen

(4) In contrast to the unreinforced specimens theaddition of the high-strength stirrups with smallspacing column-end wound CFRP and column-end outer steel plate mesh all improve the strengthdeformation capacity and energy consumptioncapacity of the specimens (e addition of the high-strength stirrups with small spacing and the col-umn-end outer steel plate mesh both altered thefailure mode of the specimen transforming it fromshear failure to bending shear failure (is showsthat the above measures can effectively improve theseismic performance of the test specimen under theaction of oblique loads with a high axial com-pression ratio

(5) Under the action of a high axial pressure ratiooblique load by selecting the appropriate fiber unitand material constitutive relationship the OpenSeesprogram can obtain a simulation result that is ingood agreement with the test hysteresis curve (isverifies the validity of the numerical simulation andprovides a certain basis for subsequent and extendednumerical simulation analyses

Data Availability

All data or models used to support the findings of this studyare included within the article Some data or models thatsupport the findings of this study are available from thecorresponding author upon reasonable request

Conflicts of Interest

(e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

(is work was supported by the Natural Science Foundationof Shandong Province under Grant nos ZR2015EQ017 andZR2018MEE044 and Off-Campus Development Project ofKey Laboratory of Beijing University of Technology underGrant no 2020B03 (e authors are grateful to the KeyLaboratory of Building Structural Retrofitting and Under-ground Space Engineering (Shandong Jianzhu University)Ministry of Education for accommodating the use of theequipment and facilities Professor Xingquan Zhao forproviding computer equipment for numerical simulation ofthe experiment and Editage (httpwwweditagecn) forEnglish language editing

References

[1] A Ghobarah and K Galal ldquoSeismic rehabilitation of shortrectangular RC columnsrdquo Journal of Earthquake Engineeringvol 8 no 1 pp 45ndash68 2004

[2] Y A Li T Y Huang and S J Hwang ldquoSeismic response ofreinforced concrete short columns failed in shearrdquo ACIStructural Journal vol 111 no 4 pp 945ndash954 2014

[3] H Takizawa and H Aoyama ldquoBiaxial effects in modellingearthquake response of RC structuresrdquo Earthquake Engi-neering amp Structural Dynamics vol 4 no 6 pp 523ndash5521976

[4] H Umehara and J O Jirsa ldquoShort rectangular RC columnsunder bidirectional loadingsrdquo Journal of Structural Engi-neering vol 110 no 3 pp 605ndash618 1984

[5] K A Woodward and J O Jirsa ldquoInfluence of reinforcementon RC short column lateral resistancerdquo Journal of StructuralEngineering vol 110 no 1 pp 90ndash104 1984

[6] K Maruyama H Ramirez and J O Jirsa ldquoShort RC columnsunder bilateral load historiesrdquo Journal of Structural Engi-neering vol 110 no 1 pp 120ndash137 1984

[7] H Rodrigues H Varum A Arede and A G CostaldquoBehaviour of reinforced concrete column under biaxial cyclicloadingmdashstate of the artrdquo International Journal of AdvancedStructural Engineering vol 5 no 1 pp 1ndash12 2013

[8] D Wang L Huang T Yu and Z Wang ldquoSeismic perfor-mance of CFRP-retrofitted large-scale square RC columnswith high axial compression ratiosrdquo Journal of Composites forConstruction vol 21 no 5 Article ID 04017031 2017

[9] J Yang and J Wang ldquoSeismic performance of shear-con-trolled CFRP-strengthened high-strength concrete squarecolumns under simulated seismic loadrdquo Journal of Compositesfor Construction vol 22 no 6 Article ID 04018061 2018

[10] X Zhou and J Liu ldquoSeismic behavior and shear strength oftubed RC short columnsrdquo Journal of Constructional SteelResearch vol 66 no 3 pp 385ndash397 2010

[11] H Ma J Xue Y Liu and X Zhang ldquoCyclic loading tests andshear strength of steel reinforced recycled concrete shortcolumnsrdquo Engineering Structures vol 92 pp 55ndash68 2015

[12] D Sokoli and W M Ghannoum ldquoHigh-strength reinforce-ment in columns under high shear stressesrdquo ACI StructuralJournal vol 113 no 3 pp 605ndash614 2016

[13] H Ding Y Liu C Han and Y Guo ldquoSeismic performance ofhigh-strength short concrete column with high-strengthstirrups constraintsrdquo Transactions of Tianjin Universityvol 23 no 4 pp 360ndash369 2017

[14] H O Shin Y S Yoon W D Cook and D Mitchell ldquoAxialload response of ultra-high-strength concrete columns andhigh-strength reinforcementrdquo Transactions of Tianjin Uni-versity vol 113 no 2 pp 325ndash336 216

[15] L A E Shehata M L A V Carneiro and L C D ShehataldquoStrength of short concrete columns confined with CFRPsheetsrdquo Materials and Structures vol 35 pp 50ndash58 2002

[16] F Colomb H Tobbi E Ferrier and P Hamelin ldquoSeismicretrofit of reinforced concrete short columns by CFRPmaterialsfit of reinforced concrete short columns by CFRPmaterialsrdquo Composite Structures vol 82 no 4 pp 475ndash4872008

[17] K Galal A Arafa and A Ghobarah ldquoRetrofit of RC squareshort columnsrdquo Engineering Structures vol 27 no 5pp 801ndash813 2005

[18] R Morshed and M T Kazemi ldquoSeismic shear strengtheningof RC beams and columns with expanded steel meshesrdquo

14 Advances in Civil Engineering

specimen SC-3 at 15mm small horizontal cracks appearedwithin a range of 200mm from the columnrsquos bottom whenthe loading continued the number of cracks increased andpenetration cracks appeared At 15mm the concrete fell offand some longitudinal reinforcements and stirrups wereexposedWhen the specimen was broken the concrete in thecore area had been crushed and some longitudinal rein-forcements were broken Accordingly specimen SC-3 hasobvious shear failure characteristics (Figure 6(c))

Regarding specimen SC-4 at 15mm small horizontalcracks appeared within a range of 150mm from the columnbottom as the loading continued the number of cracksincreased At 32mm the northwest concrete began to fall offand the longitudinal tendons broke When the specimen wasdamaged the concrete at the bottom corner of the column inthe east and west directions was crushed and the

longitudinal tendons broke Accordingly the bending andshear failure characteristics of specimen SC-4 can be seen(Figure 6(d)) Regarding specimen SC-5 at 15mm cracksappeared on the edge of the CFRP when the loadingcontinued the number of cracks increased and penetratingcracks appeared At 182mm the concrete started to fall offand the carbon fiber cloth cracked When specimen wasbroken the concrete at the bottom corner of the column inthe east and west directions was crushed (Figure 6(e)) Afterthe test the carbon fiber cloth was peeled off it was foundthat the column-angle concrete had been significantlybroken diagonally and the longitudinal tendons and stirrupshad become exposed Accordingly specimen SC-5 has shearfailure characteristics (Figure 6(f )) Regarding specimen SC-6 at 3mm cracks appeared on the edge of the steel platemesh as loading continued the number of cracks increased

(a)

90degbending part

Longitudinalreinforcement

Stirrups

NutScrew

Longitudinal reinforcement

U-shaped snap fastener

Steel plate mesh Limit switch

(b)

Longitudinalreinforcement

Stirrups

U-shaped snap

(c)

Steelskeleton

Steel planemesh

(d)

Figure 2 Details of steel skeleton production (a) Steel plate mesh (b) limit device floor plan (c) steel skeleton with U-shaped snap fastenerand (d) steel skeleton with steel plate mesh

Advances in Civil Engineering 5

Disp

lace

men

t (m

m)

Loading cycle

1 24 486

12182 22

28 3238

4350

ndash15 ndash3 ndash6ndash10

ndash15 ndash20ndash25

ndash30ndash35

ndash40ndash45

ndash60

Figure 3 Loading protocol (e tests performed via displacement-controlled loading

Reaction frame

Lifting jackConnector

Steel backing plate

MTSScrew

Steel plate

Electronic displacement meter

Spec

imen

Pedestal

Anchor boltStatic platform

Reac

tion

wal

l

Figure 4 Experimental test set-up MTS actuator with data acquisition system collects load and displacement data

S

N

WE

Specimen

y

x

Pull Push

(a)

Specimen

y xS

N

E W

Pull Push

(b)

Figure 5 Definition of specimen observation surface (a) Spindle loading (b) 45deg loading

6 Advances in Civil Engineering

At 40mm the longitudinal reinforcement was brokenWhen the specimen was broken the steel plate mesh at thebottom of the column was convex (Figure 6(g)) After thetest the steel plate mesh was peeled off it was found that theconcrete at the bottom of the column was broken and thelongitudinal steel bars were convex and partially brokenAccordingly the bending and shear failure characteristics ofspecimen SC-6 can be seen (Figure 6(h))

Overall compared with the horizontally loaded testspecimens the concrete at the corners of the diagonallyloaded test specimens fell off severely which reduced theworkability of the test specimens In particular the increasein the axial pressure ratio makes this damage more seriousCompared to the unreinforced test specimens high-strengthstirrups with small spacing column-end wrapped CFRPand column-end outer steel plate mesh enhanced the re-straint effect on concrete limited concrete falling off andimproved the seismic performance of the specimens underoblique loads

32 Hysteresis Curves (e load-displacement hysteresiscurves of each specimen demonstrate the performance ofeach specimen during the duration of the tests (Figure 7) Pis the measured horizontal load Δ is the measured hori-zontal displacement of the loading point As can be seenfrom Figure 7 compared to specimen SC-1 specimen SC-2undergoes accelerated strength degradation at a later stage ofloading and the residual deformation is larger(is could beattributed to the oblique loading that leads to the corner

concrete of the specimen being subjected to loads in twodirections resulting in serious damage to the corner con-crete (Figures 7(a) and 7(b)) In contrast to specimen SC-2specimen SC-3 has a significantly lower load at the later stageof loading this is due to the severe fall of the concrete at thelater stage of loading (Figures 7(b) and 7(c)) (ere were twosignificant drops in the hysteresis curves of SC-4 and SC-6likely due to the fracture of the high-strength longitudinalbars which led to a significant decline in the strength ofthese specimens (Figures 7(d) and 7(f)) However the high-strength stirrups with small spacing included in thesetreatments provided a strong constraint effect for high-strength longitudinal bars that enabled the specimens toretain a strong strength Compared to the hysteresis curve ofspecimen SC-4 that of specimen SC-5 is less full (is isbecause the CFRP is prone to tear and damage at the columnangle under a high axial pressure ratio (Figures 7(d) and7(e)) which causes the strength of the specimen to dropsharply In contrast to specimen SC-4 the load of specimenSC-6 decreases slowly at the later stage of loading and thehysteresis curve was relatively plump (Figures 7(d) and 7(f ))(is is because the steel plate net at the end of the columncan effectively slow the fall of concrete and exert a strongerenergy consumption

33 Skeleton Curves In the hysteretic curve under thecondition of low-cycle reciprocating loading the outerwinding line of the peak loading point of each stage is calleda skeleton curve which characterizes the characteristics of

Ordinary comparison

specimen

(a)

α = 45deg

n = 08

(b)

α = 45deg

n = 10

(c)

Dense high-strength stirrups

α = 45deg

n = 10

(d)

CFRP constraint

α = 45deg

n = 10

(e)

Remove CFRP

α = 45deg

n = 10

(f )

α = 45deg

n = 10

Steel plate mesh constraint

(g)

Remove steel plate mesh

α = 45deg

n = 10

(h)

Figure 6 Visual observations of the ultimate failure modes of short column (SC) specimens (a) SC-1 (b) SC-2 (c) SC-3 (d) SC-4 (e) SC-5(f ) SC-5 after removal of CFRP (g) SC-6 and (h) SC-6 after removal of steel plate mesh

Advances in Civil Engineering 7

stress and deformation during the loading of the specimen(e skeleton curve of each specimen is shown in Figure 8 Ascan be seen from the figure the development of the skeleton

curves of each specimen can be roughly divided into threestages (1) In the elastic stage the load changes linearly withthe displacement the specimen has yet to crack and no

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(a)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(b)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

(c)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(d)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

(e)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(f )

Figure 7 Hysteretic curves of short column (SC) specimens 1ndash6 (a) SC-1 (b) SC-2 (c) SC-3 (d) SC-4 (e) SC-5 and (f) SC-6

8 Advances in Civil Engineering

residual deformation is observed (2) During the develop-ment stage of a multicrack many cracks appear in thespecimen When residual deformation begins to appearmultiple tiny cracks appear on the surface of the specimenand the horizontal load of the specimen slowly increasesWith the accumulation of damage the specimen reaches thepeak load (3) In the load drop stage for specimens SC-1SC-2 and SC-3 the skeleton curve decreases significantly inthe later stage of loading (is is because the ordinarystirrups with large spacing cannot provide effective lateralrestraints for the specimens under a high axial compressionratio thus making the strength of the specimens dropdramatically Compared to specimen SC-3 the skeletoncurves of specimens SC-4 SC-5 and SC-6 decrease slowlyand show good deformation ability In particular the de-formation capacity of specimens SC-4 and SC-6 after thepeak point significantly improves this is conducive toimproving the seismic energy dissipation capability ofspecimens

34 Bearing Capacity and Ductility Each sample wascharacterized by the yield load point the peak load pointand the failure load point within a load-displacement curveAs shown in Figure 9 the yield point D was determined bythe equivalent elastic-plastic energy method that is wherethe area SOAB SBCD and the ultimate load was simplydefined as 85 of the peak load [20] Because the strength ofSC-1 SC-2 and SC-3 declined rapidly after reaching thepeak load and the ultimate load did not reach 85 of thepeak load the failure displacements of these were taken asthe ultimate displacement Here the ultimate displacementangle (θμ) was used to characterize the deformation ability ofthe specimen and was calculated as θμ Δul0 where l0 is thecolumnrsquos height For each specimen the characteristic loadand displacement calculation results are shown in Table 5

(e relative value is the ratio of the average of the positiveand negative corresponding coefficients of SC-2 through SC-6 and the average of the positive and negative correspondingcoefficients of SC-1

As can be seen in Table 5 compared to specimen SC-1the yield load peak load and ultimate load of specimen SC-2are reduced and the ultimate displacement angle is un-changed(is is because the concrete in the corner of the testspecimen is severely damaged under the diagonal horizontalloading making the strength of the specimen decreasehowever this has no effect on the deformation ability of thespecimen A comparison of SC-2 and SC-3 reveals thatunder the oblique load as the axial pressure ratio increasesthe strength of the specimen increases but the deformationcapacity decreases In contrast to specimen SC-4 the yieldload peak load and ultimate load of SC-5 improvedwhereas the ultimate displacement angle decreased by 1(is result indicates that although the strength of thespecimen under high axial pressure ratio improved thedeformation capacity of the specimen under high axialpressure ratio did not improve Compared to specimen SC-4 the yield load peak load and ultimate load of specimenSC-6 improved and the ultimate displacement angle in-creased by 52(is result was likely due to the column-endouter steel plate mesh providing a strong restraining effecton the column-end concrete which then increased thespecimenrsquos strength deformation capacity and seismicperformance

In comparison to SC-3 the yield load peak load andultimate load of SC-4 SC-5 and SC-6 were all greatlyimproved as were the ultimate displacement angles (isindicates that the high-strength stirrups with small spacingcolumn-end wound CFRP and column-end outer steel platemesh may improve the strength and the deformation abilityof the RC columns therefore this should be consideredwhen accounting for seismic loads in RC columns

35 Stiffness Degradation Stiffness degradation of a speci-men under cyclic loading is usually attributable to the ac-cumulation of specimen damage which has great influence

SC-1SC-2SC-3

SC-4SC-5SC-6

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

Figure 8 Skeleton curves of specimens Skeleton curves representthe outer winding line of the peak loading point of each stage

Δ (mm)

AB

D

P (k

N)

Pmax

Py085Pmax

Δy Δm Δu

C

O

Figure 9 Calculation of characteristic points for each specimen Pyis the yield load Pmax is the peak load

Advances in Civil Engineering 9

on the seismic performance of the specimens Here thesecant stiffness (Ki) was used to represent the stiffnessdegradation of the specimens (e secant stiffness Ki wascalculated as

Ki P

+i

11138681113868111386811138681113868111386811138681113868 + P

minusi

11138681113868111386811138681113868111386811138681113868

Δ+i

11138681113868111386811138681113868111386811138681113868 + Δminus

i

11138681113868111386811138681113868111386811138681113868 (1)

where Pi+ and Pminusi are the i-th positive and reverse peak loads

respectively and Δi+ and Δminusi are the i-th positive and reverse

peak displacements(e stiffness degradation curve of each test piece is

shown in Figure 10 As loading displacement increased thestiffness of each specimen gradually decreased (e stiffnessdegraded rapidly in the early stage and slowly in the laterstage (is could be due to the continuous cracking ofconcrete in the early stage of loading whereas no new crackswere generated in the late loading stages thus when thecumulative damage of the specimen reached a certain de-gree the slope of the stiffness degradation curve of thespecimen decreased Compared to specimen SC-1 thestiffness of specimen SC-2 degraded faster (is is becausethe oblique horizontal loading caused damage in the cornerof the specimen affecting each other In contrast to speci-men SC-2 the stiffness of specimen SC-3 decreased sharplyin the later stage of loading (is is due to the higher axialcompression ratio of the specimen which caused the con-crete to fall severely the stirrups to protrude and thelongitudinal bars to yield(e stiffness degradation curves ofSC-4 SC-5 and SC-6 had a slower downward trend and alonger curve extension compared to those of SC-3 (isindicates that the high-strength stirrups with small spacingthe column-end wound CFRP and the column-end outersteel plate mesh may have alleviated the damage degree ofthe specimen and thus slowed the degradation stiffnessdegradation of these specimens

36 Energy Dissipation (e energy dissipation capacity ofspecimens under earthquake action is an important indexfor evaluating their seismic performance Here the equiv-alent viscous damping coefficient (he) and cumulative energy

consumption (Ep) were used to characterize the energydissipation performance of the experimental specimens (eequivalent viscous damping coefficient characterizes theenergy dissipation performance of specimens at differentloading stages the cumulative energy consumption char-acterizes the overall energy dissipation capacity of specimensduring the whole loading process

As shown in Figure 11 the area of each hysteresis loop inthe hysteresis curve represents the energy-consuming ca-pacity of the specimens under this cycle When otherconditions are the same the larger the area of the hysteresisloop the better the energy consumption capability of thespecimen (e equivalent viscous damping coefficient he ofspecimens is calculated as

he 12π

timesSABC + SCDA

SODG + SOBH

(2)

Table 5 Experimentally derived characteristic loads and displacements for specimens SC-1 through SC-6

Specimen Loading direction Py (kN) Δy (mm) Pm (kN) Δm (mm) Pu (kN) Δu (mm) θμ () Relative value

SC-1 + 41650 986 49250 1820 46794 2500 417 1minus 40045 1205 47286 1819 46973 2500 417

SC-2 + 39470 938 46600 1817 41363 2500 417 1minus 38188 1066 45985 1820 44323 2500 417

SC-3 + 40820 850 47005 1820 44397 2000 333 080minus 41037 868 48192 1500 40963 2000 333

SC-4 + 43773 696 50493 1500 42919 3184 531 135minus 40828 972 48311 2500 41064 3595 599

SC-5 + 50121 917 57802 1820 49132 3223 761 134minus 43456 1113 51965 2800 48294 3500 798

SC-6 + 46587 1151 53813 2499 45741 4563 537 187minus 48357 1443 56164 3200 47739 4790 583

Note Py is the yield load Δy is the yield displacement Pm is the peak load Δm is the peak displacement Pu is the ultimate load Δu is the ultimate displacementand θμ is the deformation ability

100

80

60

40

20

0

Ki (k

Nm

m)

ndash10 0 10 20 30 40 50 60 70∆ (mm)

SC-1SC-2SC-3

SC-4SC-5SC-6

Figure 10 Stiffness degradation curves of specimens Stiffnessdegradation of the specimens is represented by secant stiffness Ki

10 Advances in Civil Engineering

As shown in Figure 12 the equivalent viscous dampingcoefficient (he) of the specimen and the displacement (Δ)curve of the column end were calculated for each specimenAt the initial stage of loading the energy consumption of thespecimen increased as the loading displacement increasedWhen the specimen was cracked stress redistribution oc-curred inside the specimen thereby impacting the stress anddeformation of the specimen and decreasing the energyconsumption As the loading displacement continued toincrease the crack continued opening and closing thusincreasing the energy consumption of the specimen Whenthe specimen yielded the internal longitudinal reinforce-ment of the specimen yielded and the stress redistributionoccurred again inside the specimen thus decreasing theenergy consumption of the specimen With continuousloading cracks of the specimen kept opening and closingand energy consumption continued increasing until thespecimen was destroyed (e equivalent viscous dampingcoefficient of each specimen increased as a whole whichindicated that the damage of the specimen increased as thehorizontal deformation increased during the loading pro-cess thereby increasing the energy consumption of thespecimen (Figure 12)

Cumulative energy consumption refers to the sum of allhysteresis loop areas generated from the beginning of theload application to the ultimate displacement point (elarger the value the stronger the energy dissipation capacityof the specimen and the better the seismic performance Asshown in Table 6 the cumulative energy dissipation wascalculated for each specimen

In contrast to SC-1 the cumulative energy consumptionof SC-2 increased by 37 indicating that the obliquehorizontal loading led to more serious cumulative damageand the consumption of more energy Compared to SC-2the accumulated energy consumption value of SC-3 de-creased by approximately 16 possibly due to the pre-mature failure of specimen and the increase of the axialpressure ratio which reduces the cumulative energy con-sumption capacity of specimen In contrast to specimen SC-3 the cumulative energy consumption values of specimensSC-4 SC-5 and SC-6 all improved with increase rates of222 278 and 412 respectively (is is because high-

strength stirrups with small spacing wound CFRP at the endof the column and steel plate mesh at the end of the columnlimit the shedding of concrete and thus increase the work ofthe concrete

37 OpenSees Finite Element Simulation (e open-sourcefinite element program OpenSees (Open System forEarthquake Engineering Simulation) was used as a platformto numerically simulate the experimental specimens (emodel used displacement-based nonlinear beam-columnelements (ree nodes along the height of the column wereused to form two units wherein the top node was free endand the bottom node was embedded (e P-Delta effectcaused by the vertical load was considered by the P-Del-taCrdTransf command (e fiber model was used to definethe relationship of the cross section restoring force at theunit integration point (e longitudinal reinforcement wasmodeled using the Reinforcing Steel uniaxial materialprovided in OpenSees which was based on the Chang-Mander uniaxial material model [21] and simulated theisotropic hardening behavior of steel bars (e concrete wassimulated by Concrete 02 provided by OpenSees (e ma-terial was based on the Kent-Scott-Park uniaxial material

A OG

D

B

C H Δ

P

Figure 11 PminusΔ hysteretic curve representing the energy-con-suming capacity of the specimen

Table 6 Accumulated dissipated energy (Ep) of all specimens

Specimen Ep (kNmiddotmm) Relative valueSC-1 49770 1SC-2 68307 137SC-3 41784 084SC-4 160490 322SC-5 187933 378SC-6 254794 512

SC-1SC-2SC-3

SC-4SC-5SC-6

004

006

008

010

012

014

016

018

020

022

024

he

0 10 20 30 40 50 60 70ndash10∆ (mm)

Figure 12 Viscous damping coefficient curves of each specimen(e equivalent viscous damping coefficient (he) of the specimenand the displacement (Δ) curve of the column end were calculatedfor each specimen

Advances in Civil Engineering 11

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

(a)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

(b)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

(c)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

(d)

Figure 13 Continued

12 Advances in Civil Engineering

model [22] (e model included the tensile mechanicalproperties of the concrete the stiffness degradation and theenergy dissipation behavior of the concrete during recip-rocating loading For the concrete in the core area theMander model [2324] was used to consider the restrainingeffect of stirrups on concrete Here the stress-strain rela-tionship of CFRP-constrained concrete was establishedusing the Concrete 02 material (e stress and strain at thepeak point were the same as the peak-point stress and strainof the concrete bound by the stirrup (e stress and strain atthe limit point were calculated using the peak-point stressand strain of the Lam-Teng model [2526] (ere was littleresearch on concrete columns reinforced by steel plate meshand no specific theoretical models Based on the existingsteel mesh reinforced concrete column the Concrete 02material in this study was used to establish the stress-strainrelationship of the steel plate mesh to the concrete equations(3) and (4) were used to calculate the peak concrete stress fccafter confinement [19] (e peak strain was 4 times that ofthe peak stress of unconstrained concrete the limit pointstress was twice that of the ultimate stress of unconstrainedconcrete the calculations of the remaining characteristicparameters were consistent with the calculation results of theunconstrained concrete

fcc 1 + 077λv( 1113857fck (3)

λv ρvfyv

fck

(4)

where fck is the axial compressive strength of the concrete λv isthe eigenvalue of the stirrup fyv is the yield strength of the steelplate mesh and ρv is the volumetric ratio of the steel plate mesh

(e vertical load was applied incrementally in 10 stepsusing the gravity loading module provided by OpenSees and

was held constant after the vertical load was completed (ehorizontal load was applied in time series and the loadingsystem was consistent with the experimental proceduresused in this study

(e hysteresis curves for SC-1 through SC-6 generatedby the OpenSees finite element analysis were compared tothe experimentally generated hysteresis curves as shown inFigure 13 (e curves generated by OpenSees are in goodagreement with the experimental results

4 Conclusion

Here six short concrete columns with high-strength lon-gitudinal reinforcements were subjected to low-cycle re-peated loading tests By comparing and analyzing the testresults based on observed test phenomena the followingconclusions are drawn

(1) Compared to the horizontally loaded test specimensthe strength of the diagonally loaded specimensdecreased and the stiffness degradation trendaccelerated this indicates that the effect of obliqueloading is unfavorable to the strength and stiffness ofthe specimens

(2) Under the action of oblique load as the axialcompression ratio increases the strength of thespecimen increases however the deformation ca-pacity becomes worse the stiffness becomes severelydegraded and the specimen is prone to shear brittlefailure

(3) Under the action of oblique load the reinforcementmeasures of the CFRP at the end of the columnimprove the strength and energy consumption of thespecimen however the higher axial compression

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(e)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(f)

Figure 13 OpenSees finite element simulations compared with the experimentally derived hysteresis curve for each specimen Resultscomparison of (a) SC-1 (b) SC-2 (c) SC-3 (d) SC-4 (e) SC-5 and (f) SC-6

Advances in Civil Engineering 13

ratio makes the CFRP more prone to damage anddoes not improve the deformation performance ofthe specimen However the local reinforcementmeasures of the steel plate mesh on the end of thecolumn not only increase the strength and energyconsumption of the specimen but also improve thedeformation ability of the specimen and the seismicperformance of the specimen

(4) In contrast to the unreinforced specimens theaddition of the high-strength stirrups with smallspacing column-end wound CFRP and column-end outer steel plate mesh all improve the strengthdeformation capacity and energy consumptioncapacity of the specimens (e addition of the high-strength stirrups with small spacing and the col-umn-end outer steel plate mesh both altered thefailure mode of the specimen transforming it fromshear failure to bending shear failure (is showsthat the above measures can effectively improve theseismic performance of the test specimen under theaction of oblique loads with a high axial com-pression ratio

(5) Under the action of a high axial pressure ratiooblique load by selecting the appropriate fiber unitand material constitutive relationship the OpenSeesprogram can obtain a simulation result that is ingood agreement with the test hysteresis curve (isverifies the validity of the numerical simulation andprovides a certain basis for subsequent and extendednumerical simulation analyses

Data Availability

All data or models used to support the findings of this studyare included within the article Some data or models thatsupport the findings of this study are available from thecorresponding author upon reasonable request

Conflicts of Interest

(e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

(is work was supported by the Natural Science Foundationof Shandong Province under Grant nos ZR2015EQ017 andZR2018MEE044 and Off-Campus Development Project ofKey Laboratory of Beijing University of Technology underGrant no 2020B03 (e authors are grateful to the KeyLaboratory of Building Structural Retrofitting and Under-ground Space Engineering (Shandong Jianzhu University)Ministry of Education for accommodating the use of theequipment and facilities Professor Xingquan Zhao forproviding computer equipment for numerical simulation ofthe experiment and Editage (httpwwweditagecn) forEnglish language editing

References

[1] A Ghobarah and K Galal ldquoSeismic rehabilitation of shortrectangular RC columnsrdquo Journal of Earthquake Engineeringvol 8 no 1 pp 45ndash68 2004

[2] Y A Li T Y Huang and S J Hwang ldquoSeismic response ofreinforced concrete short columns failed in shearrdquo ACIStructural Journal vol 111 no 4 pp 945ndash954 2014

[3] H Takizawa and H Aoyama ldquoBiaxial effects in modellingearthquake response of RC structuresrdquo Earthquake Engi-neering amp Structural Dynamics vol 4 no 6 pp 523ndash5521976

[4] H Umehara and J O Jirsa ldquoShort rectangular RC columnsunder bidirectional loadingsrdquo Journal of Structural Engi-neering vol 110 no 3 pp 605ndash618 1984

[5] K A Woodward and J O Jirsa ldquoInfluence of reinforcementon RC short column lateral resistancerdquo Journal of StructuralEngineering vol 110 no 1 pp 90ndash104 1984

[6] K Maruyama H Ramirez and J O Jirsa ldquoShort RC columnsunder bilateral load historiesrdquo Journal of Structural Engi-neering vol 110 no 1 pp 120ndash137 1984

[7] H Rodrigues H Varum A Arede and A G CostaldquoBehaviour of reinforced concrete column under biaxial cyclicloadingmdashstate of the artrdquo International Journal of AdvancedStructural Engineering vol 5 no 1 pp 1ndash12 2013

[8] D Wang L Huang T Yu and Z Wang ldquoSeismic perfor-mance of CFRP-retrofitted large-scale square RC columnswith high axial compression ratiosrdquo Journal of Composites forConstruction vol 21 no 5 Article ID 04017031 2017

[9] J Yang and J Wang ldquoSeismic performance of shear-con-trolled CFRP-strengthened high-strength concrete squarecolumns under simulated seismic loadrdquo Journal of Compositesfor Construction vol 22 no 6 Article ID 04018061 2018

[10] X Zhou and J Liu ldquoSeismic behavior and shear strength oftubed RC short columnsrdquo Journal of Constructional SteelResearch vol 66 no 3 pp 385ndash397 2010

[11] H Ma J Xue Y Liu and X Zhang ldquoCyclic loading tests andshear strength of steel reinforced recycled concrete shortcolumnsrdquo Engineering Structures vol 92 pp 55ndash68 2015

[12] D Sokoli and W M Ghannoum ldquoHigh-strength reinforce-ment in columns under high shear stressesrdquo ACI StructuralJournal vol 113 no 3 pp 605ndash614 2016

[13] H Ding Y Liu C Han and Y Guo ldquoSeismic performance ofhigh-strength short concrete column with high-strengthstirrups constraintsrdquo Transactions of Tianjin Universityvol 23 no 4 pp 360ndash369 2017

[14] H O Shin Y S Yoon W D Cook and D Mitchell ldquoAxialload response of ultra-high-strength concrete columns andhigh-strength reinforcementrdquo Transactions of Tianjin Uni-versity vol 113 no 2 pp 325ndash336 216

[15] L A E Shehata M L A V Carneiro and L C D ShehataldquoStrength of short concrete columns confined with CFRPsheetsrdquo Materials and Structures vol 35 pp 50ndash58 2002

[16] F Colomb H Tobbi E Ferrier and P Hamelin ldquoSeismicretrofit of reinforced concrete short columns by CFRPmaterialsfit of reinforced concrete short columns by CFRPmaterialsrdquo Composite Structures vol 82 no 4 pp 475ndash4872008

[17] K Galal A Arafa and A Ghobarah ldquoRetrofit of RC squareshort columnsrdquo Engineering Structures vol 27 no 5pp 801ndash813 2005

[18] R Morshed and M T Kazemi ldquoSeismic shear strengtheningof RC beams and columns with expanded steel meshesrdquo

14 Advances in Civil Engineering

Disp

lace

men

t (m

m)

Loading cycle

1 24 486

12182 22

28 3238

4350

ndash15 ndash3 ndash6ndash10

ndash15 ndash20ndash25

ndash30ndash35

ndash40ndash45

ndash60

Figure 3 Loading protocol (e tests performed via displacement-controlled loading

Reaction frame

Lifting jackConnector

Steel backing plate

MTSScrew

Steel plate

Electronic displacement meter

Spec

imen

Pedestal

Anchor boltStatic platform

Reac

tion

wal

l

Figure 4 Experimental test set-up MTS actuator with data acquisition system collects load and displacement data

S

N

WE

Specimen

y

x

Pull Push

(a)

Specimen

y xS

N

E W

Pull Push

(b)

Figure 5 Definition of specimen observation surface (a) Spindle loading (b) 45deg loading

6 Advances in Civil Engineering

At 40mm the longitudinal reinforcement was brokenWhen the specimen was broken the steel plate mesh at thebottom of the column was convex (Figure 6(g)) After thetest the steel plate mesh was peeled off it was found that theconcrete at the bottom of the column was broken and thelongitudinal steel bars were convex and partially brokenAccordingly the bending and shear failure characteristics ofspecimen SC-6 can be seen (Figure 6(h))

Overall compared with the horizontally loaded testspecimens the concrete at the corners of the diagonallyloaded test specimens fell off severely which reduced theworkability of the test specimens In particular the increasein the axial pressure ratio makes this damage more seriousCompared to the unreinforced test specimens high-strengthstirrups with small spacing column-end wrapped CFRPand column-end outer steel plate mesh enhanced the re-straint effect on concrete limited concrete falling off andimproved the seismic performance of the specimens underoblique loads

32 Hysteresis Curves (e load-displacement hysteresiscurves of each specimen demonstrate the performance ofeach specimen during the duration of the tests (Figure 7) Pis the measured horizontal load Δ is the measured hori-zontal displacement of the loading point As can be seenfrom Figure 7 compared to specimen SC-1 specimen SC-2undergoes accelerated strength degradation at a later stage ofloading and the residual deformation is larger(is could beattributed to the oblique loading that leads to the corner

concrete of the specimen being subjected to loads in twodirections resulting in serious damage to the corner con-crete (Figures 7(a) and 7(b)) In contrast to specimen SC-2specimen SC-3 has a significantly lower load at the later stageof loading this is due to the severe fall of the concrete at thelater stage of loading (Figures 7(b) and 7(c)) (ere were twosignificant drops in the hysteresis curves of SC-4 and SC-6likely due to the fracture of the high-strength longitudinalbars which led to a significant decline in the strength ofthese specimens (Figures 7(d) and 7(f)) However the high-strength stirrups with small spacing included in thesetreatments provided a strong constraint effect for high-strength longitudinal bars that enabled the specimens toretain a strong strength Compared to the hysteresis curve ofspecimen SC-4 that of specimen SC-5 is less full (is isbecause the CFRP is prone to tear and damage at the columnangle under a high axial pressure ratio (Figures 7(d) and7(e)) which causes the strength of the specimen to dropsharply In contrast to specimen SC-4 the load of specimenSC-6 decreases slowly at the later stage of loading and thehysteresis curve was relatively plump (Figures 7(d) and 7(f ))(is is because the steel plate net at the end of the columncan effectively slow the fall of concrete and exert a strongerenergy consumption

33 Skeleton Curves In the hysteretic curve under thecondition of low-cycle reciprocating loading the outerwinding line of the peak loading point of each stage is calleda skeleton curve which characterizes the characteristics of

Ordinary comparison

specimen

(a)

α = 45deg

n = 08

(b)

α = 45deg

n = 10

(c)

Dense high-strength stirrups

α = 45deg

n = 10

(d)

CFRP constraint

α = 45deg

n = 10

(e)

Remove CFRP

α = 45deg

n = 10

(f )

α = 45deg

n = 10

Steel plate mesh constraint

(g)

Remove steel plate mesh

α = 45deg

n = 10

(h)

Figure 6 Visual observations of the ultimate failure modes of short column (SC) specimens (a) SC-1 (b) SC-2 (c) SC-3 (d) SC-4 (e) SC-5(f ) SC-5 after removal of CFRP (g) SC-6 and (h) SC-6 after removal of steel plate mesh

Advances in Civil Engineering 7

stress and deformation during the loading of the specimen(e skeleton curve of each specimen is shown in Figure 8 Ascan be seen from the figure the development of the skeleton

curves of each specimen can be roughly divided into threestages (1) In the elastic stage the load changes linearly withthe displacement the specimen has yet to crack and no

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(a)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(b)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

(c)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(d)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

(e)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(f )

Figure 7 Hysteretic curves of short column (SC) specimens 1ndash6 (a) SC-1 (b) SC-2 (c) SC-3 (d) SC-4 (e) SC-5 and (f) SC-6

8 Advances in Civil Engineering

residual deformation is observed (2) During the develop-ment stage of a multicrack many cracks appear in thespecimen When residual deformation begins to appearmultiple tiny cracks appear on the surface of the specimenand the horizontal load of the specimen slowly increasesWith the accumulation of damage the specimen reaches thepeak load (3) In the load drop stage for specimens SC-1SC-2 and SC-3 the skeleton curve decreases significantly inthe later stage of loading (is is because the ordinarystirrups with large spacing cannot provide effective lateralrestraints for the specimens under a high axial compressionratio thus making the strength of the specimens dropdramatically Compared to specimen SC-3 the skeletoncurves of specimens SC-4 SC-5 and SC-6 decrease slowlyand show good deformation ability In particular the de-formation capacity of specimens SC-4 and SC-6 after thepeak point significantly improves this is conducive toimproving the seismic energy dissipation capability ofspecimens

34 Bearing Capacity and Ductility Each sample wascharacterized by the yield load point the peak load pointand the failure load point within a load-displacement curveAs shown in Figure 9 the yield point D was determined bythe equivalent elastic-plastic energy method that is wherethe area SOAB SBCD and the ultimate load was simplydefined as 85 of the peak load [20] Because the strength ofSC-1 SC-2 and SC-3 declined rapidly after reaching thepeak load and the ultimate load did not reach 85 of thepeak load the failure displacements of these were taken asthe ultimate displacement Here the ultimate displacementangle (θμ) was used to characterize the deformation ability ofthe specimen and was calculated as θμ Δul0 where l0 is thecolumnrsquos height For each specimen the characteristic loadand displacement calculation results are shown in Table 5

(e relative value is the ratio of the average of the positiveand negative corresponding coefficients of SC-2 through SC-6 and the average of the positive and negative correspondingcoefficients of SC-1

As can be seen in Table 5 compared to specimen SC-1the yield load peak load and ultimate load of specimen SC-2are reduced and the ultimate displacement angle is un-changed(is is because the concrete in the corner of the testspecimen is severely damaged under the diagonal horizontalloading making the strength of the specimen decreasehowever this has no effect on the deformation ability of thespecimen A comparison of SC-2 and SC-3 reveals thatunder the oblique load as the axial pressure ratio increasesthe strength of the specimen increases but the deformationcapacity decreases In contrast to specimen SC-4 the yieldload peak load and ultimate load of SC-5 improvedwhereas the ultimate displacement angle decreased by 1(is result indicates that although the strength of thespecimen under high axial pressure ratio improved thedeformation capacity of the specimen under high axialpressure ratio did not improve Compared to specimen SC-4 the yield load peak load and ultimate load of specimenSC-6 improved and the ultimate displacement angle in-creased by 52(is result was likely due to the column-endouter steel plate mesh providing a strong restraining effecton the column-end concrete which then increased thespecimenrsquos strength deformation capacity and seismicperformance

In comparison to SC-3 the yield load peak load andultimate load of SC-4 SC-5 and SC-6 were all greatlyimproved as were the ultimate displacement angles (isindicates that the high-strength stirrups with small spacingcolumn-end wound CFRP and column-end outer steel platemesh may improve the strength and the deformation abilityof the RC columns therefore this should be consideredwhen accounting for seismic loads in RC columns

35 Stiffness Degradation Stiffness degradation of a speci-men under cyclic loading is usually attributable to the ac-cumulation of specimen damage which has great influence

SC-1SC-2SC-3

SC-4SC-5SC-6

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

Figure 8 Skeleton curves of specimens Skeleton curves representthe outer winding line of the peak loading point of each stage

Δ (mm)

AB

D

P (k

N)

Pmax

Py085Pmax

Δy Δm Δu

C

O

Figure 9 Calculation of characteristic points for each specimen Pyis the yield load Pmax is the peak load

Advances in Civil Engineering 9

on the seismic performance of the specimens Here thesecant stiffness (Ki) was used to represent the stiffnessdegradation of the specimens (e secant stiffness Ki wascalculated as

Ki P

+i

11138681113868111386811138681113868111386811138681113868 + P

minusi

11138681113868111386811138681113868111386811138681113868

Δ+i

11138681113868111386811138681113868111386811138681113868 + Δminus

i

11138681113868111386811138681113868111386811138681113868 (1)

where Pi+ and Pminusi are the i-th positive and reverse peak loads

respectively and Δi+ and Δminusi are the i-th positive and reverse

peak displacements(e stiffness degradation curve of each test piece is

shown in Figure 10 As loading displacement increased thestiffness of each specimen gradually decreased (e stiffnessdegraded rapidly in the early stage and slowly in the laterstage (is could be due to the continuous cracking ofconcrete in the early stage of loading whereas no new crackswere generated in the late loading stages thus when thecumulative damage of the specimen reached a certain de-gree the slope of the stiffness degradation curve of thespecimen decreased Compared to specimen SC-1 thestiffness of specimen SC-2 degraded faster (is is becausethe oblique horizontal loading caused damage in the cornerof the specimen affecting each other In contrast to speci-men SC-2 the stiffness of specimen SC-3 decreased sharplyin the later stage of loading (is is due to the higher axialcompression ratio of the specimen which caused the con-crete to fall severely the stirrups to protrude and thelongitudinal bars to yield(e stiffness degradation curves ofSC-4 SC-5 and SC-6 had a slower downward trend and alonger curve extension compared to those of SC-3 (isindicates that the high-strength stirrups with small spacingthe column-end wound CFRP and the column-end outersteel plate mesh may have alleviated the damage degree ofthe specimen and thus slowed the degradation stiffnessdegradation of these specimens

36 Energy Dissipation (e energy dissipation capacity ofspecimens under earthquake action is an important indexfor evaluating their seismic performance Here the equiv-alent viscous damping coefficient (he) and cumulative energy

consumption (Ep) were used to characterize the energydissipation performance of the experimental specimens (eequivalent viscous damping coefficient characterizes theenergy dissipation performance of specimens at differentloading stages the cumulative energy consumption char-acterizes the overall energy dissipation capacity of specimensduring the whole loading process

As shown in Figure 11 the area of each hysteresis loop inthe hysteresis curve represents the energy-consuming ca-pacity of the specimens under this cycle When otherconditions are the same the larger the area of the hysteresisloop the better the energy consumption capability of thespecimen (e equivalent viscous damping coefficient he ofspecimens is calculated as

he 12π

timesSABC + SCDA

SODG + SOBH

(2)

Table 5 Experimentally derived characteristic loads and displacements for specimens SC-1 through SC-6

Specimen Loading direction Py (kN) Δy (mm) Pm (kN) Δm (mm) Pu (kN) Δu (mm) θμ () Relative value

SC-1 + 41650 986 49250 1820 46794 2500 417 1minus 40045 1205 47286 1819 46973 2500 417

SC-2 + 39470 938 46600 1817 41363 2500 417 1minus 38188 1066 45985 1820 44323 2500 417

SC-3 + 40820 850 47005 1820 44397 2000 333 080minus 41037 868 48192 1500 40963 2000 333

SC-4 + 43773 696 50493 1500 42919 3184 531 135minus 40828 972 48311 2500 41064 3595 599

SC-5 + 50121 917 57802 1820 49132 3223 761 134minus 43456 1113 51965 2800 48294 3500 798

SC-6 + 46587 1151 53813 2499 45741 4563 537 187minus 48357 1443 56164 3200 47739 4790 583

Note Py is the yield load Δy is the yield displacement Pm is the peak load Δm is the peak displacement Pu is the ultimate load Δu is the ultimate displacementand θμ is the deformation ability

100

80

60

40

20

0

Ki (k

Nm

m)

ndash10 0 10 20 30 40 50 60 70∆ (mm)

SC-1SC-2SC-3

SC-4SC-5SC-6

Figure 10 Stiffness degradation curves of specimens Stiffnessdegradation of the specimens is represented by secant stiffness Ki

10 Advances in Civil Engineering

As shown in Figure 12 the equivalent viscous dampingcoefficient (he) of the specimen and the displacement (Δ)curve of the column end were calculated for each specimenAt the initial stage of loading the energy consumption of thespecimen increased as the loading displacement increasedWhen the specimen was cracked stress redistribution oc-curred inside the specimen thereby impacting the stress anddeformation of the specimen and decreasing the energyconsumption As the loading displacement continued toincrease the crack continued opening and closing thusincreasing the energy consumption of the specimen Whenthe specimen yielded the internal longitudinal reinforce-ment of the specimen yielded and the stress redistributionoccurred again inside the specimen thus decreasing theenergy consumption of the specimen With continuousloading cracks of the specimen kept opening and closingand energy consumption continued increasing until thespecimen was destroyed (e equivalent viscous dampingcoefficient of each specimen increased as a whole whichindicated that the damage of the specimen increased as thehorizontal deformation increased during the loading pro-cess thereby increasing the energy consumption of thespecimen (Figure 12)

Cumulative energy consumption refers to the sum of allhysteresis loop areas generated from the beginning of theload application to the ultimate displacement point (elarger the value the stronger the energy dissipation capacityof the specimen and the better the seismic performance Asshown in Table 6 the cumulative energy dissipation wascalculated for each specimen

In contrast to SC-1 the cumulative energy consumptionof SC-2 increased by 37 indicating that the obliquehorizontal loading led to more serious cumulative damageand the consumption of more energy Compared to SC-2the accumulated energy consumption value of SC-3 de-creased by approximately 16 possibly due to the pre-mature failure of specimen and the increase of the axialpressure ratio which reduces the cumulative energy con-sumption capacity of specimen In contrast to specimen SC-3 the cumulative energy consumption values of specimensSC-4 SC-5 and SC-6 all improved with increase rates of222 278 and 412 respectively (is is because high-

strength stirrups with small spacing wound CFRP at the endof the column and steel plate mesh at the end of the columnlimit the shedding of concrete and thus increase the work ofthe concrete

37 OpenSees Finite Element Simulation (e open-sourcefinite element program OpenSees (Open System forEarthquake Engineering Simulation) was used as a platformto numerically simulate the experimental specimens (emodel used displacement-based nonlinear beam-columnelements (ree nodes along the height of the column wereused to form two units wherein the top node was free endand the bottom node was embedded (e P-Delta effectcaused by the vertical load was considered by the P-Del-taCrdTransf command (e fiber model was used to definethe relationship of the cross section restoring force at theunit integration point (e longitudinal reinforcement wasmodeled using the Reinforcing Steel uniaxial materialprovided in OpenSees which was based on the Chang-Mander uniaxial material model [21] and simulated theisotropic hardening behavior of steel bars (e concrete wassimulated by Concrete 02 provided by OpenSees (e ma-terial was based on the Kent-Scott-Park uniaxial material

A OG

D

B

C H Δ

P

Figure 11 PminusΔ hysteretic curve representing the energy-con-suming capacity of the specimen

Table 6 Accumulated dissipated energy (Ep) of all specimens

Specimen Ep (kNmiddotmm) Relative valueSC-1 49770 1SC-2 68307 137SC-3 41784 084SC-4 160490 322SC-5 187933 378SC-6 254794 512

SC-1SC-2SC-3

SC-4SC-5SC-6

004

006

008

010

012

014

016

018

020

022

024

he

0 10 20 30 40 50 60 70ndash10∆ (mm)

Figure 12 Viscous damping coefficient curves of each specimen(e equivalent viscous damping coefficient (he) of the specimenand the displacement (Δ) curve of the column end were calculatedfor each specimen

Advances in Civil Engineering 11

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

(a)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

(b)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

(c)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

(d)

Figure 13 Continued

12 Advances in Civil Engineering

model [22] (e model included the tensile mechanicalproperties of the concrete the stiffness degradation and theenergy dissipation behavior of the concrete during recip-rocating loading For the concrete in the core area theMander model [2324] was used to consider the restrainingeffect of stirrups on concrete Here the stress-strain rela-tionship of CFRP-constrained concrete was establishedusing the Concrete 02 material (e stress and strain at thepeak point were the same as the peak-point stress and strainof the concrete bound by the stirrup (e stress and strain atthe limit point were calculated using the peak-point stressand strain of the Lam-Teng model [2526] (ere was littleresearch on concrete columns reinforced by steel plate meshand no specific theoretical models Based on the existingsteel mesh reinforced concrete column the Concrete 02material in this study was used to establish the stress-strainrelationship of the steel plate mesh to the concrete equations(3) and (4) were used to calculate the peak concrete stress fccafter confinement [19] (e peak strain was 4 times that ofthe peak stress of unconstrained concrete the limit pointstress was twice that of the ultimate stress of unconstrainedconcrete the calculations of the remaining characteristicparameters were consistent with the calculation results of theunconstrained concrete

fcc 1 + 077λv( 1113857fck (3)

λv ρvfyv

fck

(4)

where fck is the axial compressive strength of the concrete λv isthe eigenvalue of the stirrup fyv is the yield strength of the steelplate mesh and ρv is the volumetric ratio of the steel plate mesh

(e vertical load was applied incrementally in 10 stepsusing the gravity loading module provided by OpenSees and

was held constant after the vertical load was completed (ehorizontal load was applied in time series and the loadingsystem was consistent with the experimental proceduresused in this study

(e hysteresis curves for SC-1 through SC-6 generatedby the OpenSees finite element analysis were compared tothe experimentally generated hysteresis curves as shown inFigure 13 (e curves generated by OpenSees are in goodagreement with the experimental results

4 Conclusion

Here six short concrete columns with high-strength lon-gitudinal reinforcements were subjected to low-cycle re-peated loading tests By comparing and analyzing the testresults based on observed test phenomena the followingconclusions are drawn

(1) Compared to the horizontally loaded test specimensthe strength of the diagonally loaded specimensdecreased and the stiffness degradation trendaccelerated this indicates that the effect of obliqueloading is unfavorable to the strength and stiffness ofthe specimens

(2) Under the action of oblique load as the axialcompression ratio increases the strength of thespecimen increases however the deformation ca-pacity becomes worse the stiffness becomes severelydegraded and the specimen is prone to shear brittlefailure

(3) Under the action of oblique load the reinforcementmeasures of the CFRP at the end of the columnimprove the strength and energy consumption of thespecimen however the higher axial compression

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(e)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(f)

Figure 13 OpenSees finite element simulations compared with the experimentally derived hysteresis curve for each specimen Resultscomparison of (a) SC-1 (b) SC-2 (c) SC-3 (d) SC-4 (e) SC-5 and (f) SC-6

Advances in Civil Engineering 13

ratio makes the CFRP more prone to damage anddoes not improve the deformation performance ofthe specimen However the local reinforcementmeasures of the steel plate mesh on the end of thecolumn not only increase the strength and energyconsumption of the specimen but also improve thedeformation ability of the specimen and the seismicperformance of the specimen

(4) In contrast to the unreinforced specimens theaddition of the high-strength stirrups with smallspacing column-end wound CFRP and column-end outer steel plate mesh all improve the strengthdeformation capacity and energy consumptioncapacity of the specimens (e addition of the high-strength stirrups with small spacing and the col-umn-end outer steel plate mesh both altered thefailure mode of the specimen transforming it fromshear failure to bending shear failure (is showsthat the above measures can effectively improve theseismic performance of the test specimen under theaction of oblique loads with a high axial com-pression ratio

(5) Under the action of a high axial pressure ratiooblique load by selecting the appropriate fiber unitand material constitutive relationship the OpenSeesprogram can obtain a simulation result that is ingood agreement with the test hysteresis curve (isverifies the validity of the numerical simulation andprovides a certain basis for subsequent and extendednumerical simulation analyses

Data Availability

All data or models used to support the findings of this studyare included within the article Some data or models thatsupport the findings of this study are available from thecorresponding author upon reasonable request

Conflicts of Interest

(e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

(is work was supported by the Natural Science Foundationof Shandong Province under Grant nos ZR2015EQ017 andZR2018MEE044 and Off-Campus Development Project ofKey Laboratory of Beijing University of Technology underGrant no 2020B03 (e authors are grateful to the KeyLaboratory of Building Structural Retrofitting and Under-ground Space Engineering (Shandong Jianzhu University)Ministry of Education for accommodating the use of theequipment and facilities Professor Xingquan Zhao forproviding computer equipment for numerical simulation ofthe experiment and Editage (httpwwweditagecn) forEnglish language editing

References

[1] A Ghobarah and K Galal ldquoSeismic rehabilitation of shortrectangular RC columnsrdquo Journal of Earthquake Engineeringvol 8 no 1 pp 45ndash68 2004

[2] Y A Li T Y Huang and S J Hwang ldquoSeismic response ofreinforced concrete short columns failed in shearrdquo ACIStructural Journal vol 111 no 4 pp 945ndash954 2014

[3] H Takizawa and H Aoyama ldquoBiaxial effects in modellingearthquake response of RC structuresrdquo Earthquake Engi-neering amp Structural Dynamics vol 4 no 6 pp 523ndash5521976

[4] H Umehara and J O Jirsa ldquoShort rectangular RC columnsunder bidirectional loadingsrdquo Journal of Structural Engi-neering vol 110 no 3 pp 605ndash618 1984

[5] K A Woodward and J O Jirsa ldquoInfluence of reinforcementon RC short column lateral resistancerdquo Journal of StructuralEngineering vol 110 no 1 pp 90ndash104 1984

[6] K Maruyama H Ramirez and J O Jirsa ldquoShort RC columnsunder bilateral load historiesrdquo Journal of Structural Engi-neering vol 110 no 1 pp 120ndash137 1984

[7] H Rodrigues H Varum A Arede and A G CostaldquoBehaviour of reinforced concrete column under biaxial cyclicloadingmdashstate of the artrdquo International Journal of AdvancedStructural Engineering vol 5 no 1 pp 1ndash12 2013

[8] D Wang L Huang T Yu and Z Wang ldquoSeismic perfor-mance of CFRP-retrofitted large-scale square RC columnswith high axial compression ratiosrdquo Journal of Composites forConstruction vol 21 no 5 Article ID 04017031 2017

[9] J Yang and J Wang ldquoSeismic performance of shear-con-trolled CFRP-strengthened high-strength concrete squarecolumns under simulated seismic loadrdquo Journal of Compositesfor Construction vol 22 no 6 Article ID 04018061 2018

[10] X Zhou and J Liu ldquoSeismic behavior and shear strength oftubed RC short columnsrdquo Journal of Constructional SteelResearch vol 66 no 3 pp 385ndash397 2010

[11] H Ma J Xue Y Liu and X Zhang ldquoCyclic loading tests andshear strength of steel reinforced recycled concrete shortcolumnsrdquo Engineering Structures vol 92 pp 55ndash68 2015

[12] D Sokoli and W M Ghannoum ldquoHigh-strength reinforce-ment in columns under high shear stressesrdquo ACI StructuralJournal vol 113 no 3 pp 605ndash614 2016

[13] H Ding Y Liu C Han and Y Guo ldquoSeismic performance ofhigh-strength short concrete column with high-strengthstirrups constraintsrdquo Transactions of Tianjin Universityvol 23 no 4 pp 360ndash369 2017

[14] H O Shin Y S Yoon W D Cook and D Mitchell ldquoAxialload response of ultra-high-strength concrete columns andhigh-strength reinforcementrdquo Transactions of Tianjin Uni-versity vol 113 no 2 pp 325ndash336 216

[15] L A E Shehata M L A V Carneiro and L C D ShehataldquoStrength of short concrete columns confined with CFRPsheetsrdquo Materials and Structures vol 35 pp 50ndash58 2002

[16] F Colomb H Tobbi E Ferrier and P Hamelin ldquoSeismicretrofit of reinforced concrete short columns by CFRPmaterialsfit of reinforced concrete short columns by CFRPmaterialsrdquo Composite Structures vol 82 no 4 pp 475ndash4872008

[17] K Galal A Arafa and A Ghobarah ldquoRetrofit of RC squareshort columnsrdquo Engineering Structures vol 27 no 5pp 801ndash813 2005

[18] R Morshed and M T Kazemi ldquoSeismic shear strengtheningof RC beams and columns with expanded steel meshesrdquo

14 Advances in Civil Engineering

At 40mm the longitudinal reinforcement was brokenWhen the specimen was broken the steel plate mesh at thebottom of the column was convex (Figure 6(g)) After thetest the steel plate mesh was peeled off it was found that theconcrete at the bottom of the column was broken and thelongitudinal steel bars were convex and partially brokenAccordingly the bending and shear failure characteristics ofspecimen SC-6 can be seen (Figure 6(h))

Overall compared with the horizontally loaded testspecimens the concrete at the corners of the diagonallyloaded test specimens fell off severely which reduced theworkability of the test specimens In particular the increasein the axial pressure ratio makes this damage more seriousCompared to the unreinforced test specimens high-strengthstirrups with small spacing column-end wrapped CFRPand column-end outer steel plate mesh enhanced the re-straint effect on concrete limited concrete falling off andimproved the seismic performance of the specimens underoblique loads

32 Hysteresis Curves (e load-displacement hysteresiscurves of each specimen demonstrate the performance ofeach specimen during the duration of the tests (Figure 7) Pis the measured horizontal load Δ is the measured hori-zontal displacement of the loading point As can be seenfrom Figure 7 compared to specimen SC-1 specimen SC-2undergoes accelerated strength degradation at a later stage ofloading and the residual deformation is larger(is could beattributed to the oblique loading that leads to the corner

concrete of the specimen being subjected to loads in twodirections resulting in serious damage to the corner con-crete (Figures 7(a) and 7(b)) In contrast to specimen SC-2specimen SC-3 has a significantly lower load at the later stageof loading this is due to the severe fall of the concrete at thelater stage of loading (Figures 7(b) and 7(c)) (ere were twosignificant drops in the hysteresis curves of SC-4 and SC-6likely due to the fracture of the high-strength longitudinalbars which led to a significant decline in the strength ofthese specimens (Figures 7(d) and 7(f)) However the high-strength stirrups with small spacing included in thesetreatments provided a strong constraint effect for high-strength longitudinal bars that enabled the specimens toretain a strong strength Compared to the hysteresis curve ofspecimen SC-4 that of specimen SC-5 is less full (is isbecause the CFRP is prone to tear and damage at the columnangle under a high axial pressure ratio (Figures 7(d) and7(e)) which causes the strength of the specimen to dropsharply In contrast to specimen SC-4 the load of specimenSC-6 decreases slowly at the later stage of loading and thehysteresis curve was relatively plump (Figures 7(d) and 7(f ))(is is because the steel plate net at the end of the columncan effectively slow the fall of concrete and exert a strongerenergy consumption

33 Skeleton Curves In the hysteretic curve under thecondition of low-cycle reciprocating loading the outerwinding line of the peak loading point of each stage is calleda skeleton curve which characterizes the characteristics of

Ordinary comparison

specimen

(a)

α = 45deg

n = 08

(b)

α = 45deg

n = 10

(c)

Dense high-strength stirrups

α = 45deg

n = 10

(d)

CFRP constraint

α = 45deg

n = 10

(e)

Remove CFRP

α = 45deg

n = 10

(f )

α = 45deg

n = 10

Steel plate mesh constraint

(g)

Remove steel plate mesh

α = 45deg

n = 10

(h)

Figure 6 Visual observations of the ultimate failure modes of short column (SC) specimens (a) SC-1 (b) SC-2 (c) SC-3 (d) SC-4 (e) SC-5(f ) SC-5 after removal of CFRP (g) SC-6 and (h) SC-6 after removal of steel plate mesh

Advances in Civil Engineering 7

stress and deformation during the loading of the specimen(e skeleton curve of each specimen is shown in Figure 8 Ascan be seen from the figure the development of the skeleton

curves of each specimen can be roughly divided into threestages (1) In the elastic stage the load changes linearly withthe displacement the specimen has yet to crack and no

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(a)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(b)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

(c)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(d)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

(e)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(f )

Figure 7 Hysteretic curves of short column (SC) specimens 1ndash6 (a) SC-1 (b) SC-2 (c) SC-3 (d) SC-4 (e) SC-5 and (f) SC-6

8 Advances in Civil Engineering

residual deformation is observed (2) During the develop-ment stage of a multicrack many cracks appear in thespecimen When residual deformation begins to appearmultiple tiny cracks appear on the surface of the specimenand the horizontal load of the specimen slowly increasesWith the accumulation of damage the specimen reaches thepeak load (3) In the load drop stage for specimens SC-1SC-2 and SC-3 the skeleton curve decreases significantly inthe later stage of loading (is is because the ordinarystirrups with large spacing cannot provide effective lateralrestraints for the specimens under a high axial compressionratio thus making the strength of the specimens dropdramatically Compared to specimen SC-3 the skeletoncurves of specimens SC-4 SC-5 and SC-6 decrease slowlyand show good deformation ability In particular the de-formation capacity of specimens SC-4 and SC-6 after thepeak point significantly improves this is conducive toimproving the seismic energy dissipation capability ofspecimens

34 Bearing Capacity and Ductility Each sample wascharacterized by the yield load point the peak load pointand the failure load point within a load-displacement curveAs shown in Figure 9 the yield point D was determined bythe equivalent elastic-plastic energy method that is wherethe area SOAB SBCD and the ultimate load was simplydefined as 85 of the peak load [20] Because the strength ofSC-1 SC-2 and SC-3 declined rapidly after reaching thepeak load and the ultimate load did not reach 85 of thepeak load the failure displacements of these were taken asthe ultimate displacement Here the ultimate displacementangle (θμ) was used to characterize the deformation ability ofthe specimen and was calculated as θμ Δul0 where l0 is thecolumnrsquos height For each specimen the characteristic loadand displacement calculation results are shown in Table 5

(e relative value is the ratio of the average of the positiveand negative corresponding coefficients of SC-2 through SC-6 and the average of the positive and negative correspondingcoefficients of SC-1

As can be seen in Table 5 compared to specimen SC-1the yield load peak load and ultimate load of specimen SC-2are reduced and the ultimate displacement angle is un-changed(is is because the concrete in the corner of the testspecimen is severely damaged under the diagonal horizontalloading making the strength of the specimen decreasehowever this has no effect on the deformation ability of thespecimen A comparison of SC-2 and SC-3 reveals thatunder the oblique load as the axial pressure ratio increasesthe strength of the specimen increases but the deformationcapacity decreases In contrast to specimen SC-4 the yieldload peak load and ultimate load of SC-5 improvedwhereas the ultimate displacement angle decreased by 1(is result indicates that although the strength of thespecimen under high axial pressure ratio improved thedeformation capacity of the specimen under high axialpressure ratio did not improve Compared to specimen SC-4 the yield load peak load and ultimate load of specimenSC-6 improved and the ultimate displacement angle in-creased by 52(is result was likely due to the column-endouter steel plate mesh providing a strong restraining effecton the column-end concrete which then increased thespecimenrsquos strength deformation capacity and seismicperformance

In comparison to SC-3 the yield load peak load andultimate load of SC-4 SC-5 and SC-6 were all greatlyimproved as were the ultimate displacement angles (isindicates that the high-strength stirrups with small spacingcolumn-end wound CFRP and column-end outer steel platemesh may improve the strength and the deformation abilityof the RC columns therefore this should be consideredwhen accounting for seismic loads in RC columns

35 Stiffness Degradation Stiffness degradation of a speci-men under cyclic loading is usually attributable to the ac-cumulation of specimen damage which has great influence

SC-1SC-2SC-3

SC-4SC-5SC-6

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

Figure 8 Skeleton curves of specimens Skeleton curves representthe outer winding line of the peak loading point of each stage

Δ (mm)

AB

D

P (k

N)

Pmax

Py085Pmax

Δy Δm Δu

C

O

Figure 9 Calculation of characteristic points for each specimen Pyis the yield load Pmax is the peak load

Advances in Civil Engineering 9

on the seismic performance of the specimens Here thesecant stiffness (Ki) was used to represent the stiffnessdegradation of the specimens (e secant stiffness Ki wascalculated as

Ki P

+i

11138681113868111386811138681113868111386811138681113868 + P

minusi

11138681113868111386811138681113868111386811138681113868

Δ+i

11138681113868111386811138681113868111386811138681113868 + Δminus

i

11138681113868111386811138681113868111386811138681113868 (1)

where Pi+ and Pminusi are the i-th positive and reverse peak loads

respectively and Δi+ and Δminusi are the i-th positive and reverse

peak displacements(e stiffness degradation curve of each test piece is

shown in Figure 10 As loading displacement increased thestiffness of each specimen gradually decreased (e stiffnessdegraded rapidly in the early stage and slowly in the laterstage (is could be due to the continuous cracking ofconcrete in the early stage of loading whereas no new crackswere generated in the late loading stages thus when thecumulative damage of the specimen reached a certain de-gree the slope of the stiffness degradation curve of thespecimen decreased Compared to specimen SC-1 thestiffness of specimen SC-2 degraded faster (is is becausethe oblique horizontal loading caused damage in the cornerof the specimen affecting each other In contrast to speci-men SC-2 the stiffness of specimen SC-3 decreased sharplyin the later stage of loading (is is due to the higher axialcompression ratio of the specimen which caused the con-crete to fall severely the stirrups to protrude and thelongitudinal bars to yield(e stiffness degradation curves ofSC-4 SC-5 and SC-6 had a slower downward trend and alonger curve extension compared to those of SC-3 (isindicates that the high-strength stirrups with small spacingthe column-end wound CFRP and the column-end outersteel plate mesh may have alleviated the damage degree ofthe specimen and thus slowed the degradation stiffnessdegradation of these specimens

36 Energy Dissipation (e energy dissipation capacity ofspecimens under earthquake action is an important indexfor evaluating their seismic performance Here the equiv-alent viscous damping coefficient (he) and cumulative energy

consumption (Ep) were used to characterize the energydissipation performance of the experimental specimens (eequivalent viscous damping coefficient characterizes theenergy dissipation performance of specimens at differentloading stages the cumulative energy consumption char-acterizes the overall energy dissipation capacity of specimensduring the whole loading process

As shown in Figure 11 the area of each hysteresis loop inthe hysteresis curve represents the energy-consuming ca-pacity of the specimens under this cycle When otherconditions are the same the larger the area of the hysteresisloop the better the energy consumption capability of thespecimen (e equivalent viscous damping coefficient he ofspecimens is calculated as

he 12π

timesSABC + SCDA

SODG + SOBH

(2)

Table 5 Experimentally derived characteristic loads and displacements for specimens SC-1 through SC-6

Specimen Loading direction Py (kN) Δy (mm) Pm (kN) Δm (mm) Pu (kN) Δu (mm) θμ () Relative value

SC-1 + 41650 986 49250 1820 46794 2500 417 1minus 40045 1205 47286 1819 46973 2500 417

SC-2 + 39470 938 46600 1817 41363 2500 417 1minus 38188 1066 45985 1820 44323 2500 417

SC-3 + 40820 850 47005 1820 44397 2000 333 080minus 41037 868 48192 1500 40963 2000 333

SC-4 + 43773 696 50493 1500 42919 3184 531 135minus 40828 972 48311 2500 41064 3595 599

SC-5 + 50121 917 57802 1820 49132 3223 761 134minus 43456 1113 51965 2800 48294 3500 798

SC-6 + 46587 1151 53813 2499 45741 4563 537 187minus 48357 1443 56164 3200 47739 4790 583

Note Py is the yield load Δy is the yield displacement Pm is the peak load Δm is the peak displacement Pu is the ultimate load Δu is the ultimate displacementand θμ is the deformation ability

100

80

60

40

20

0

Ki (k

Nm

m)

ndash10 0 10 20 30 40 50 60 70∆ (mm)

SC-1SC-2SC-3

SC-4SC-5SC-6

Figure 10 Stiffness degradation curves of specimens Stiffnessdegradation of the specimens is represented by secant stiffness Ki

10 Advances in Civil Engineering

As shown in Figure 12 the equivalent viscous dampingcoefficient (he) of the specimen and the displacement (Δ)curve of the column end were calculated for each specimenAt the initial stage of loading the energy consumption of thespecimen increased as the loading displacement increasedWhen the specimen was cracked stress redistribution oc-curred inside the specimen thereby impacting the stress anddeformation of the specimen and decreasing the energyconsumption As the loading displacement continued toincrease the crack continued opening and closing thusincreasing the energy consumption of the specimen Whenthe specimen yielded the internal longitudinal reinforce-ment of the specimen yielded and the stress redistributionoccurred again inside the specimen thus decreasing theenergy consumption of the specimen With continuousloading cracks of the specimen kept opening and closingand energy consumption continued increasing until thespecimen was destroyed (e equivalent viscous dampingcoefficient of each specimen increased as a whole whichindicated that the damage of the specimen increased as thehorizontal deformation increased during the loading pro-cess thereby increasing the energy consumption of thespecimen (Figure 12)

Cumulative energy consumption refers to the sum of allhysteresis loop areas generated from the beginning of theload application to the ultimate displacement point (elarger the value the stronger the energy dissipation capacityof the specimen and the better the seismic performance Asshown in Table 6 the cumulative energy dissipation wascalculated for each specimen

In contrast to SC-1 the cumulative energy consumptionof SC-2 increased by 37 indicating that the obliquehorizontal loading led to more serious cumulative damageand the consumption of more energy Compared to SC-2the accumulated energy consumption value of SC-3 de-creased by approximately 16 possibly due to the pre-mature failure of specimen and the increase of the axialpressure ratio which reduces the cumulative energy con-sumption capacity of specimen In contrast to specimen SC-3 the cumulative energy consumption values of specimensSC-4 SC-5 and SC-6 all improved with increase rates of222 278 and 412 respectively (is is because high-

strength stirrups with small spacing wound CFRP at the endof the column and steel plate mesh at the end of the columnlimit the shedding of concrete and thus increase the work ofthe concrete

37 OpenSees Finite Element Simulation (e open-sourcefinite element program OpenSees (Open System forEarthquake Engineering Simulation) was used as a platformto numerically simulate the experimental specimens (emodel used displacement-based nonlinear beam-columnelements (ree nodes along the height of the column wereused to form two units wherein the top node was free endand the bottom node was embedded (e P-Delta effectcaused by the vertical load was considered by the P-Del-taCrdTransf command (e fiber model was used to definethe relationship of the cross section restoring force at theunit integration point (e longitudinal reinforcement wasmodeled using the Reinforcing Steel uniaxial materialprovided in OpenSees which was based on the Chang-Mander uniaxial material model [21] and simulated theisotropic hardening behavior of steel bars (e concrete wassimulated by Concrete 02 provided by OpenSees (e ma-terial was based on the Kent-Scott-Park uniaxial material

A OG

D

B

C H Δ

P

Figure 11 PminusΔ hysteretic curve representing the energy-con-suming capacity of the specimen

Table 6 Accumulated dissipated energy (Ep) of all specimens

Specimen Ep (kNmiddotmm) Relative valueSC-1 49770 1SC-2 68307 137SC-3 41784 084SC-4 160490 322SC-5 187933 378SC-6 254794 512

SC-1SC-2SC-3

SC-4SC-5SC-6

004

006

008

010

012

014

016

018

020

022

024

he

0 10 20 30 40 50 60 70ndash10∆ (mm)

Figure 12 Viscous damping coefficient curves of each specimen(e equivalent viscous damping coefficient (he) of the specimenand the displacement (Δ) curve of the column end were calculatedfor each specimen

Advances in Civil Engineering 11

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

(a)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

(b)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

(c)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

(d)

Figure 13 Continued

12 Advances in Civil Engineering

model [22] (e model included the tensile mechanicalproperties of the concrete the stiffness degradation and theenergy dissipation behavior of the concrete during recip-rocating loading For the concrete in the core area theMander model [2324] was used to consider the restrainingeffect of stirrups on concrete Here the stress-strain rela-tionship of CFRP-constrained concrete was establishedusing the Concrete 02 material (e stress and strain at thepeak point were the same as the peak-point stress and strainof the concrete bound by the stirrup (e stress and strain atthe limit point were calculated using the peak-point stressand strain of the Lam-Teng model [2526] (ere was littleresearch on concrete columns reinforced by steel plate meshand no specific theoretical models Based on the existingsteel mesh reinforced concrete column the Concrete 02material in this study was used to establish the stress-strainrelationship of the steel plate mesh to the concrete equations(3) and (4) were used to calculate the peak concrete stress fccafter confinement [19] (e peak strain was 4 times that ofthe peak stress of unconstrained concrete the limit pointstress was twice that of the ultimate stress of unconstrainedconcrete the calculations of the remaining characteristicparameters were consistent with the calculation results of theunconstrained concrete

fcc 1 + 077λv( 1113857fck (3)

λv ρvfyv

fck

(4)

where fck is the axial compressive strength of the concrete λv isthe eigenvalue of the stirrup fyv is the yield strength of the steelplate mesh and ρv is the volumetric ratio of the steel plate mesh

(e vertical load was applied incrementally in 10 stepsusing the gravity loading module provided by OpenSees and

was held constant after the vertical load was completed (ehorizontal load was applied in time series and the loadingsystem was consistent with the experimental proceduresused in this study

(e hysteresis curves for SC-1 through SC-6 generatedby the OpenSees finite element analysis were compared tothe experimentally generated hysteresis curves as shown inFigure 13 (e curves generated by OpenSees are in goodagreement with the experimental results

4 Conclusion

Here six short concrete columns with high-strength lon-gitudinal reinforcements were subjected to low-cycle re-peated loading tests By comparing and analyzing the testresults based on observed test phenomena the followingconclusions are drawn

(1) Compared to the horizontally loaded test specimensthe strength of the diagonally loaded specimensdecreased and the stiffness degradation trendaccelerated this indicates that the effect of obliqueloading is unfavorable to the strength and stiffness ofthe specimens

(2) Under the action of oblique load as the axialcompression ratio increases the strength of thespecimen increases however the deformation ca-pacity becomes worse the stiffness becomes severelydegraded and the specimen is prone to shear brittlefailure

(3) Under the action of oblique load the reinforcementmeasures of the CFRP at the end of the columnimprove the strength and energy consumption of thespecimen however the higher axial compression

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(e)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(f)

Figure 13 OpenSees finite element simulations compared with the experimentally derived hysteresis curve for each specimen Resultscomparison of (a) SC-1 (b) SC-2 (c) SC-3 (d) SC-4 (e) SC-5 and (f) SC-6

Advances in Civil Engineering 13

ratio makes the CFRP more prone to damage anddoes not improve the deformation performance ofthe specimen However the local reinforcementmeasures of the steel plate mesh on the end of thecolumn not only increase the strength and energyconsumption of the specimen but also improve thedeformation ability of the specimen and the seismicperformance of the specimen

(4) In contrast to the unreinforced specimens theaddition of the high-strength stirrups with smallspacing column-end wound CFRP and column-end outer steel plate mesh all improve the strengthdeformation capacity and energy consumptioncapacity of the specimens (e addition of the high-strength stirrups with small spacing and the col-umn-end outer steel plate mesh both altered thefailure mode of the specimen transforming it fromshear failure to bending shear failure (is showsthat the above measures can effectively improve theseismic performance of the test specimen under theaction of oblique loads with a high axial com-pression ratio

(5) Under the action of a high axial pressure ratiooblique load by selecting the appropriate fiber unitand material constitutive relationship the OpenSeesprogram can obtain a simulation result that is ingood agreement with the test hysteresis curve (isverifies the validity of the numerical simulation andprovides a certain basis for subsequent and extendednumerical simulation analyses

Data Availability

All data or models used to support the findings of this studyare included within the article Some data or models thatsupport the findings of this study are available from thecorresponding author upon reasonable request

Conflicts of Interest

(e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

(is work was supported by the Natural Science Foundationof Shandong Province under Grant nos ZR2015EQ017 andZR2018MEE044 and Off-Campus Development Project ofKey Laboratory of Beijing University of Technology underGrant no 2020B03 (e authors are grateful to the KeyLaboratory of Building Structural Retrofitting and Under-ground Space Engineering (Shandong Jianzhu University)Ministry of Education for accommodating the use of theequipment and facilities Professor Xingquan Zhao forproviding computer equipment for numerical simulation ofthe experiment and Editage (httpwwweditagecn) forEnglish language editing

References

[1] A Ghobarah and K Galal ldquoSeismic rehabilitation of shortrectangular RC columnsrdquo Journal of Earthquake Engineeringvol 8 no 1 pp 45ndash68 2004

[2] Y A Li T Y Huang and S J Hwang ldquoSeismic response ofreinforced concrete short columns failed in shearrdquo ACIStructural Journal vol 111 no 4 pp 945ndash954 2014

[3] H Takizawa and H Aoyama ldquoBiaxial effects in modellingearthquake response of RC structuresrdquo Earthquake Engi-neering amp Structural Dynamics vol 4 no 6 pp 523ndash5521976

[4] H Umehara and J O Jirsa ldquoShort rectangular RC columnsunder bidirectional loadingsrdquo Journal of Structural Engi-neering vol 110 no 3 pp 605ndash618 1984

[5] K A Woodward and J O Jirsa ldquoInfluence of reinforcementon RC short column lateral resistancerdquo Journal of StructuralEngineering vol 110 no 1 pp 90ndash104 1984

[6] K Maruyama H Ramirez and J O Jirsa ldquoShort RC columnsunder bilateral load historiesrdquo Journal of Structural Engi-neering vol 110 no 1 pp 120ndash137 1984

[7] H Rodrigues H Varum A Arede and A G CostaldquoBehaviour of reinforced concrete column under biaxial cyclicloadingmdashstate of the artrdquo International Journal of AdvancedStructural Engineering vol 5 no 1 pp 1ndash12 2013

[8] D Wang L Huang T Yu and Z Wang ldquoSeismic perfor-mance of CFRP-retrofitted large-scale square RC columnswith high axial compression ratiosrdquo Journal of Composites forConstruction vol 21 no 5 Article ID 04017031 2017

[9] J Yang and J Wang ldquoSeismic performance of shear-con-trolled CFRP-strengthened high-strength concrete squarecolumns under simulated seismic loadrdquo Journal of Compositesfor Construction vol 22 no 6 Article ID 04018061 2018

[10] X Zhou and J Liu ldquoSeismic behavior and shear strength oftubed RC short columnsrdquo Journal of Constructional SteelResearch vol 66 no 3 pp 385ndash397 2010

[11] H Ma J Xue Y Liu and X Zhang ldquoCyclic loading tests andshear strength of steel reinforced recycled concrete shortcolumnsrdquo Engineering Structures vol 92 pp 55ndash68 2015

[12] D Sokoli and W M Ghannoum ldquoHigh-strength reinforce-ment in columns under high shear stressesrdquo ACI StructuralJournal vol 113 no 3 pp 605ndash614 2016

[13] H Ding Y Liu C Han and Y Guo ldquoSeismic performance ofhigh-strength short concrete column with high-strengthstirrups constraintsrdquo Transactions of Tianjin Universityvol 23 no 4 pp 360ndash369 2017

[14] H O Shin Y S Yoon W D Cook and D Mitchell ldquoAxialload response of ultra-high-strength concrete columns andhigh-strength reinforcementrdquo Transactions of Tianjin Uni-versity vol 113 no 2 pp 325ndash336 216

[15] L A E Shehata M L A V Carneiro and L C D ShehataldquoStrength of short concrete columns confined with CFRPsheetsrdquo Materials and Structures vol 35 pp 50ndash58 2002

[16] F Colomb H Tobbi E Ferrier and P Hamelin ldquoSeismicretrofit of reinforced concrete short columns by CFRPmaterialsfit of reinforced concrete short columns by CFRPmaterialsrdquo Composite Structures vol 82 no 4 pp 475ndash4872008

[17] K Galal A Arafa and A Ghobarah ldquoRetrofit of RC squareshort columnsrdquo Engineering Structures vol 27 no 5pp 801ndash813 2005

[18] R Morshed and M T Kazemi ldquoSeismic shear strengtheningof RC beams and columns with expanded steel meshesrdquo

14 Advances in Civil Engineering

stress and deformation during the loading of the specimen(e skeleton curve of each specimen is shown in Figure 8 Ascan be seen from the figure the development of the skeleton

curves of each specimen can be roughly divided into threestages (1) In the elastic stage the load changes linearly withthe displacement the specimen has yet to crack and no

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(a)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(b)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

(c)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(d)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

(e)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(f )

Figure 7 Hysteretic curves of short column (SC) specimens 1ndash6 (a) SC-1 (b) SC-2 (c) SC-3 (d) SC-4 (e) SC-5 and (f) SC-6

8 Advances in Civil Engineering

residual deformation is observed (2) During the develop-ment stage of a multicrack many cracks appear in thespecimen When residual deformation begins to appearmultiple tiny cracks appear on the surface of the specimenand the horizontal load of the specimen slowly increasesWith the accumulation of damage the specimen reaches thepeak load (3) In the load drop stage for specimens SC-1SC-2 and SC-3 the skeleton curve decreases significantly inthe later stage of loading (is is because the ordinarystirrups with large spacing cannot provide effective lateralrestraints for the specimens under a high axial compressionratio thus making the strength of the specimens dropdramatically Compared to specimen SC-3 the skeletoncurves of specimens SC-4 SC-5 and SC-6 decrease slowlyand show good deformation ability In particular the de-formation capacity of specimens SC-4 and SC-6 after thepeak point significantly improves this is conducive toimproving the seismic energy dissipation capability ofspecimens

34 Bearing Capacity and Ductility Each sample wascharacterized by the yield load point the peak load pointand the failure load point within a load-displacement curveAs shown in Figure 9 the yield point D was determined bythe equivalent elastic-plastic energy method that is wherethe area SOAB SBCD and the ultimate load was simplydefined as 85 of the peak load [20] Because the strength ofSC-1 SC-2 and SC-3 declined rapidly after reaching thepeak load and the ultimate load did not reach 85 of thepeak load the failure displacements of these were taken asthe ultimate displacement Here the ultimate displacementangle (θμ) was used to characterize the deformation ability ofthe specimen and was calculated as θμ Δul0 where l0 is thecolumnrsquos height For each specimen the characteristic loadand displacement calculation results are shown in Table 5

(e relative value is the ratio of the average of the positiveand negative corresponding coefficients of SC-2 through SC-6 and the average of the positive and negative correspondingcoefficients of SC-1

As can be seen in Table 5 compared to specimen SC-1the yield load peak load and ultimate load of specimen SC-2are reduced and the ultimate displacement angle is un-changed(is is because the concrete in the corner of the testspecimen is severely damaged under the diagonal horizontalloading making the strength of the specimen decreasehowever this has no effect on the deformation ability of thespecimen A comparison of SC-2 and SC-3 reveals thatunder the oblique load as the axial pressure ratio increasesthe strength of the specimen increases but the deformationcapacity decreases In contrast to specimen SC-4 the yieldload peak load and ultimate load of SC-5 improvedwhereas the ultimate displacement angle decreased by 1(is result indicates that although the strength of thespecimen under high axial pressure ratio improved thedeformation capacity of the specimen under high axialpressure ratio did not improve Compared to specimen SC-4 the yield load peak load and ultimate load of specimenSC-6 improved and the ultimate displacement angle in-creased by 52(is result was likely due to the column-endouter steel plate mesh providing a strong restraining effecton the column-end concrete which then increased thespecimenrsquos strength deformation capacity and seismicperformance

In comparison to SC-3 the yield load peak load andultimate load of SC-4 SC-5 and SC-6 were all greatlyimproved as were the ultimate displacement angles (isindicates that the high-strength stirrups with small spacingcolumn-end wound CFRP and column-end outer steel platemesh may improve the strength and the deformation abilityof the RC columns therefore this should be consideredwhen accounting for seismic loads in RC columns

35 Stiffness Degradation Stiffness degradation of a speci-men under cyclic loading is usually attributable to the ac-cumulation of specimen damage which has great influence

SC-1SC-2SC-3

SC-4SC-5SC-6

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

Figure 8 Skeleton curves of specimens Skeleton curves representthe outer winding line of the peak loading point of each stage

Δ (mm)

AB

D

P (k

N)

Pmax

Py085Pmax

Δy Δm Δu

C

O

Figure 9 Calculation of characteristic points for each specimen Pyis the yield load Pmax is the peak load

Advances in Civil Engineering 9

on the seismic performance of the specimens Here thesecant stiffness (Ki) was used to represent the stiffnessdegradation of the specimens (e secant stiffness Ki wascalculated as

Ki P

+i

11138681113868111386811138681113868111386811138681113868 + P

minusi

11138681113868111386811138681113868111386811138681113868

Δ+i

11138681113868111386811138681113868111386811138681113868 + Δminus

i

11138681113868111386811138681113868111386811138681113868 (1)

where Pi+ and Pminusi are the i-th positive and reverse peak loads

respectively and Δi+ and Δminusi are the i-th positive and reverse

peak displacements(e stiffness degradation curve of each test piece is

shown in Figure 10 As loading displacement increased thestiffness of each specimen gradually decreased (e stiffnessdegraded rapidly in the early stage and slowly in the laterstage (is could be due to the continuous cracking ofconcrete in the early stage of loading whereas no new crackswere generated in the late loading stages thus when thecumulative damage of the specimen reached a certain de-gree the slope of the stiffness degradation curve of thespecimen decreased Compared to specimen SC-1 thestiffness of specimen SC-2 degraded faster (is is becausethe oblique horizontal loading caused damage in the cornerof the specimen affecting each other In contrast to speci-men SC-2 the stiffness of specimen SC-3 decreased sharplyin the later stage of loading (is is due to the higher axialcompression ratio of the specimen which caused the con-crete to fall severely the stirrups to protrude and thelongitudinal bars to yield(e stiffness degradation curves ofSC-4 SC-5 and SC-6 had a slower downward trend and alonger curve extension compared to those of SC-3 (isindicates that the high-strength stirrups with small spacingthe column-end wound CFRP and the column-end outersteel plate mesh may have alleviated the damage degree ofthe specimen and thus slowed the degradation stiffnessdegradation of these specimens

36 Energy Dissipation (e energy dissipation capacity ofspecimens under earthquake action is an important indexfor evaluating their seismic performance Here the equiv-alent viscous damping coefficient (he) and cumulative energy

consumption (Ep) were used to characterize the energydissipation performance of the experimental specimens (eequivalent viscous damping coefficient characterizes theenergy dissipation performance of specimens at differentloading stages the cumulative energy consumption char-acterizes the overall energy dissipation capacity of specimensduring the whole loading process

As shown in Figure 11 the area of each hysteresis loop inthe hysteresis curve represents the energy-consuming ca-pacity of the specimens under this cycle When otherconditions are the same the larger the area of the hysteresisloop the better the energy consumption capability of thespecimen (e equivalent viscous damping coefficient he ofspecimens is calculated as

he 12π

timesSABC + SCDA

SODG + SOBH

(2)

Table 5 Experimentally derived characteristic loads and displacements for specimens SC-1 through SC-6

Specimen Loading direction Py (kN) Δy (mm) Pm (kN) Δm (mm) Pu (kN) Δu (mm) θμ () Relative value

SC-1 + 41650 986 49250 1820 46794 2500 417 1minus 40045 1205 47286 1819 46973 2500 417

SC-2 + 39470 938 46600 1817 41363 2500 417 1minus 38188 1066 45985 1820 44323 2500 417

SC-3 + 40820 850 47005 1820 44397 2000 333 080minus 41037 868 48192 1500 40963 2000 333

SC-4 + 43773 696 50493 1500 42919 3184 531 135minus 40828 972 48311 2500 41064 3595 599

SC-5 + 50121 917 57802 1820 49132 3223 761 134minus 43456 1113 51965 2800 48294 3500 798

SC-6 + 46587 1151 53813 2499 45741 4563 537 187minus 48357 1443 56164 3200 47739 4790 583

Note Py is the yield load Δy is the yield displacement Pm is the peak load Δm is the peak displacement Pu is the ultimate load Δu is the ultimate displacementand θμ is the deformation ability

100

80

60

40

20

0

Ki (k

Nm

m)

ndash10 0 10 20 30 40 50 60 70∆ (mm)

SC-1SC-2SC-3

SC-4SC-5SC-6

Figure 10 Stiffness degradation curves of specimens Stiffnessdegradation of the specimens is represented by secant stiffness Ki

10 Advances in Civil Engineering

As shown in Figure 12 the equivalent viscous dampingcoefficient (he) of the specimen and the displacement (Δ)curve of the column end were calculated for each specimenAt the initial stage of loading the energy consumption of thespecimen increased as the loading displacement increasedWhen the specimen was cracked stress redistribution oc-curred inside the specimen thereby impacting the stress anddeformation of the specimen and decreasing the energyconsumption As the loading displacement continued toincrease the crack continued opening and closing thusincreasing the energy consumption of the specimen Whenthe specimen yielded the internal longitudinal reinforce-ment of the specimen yielded and the stress redistributionoccurred again inside the specimen thus decreasing theenergy consumption of the specimen With continuousloading cracks of the specimen kept opening and closingand energy consumption continued increasing until thespecimen was destroyed (e equivalent viscous dampingcoefficient of each specimen increased as a whole whichindicated that the damage of the specimen increased as thehorizontal deformation increased during the loading pro-cess thereby increasing the energy consumption of thespecimen (Figure 12)

Cumulative energy consumption refers to the sum of allhysteresis loop areas generated from the beginning of theload application to the ultimate displacement point (elarger the value the stronger the energy dissipation capacityof the specimen and the better the seismic performance Asshown in Table 6 the cumulative energy dissipation wascalculated for each specimen

In contrast to SC-1 the cumulative energy consumptionof SC-2 increased by 37 indicating that the obliquehorizontal loading led to more serious cumulative damageand the consumption of more energy Compared to SC-2the accumulated energy consumption value of SC-3 de-creased by approximately 16 possibly due to the pre-mature failure of specimen and the increase of the axialpressure ratio which reduces the cumulative energy con-sumption capacity of specimen In contrast to specimen SC-3 the cumulative energy consumption values of specimensSC-4 SC-5 and SC-6 all improved with increase rates of222 278 and 412 respectively (is is because high-

strength stirrups with small spacing wound CFRP at the endof the column and steel plate mesh at the end of the columnlimit the shedding of concrete and thus increase the work ofthe concrete

37 OpenSees Finite Element Simulation (e open-sourcefinite element program OpenSees (Open System forEarthquake Engineering Simulation) was used as a platformto numerically simulate the experimental specimens (emodel used displacement-based nonlinear beam-columnelements (ree nodes along the height of the column wereused to form two units wherein the top node was free endand the bottom node was embedded (e P-Delta effectcaused by the vertical load was considered by the P-Del-taCrdTransf command (e fiber model was used to definethe relationship of the cross section restoring force at theunit integration point (e longitudinal reinforcement wasmodeled using the Reinforcing Steel uniaxial materialprovided in OpenSees which was based on the Chang-Mander uniaxial material model [21] and simulated theisotropic hardening behavior of steel bars (e concrete wassimulated by Concrete 02 provided by OpenSees (e ma-terial was based on the Kent-Scott-Park uniaxial material

A OG

D

B

C H Δ

P

Figure 11 PminusΔ hysteretic curve representing the energy-con-suming capacity of the specimen

Table 6 Accumulated dissipated energy (Ep) of all specimens

Specimen Ep (kNmiddotmm) Relative valueSC-1 49770 1SC-2 68307 137SC-3 41784 084SC-4 160490 322SC-5 187933 378SC-6 254794 512

SC-1SC-2SC-3

SC-4SC-5SC-6

004

006

008

010

012

014

016

018

020

022

024

he

0 10 20 30 40 50 60 70ndash10∆ (mm)

Figure 12 Viscous damping coefficient curves of each specimen(e equivalent viscous damping coefficient (he) of the specimenand the displacement (Δ) curve of the column end were calculatedfor each specimen

Advances in Civil Engineering 11

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

(a)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

(b)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

(c)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

(d)

Figure 13 Continued

12 Advances in Civil Engineering

model [22] (e model included the tensile mechanicalproperties of the concrete the stiffness degradation and theenergy dissipation behavior of the concrete during recip-rocating loading For the concrete in the core area theMander model [2324] was used to consider the restrainingeffect of stirrups on concrete Here the stress-strain rela-tionship of CFRP-constrained concrete was establishedusing the Concrete 02 material (e stress and strain at thepeak point were the same as the peak-point stress and strainof the concrete bound by the stirrup (e stress and strain atthe limit point were calculated using the peak-point stressand strain of the Lam-Teng model [2526] (ere was littleresearch on concrete columns reinforced by steel plate meshand no specific theoretical models Based on the existingsteel mesh reinforced concrete column the Concrete 02material in this study was used to establish the stress-strainrelationship of the steel plate mesh to the concrete equations(3) and (4) were used to calculate the peak concrete stress fccafter confinement [19] (e peak strain was 4 times that ofthe peak stress of unconstrained concrete the limit pointstress was twice that of the ultimate stress of unconstrainedconcrete the calculations of the remaining characteristicparameters were consistent with the calculation results of theunconstrained concrete

fcc 1 + 077λv( 1113857fck (3)

λv ρvfyv

fck

(4)

where fck is the axial compressive strength of the concrete λv isthe eigenvalue of the stirrup fyv is the yield strength of the steelplate mesh and ρv is the volumetric ratio of the steel plate mesh

(e vertical load was applied incrementally in 10 stepsusing the gravity loading module provided by OpenSees and

was held constant after the vertical load was completed (ehorizontal load was applied in time series and the loadingsystem was consistent with the experimental proceduresused in this study

(e hysteresis curves for SC-1 through SC-6 generatedby the OpenSees finite element analysis were compared tothe experimentally generated hysteresis curves as shown inFigure 13 (e curves generated by OpenSees are in goodagreement with the experimental results

4 Conclusion

Here six short concrete columns with high-strength lon-gitudinal reinforcements were subjected to low-cycle re-peated loading tests By comparing and analyzing the testresults based on observed test phenomena the followingconclusions are drawn

(1) Compared to the horizontally loaded test specimensthe strength of the diagonally loaded specimensdecreased and the stiffness degradation trendaccelerated this indicates that the effect of obliqueloading is unfavorable to the strength and stiffness ofthe specimens

(2) Under the action of oblique load as the axialcompression ratio increases the strength of thespecimen increases however the deformation ca-pacity becomes worse the stiffness becomes severelydegraded and the specimen is prone to shear brittlefailure

(3) Under the action of oblique load the reinforcementmeasures of the CFRP at the end of the columnimprove the strength and energy consumption of thespecimen however the higher axial compression

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(e)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(f)

Figure 13 OpenSees finite element simulations compared with the experimentally derived hysteresis curve for each specimen Resultscomparison of (a) SC-1 (b) SC-2 (c) SC-3 (d) SC-4 (e) SC-5 and (f) SC-6

Advances in Civil Engineering 13

ratio makes the CFRP more prone to damage anddoes not improve the deformation performance ofthe specimen However the local reinforcementmeasures of the steel plate mesh on the end of thecolumn not only increase the strength and energyconsumption of the specimen but also improve thedeformation ability of the specimen and the seismicperformance of the specimen

(4) In contrast to the unreinforced specimens theaddition of the high-strength stirrups with smallspacing column-end wound CFRP and column-end outer steel plate mesh all improve the strengthdeformation capacity and energy consumptioncapacity of the specimens (e addition of the high-strength stirrups with small spacing and the col-umn-end outer steel plate mesh both altered thefailure mode of the specimen transforming it fromshear failure to bending shear failure (is showsthat the above measures can effectively improve theseismic performance of the test specimen under theaction of oblique loads with a high axial com-pression ratio

(5) Under the action of a high axial pressure ratiooblique load by selecting the appropriate fiber unitand material constitutive relationship the OpenSeesprogram can obtain a simulation result that is ingood agreement with the test hysteresis curve (isverifies the validity of the numerical simulation andprovides a certain basis for subsequent and extendednumerical simulation analyses

Data Availability

All data or models used to support the findings of this studyare included within the article Some data or models thatsupport the findings of this study are available from thecorresponding author upon reasonable request

Conflicts of Interest

(e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

(is work was supported by the Natural Science Foundationof Shandong Province under Grant nos ZR2015EQ017 andZR2018MEE044 and Off-Campus Development Project ofKey Laboratory of Beijing University of Technology underGrant no 2020B03 (e authors are grateful to the KeyLaboratory of Building Structural Retrofitting and Under-ground Space Engineering (Shandong Jianzhu University)Ministry of Education for accommodating the use of theequipment and facilities Professor Xingquan Zhao forproviding computer equipment for numerical simulation ofthe experiment and Editage (httpwwweditagecn) forEnglish language editing

References

[1] A Ghobarah and K Galal ldquoSeismic rehabilitation of shortrectangular RC columnsrdquo Journal of Earthquake Engineeringvol 8 no 1 pp 45ndash68 2004

[2] Y A Li T Y Huang and S J Hwang ldquoSeismic response ofreinforced concrete short columns failed in shearrdquo ACIStructural Journal vol 111 no 4 pp 945ndash954 2014

[3] H Takizawa and H Aoyama ldquoBiaxial effects in modellingearthquake response of RC structuresrdquo Earthquake Engi-neering amp Structural Dynamics vol 4 no 6 pp 523ndash5521976

[4] H Umehara and J O Jirsa ldquoShort rectangular RC columnsunder bidirectional loadingsrdquo Journal of Structural Engi-neering vol 110 no 3 pp 605ndash618 1984

[5] K A Woodward and J O Jirsa ldquoInfluence of reinforcementon RC short column lateral resistancerdquo Journal of StructuralEngineering vol 110 no 1 pp 90ndash104 1984

[6] K Maruyama H Ramirez and J O Jirsa ldquoShort RC columnsunder bilateral load historiesrdquo Journal of Structural Engi-neering vol 110 no 1 pp 120ndash137 1984

[7] H Rodrigues H Varum A Arede and A G CostaldquoBehaviour of reinforced concrete column under biaxial cyclicloadingmdashstate of the artrdquo International Journal of AdvancedStructural Engineering vol 5 no 1 pp 1ndash12 2013

[8] D Wang L Huang T Yu and Z Wang ldquoSeismic perfor-mance of CFRP-retrofitted large-scale square RC columnswith high axial compression ratiosrdquo Journal of Composites forConstruction vol 21 no 5 Article ID 04017031 2017

[9] J Yang and J Wang ldquoSeismic performance of shear-con-trolled CFRP-strengthened high-strength concrete squarecolumns under simulated seismic loadrdquo Journal of Compositesfor Construction vol 22 no 6 Article ID 04018061 2018

[10] X Zhou and J Liu ldquoSeismic behavior and shear strength oftubed RC short columnsrdquo Journal of Constructional SteelResearch vol 66 no 3 pp 385ndash397 2010

[11] H Ma J Xue Y Liu and X Zhang ldquoCyclic loading tests andshear strength of steel reinforced recycled concrete shortcolumnsrdquo Engineering Structures vol 92 pp 55ndash68 2015

[12] D Sokoli and W M Ghannoum ldquoHigh-strength reinforce-ment in columns under high shear stressesrdquo ACI StructuralJournal vol 113 no 3 pp 605ndash614 2016

[13] H Ding Y Liu C Han and Y Guo ldquoSeismic performance ofhigh-strength short concrete column with high-strengthstirrups constraintsrdquo Transactions of Tianjin Universityvol 23 no 4 pp 360ndash369 2017

[14] H O Shin Y S Yoon W D Cook and D Mitchell ldquoAxialload response of ultra-high-strength concrete columns andhigh-strength reinforcementrdquo Transactions of Tianjin Uni-versity vol 113 no 2 pp 325ndash336 216

[15] L A E Shehata M L A V Carneiro and L C D ShehataldquoStrength of short concrete columns confined with CFRPsheetsrdquo Materials and Structures vol 35 pp 50ndash58 2002

[16] F Colomb H Tobbi E Ferrier and P Hamelin ldquoSeismicretrofit of reinforced concrete short columns by CFRPmaterialsfit of reinforced concrete short columns by CFRPmaterialsrdquo Composite Structures vol 82 no 4 pp 475ndash4872008

[17] K Galal A Arafa and A Ghobarah ldquoRetrofit of RC squareshort columnsrdquo Engineering Structures vol 27 no 5pp 801ndash813 2005

[18] R Morshed and M T Kazemi ldquoSeismic shear strengtheningof RC beams and columns with expanded steel meshesrdquo

14 Advances in Civil Engineering

residual deformation is observed (2) During the develop-ment stage of a multicrack many cracks appear in thespecimen When residual deformation begins to appearmultiple tiny cracks appear on the surface of the specimenand the horizontal load of the specimen slowly increasesWith the accumulation of damage the specimen reaches thepeak load (3) In the load drop stage for specimens SC-1SC-2 and SC-3 the skeleton curve decreases significantly inthe later stage of loading (is is because the ordinarystirrups with large spacing cannot provide effective lateralrestraints for the specimens under a high axial compressionratio thus making the strength of the specimens dropdramatically Compared to specimen SC-3 the skeletoncurves of specimens SC-4 SC-5 and SC-6 decrease slowlyand show good deformation ability In particular the de-formation capacity of specimens SC-4 and SC-6 after thepeak point significantly improves this is conducive toimproving the seismic energy dissipation capability ofspecimens

34 Bearing Capacity and Ductility Each sample wascharacterized by the yield load point the peak load pointand the failure load point within a load-displacement curveAs shown in Figure 9 the yield point D was determined bythe equivalent elastic-plastic energy method that is wherethe area SOAB SBCD and the ultimate load was simplydefined as 85 of the peak load [20] Because the strength ofSC-1 SC-2 and SC-3 declined rapidly after reaching thepeak load and the ultimate load did not reach 85 of thepeak load the failure displacements of these were taken asthe ultimate displacement Here the ultimate displacementangle (θμ) was used to characterize the deformation ability ofthe specimen and was calculated as θμ Δul0 where l0 is thecolumnrsquos height For each specimen the characteristic loadand displacement calculation results are shown in Table 5

(e relative value is the ratio of the average of the positiveand negative corresponding coefficients of SC-2 through SC-6 and the average of the positive and negative correspondingcoefficients of SC-1

As can be seen in Table 5 compared to specimen SC-1the yield load peak load and ultimate load of specimen SC-2are reduced and the ultimate displacement angle is un-changed(is is because the concrete in the corner of the testspecimen is severely damaged under the diagonal horizontalloading making the strength of the specimen decreasehowever this has no effect on the deformation ability of thespecimen A comparison of SC-2 and SC-3 reveals thatunder the oblique load as the axial pressure ratio increasesthe strength of the specimen increases but the deformationcapacity decreases In contrast to specimen SC-4 the yieldload peak load and ultimate load of SC-5 improvedwhereas the ultimate displacement angle decreased by 1(is result indicates that although the strength of thespecimen under high axial pressure ratio improved thedeformation capacity of the specimen under high axialpressure ratio did not improve Compared to specimen SC-4 the yield load peak load and ultimate load of specimenSC-6 improved and the ultimate displacement angle in-creased by 52(is result was likely due to the column-endouter steel plate mesh providing a strong restraining effecton the column-end concrete which then increased thespecimenrsquos strength deformation capacity and seismicperformance

In comparison to SC-3 the yield load peak load andultimate load of SC-4 SC-5 and SC-6 were all greatlyimproved as were the ultimate displacement angles (isindicates that the high-strength stirrups with small spacingcolumn-end wound CFRP and column-end outer steel platemesh may improve the strength and the deformation abilityof the RC columns therefore this should be consideredwhen accounting for seismic loads in RC columns

35 Stiffness Degradation Stiffness degradation of a speci-men under cyclic loading is usually attributable to the ac-cumulation of specimen damage which has great influence

SC-1SC-2SC-3

SC-4SC-5SC-6

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

Figure 8 Skeleton curves of specimens Skeleton curves representthe outer winding line of the peak loading point of each stage

Δ (mm)

AB

D

P (k

N)

Pmax

Py085Pmax

Δy Δm Δu

C

O

Figure 9 Calculation of characteristic points for each specimen Pyis the yield load Pmax is the peak load

Advances in Civil Engineering 9

on the seismic performance of the specimens Here thesecant stiffness (Ki) was used to represent the stiffnessdegradation of the specimens (e secant stiffness Ki wascalculated as

Ki P

+i

11138681113868111386811138681113868111386811138681113868 + P

minusi

11138681113868111386811138681113868111386811138681113868

Δ+i

11138681113868111386811138681113868111386811138681113868 + Δminus

i

11138681113868111386811138681113868111386811138681113868 (1)

where Pi+ and Pminusi are the i-th positive and reverse peak loads

respectively and Δi+ and Δminusi are the i-th positive and reverse

peak displacements(e stiffness degradation curve of each test piece is

shown in Figure 10 As loading displacement increased thestiffness of each specimen gradually decreased (e stiffnessdegraded rapidly in the early stage and slowly in the laterstage (is could be due to the continuous cracking ofconcrete in the early stage of loading whereas no new crackswere generated in the late loading stages thus when thecumulative damage of the specimen reached a certain de-gree the slope of the stiffness degradation curve of thespecimen decreased Compared to specimen SC-1 thestiffness of specimen SC-2 degraded faster (is is becausethe oblique horizontal loading caused damage in the cornerof the specimen affecting each other In contrast to speci-men SC-2 the stiffness of specimen SC-3 decreased sharplyin the later stage of loading (is is due to the higher axialcompression ratio of the specimen which caused the con-crete to fall severely the stirrups to protrude and thelongitudinal bars to yield(e stiffness degradation curves ofSC-4 SC-5 and SC-6 had a slower downward trend and alonger curve extension compared to those of SC-3 (isindicates that the high-strength stirrups with small spacingthe column-end wound CFRP and the column-end outersteel plate mesh may have alleviated the damage degree ofthe specimen and thus slowed the degradation stiffnessdegradation of these specimens

36 Energy Dissipation (e energy dissipation capacity ofspecimens under earthquake action is an important indexfor evaluating their seismic performance Here the equiv-alent viscous damping coefficient (he) and cumulative energy

consumption (Ep) were used to characterize the energydissipation performance of the experimental specimens (eequivalent viscous damping coefficient characterizes theenergy dissipation performance of specimens at differentloading stages the cumulative energy consumption char-acterizes the overall energy dissipation capacity of specimensduring the whole loading process

As shown in Figure 11 the area of each hysteresis loop inthe hysteresis curve represents the energy-consuming ca-pacity of the specimens under this cycle When otherconditions are the same the larger the area of the hysteresisloop the better the energy consumption capability of thespecimen (e equivalent viscous damping coefficient he ofspecimens is calculated as

he 12π

timesSABC + SCDA

SODG + SOBH

(2)

Table 5 Experimentally derived characteristic loads and displacements for specimens SC-1 through SC-6

Specimen Loading direction Py (kN) Δy (mm) Pm (kN) Δm (mm) Pu (kN) Δu (mm) θμ () Relative value

SC-1 + 41650 986 49250 1820 46794 2500 417 1minus 40045 1205 47286 1819 46973 2500 417

SC-2 + 39470 938 46600 1817 41363 2500 417 1minus 38188 1066 45985 1820 44323 2500 417

SC-3 + 40820 850 47005 1820 44397 2000 333 080minus 41037 868 48192 1500 40963 2000 333

SC-4 + 43773 696 50493 1500 42919 3184 531 135minus 40828 972 48311 2500 41064 3595 599

SC-5 + 50121 917 57802 1820 49132 3223 761 134minus 43456 1113 51965 2800 48294 3500 798

SC-6 + 46587 1151 53813 2499 45741 4563 537 187minus 48357 1443 56164 3200 47739 4790 583

Note Py is the yield load Δy is the yield displacement Pm is the peak load Δm is the peak displacement Pu is the ultimate load Δu is the ultimate displacementand θμ is the deformation ability

100

80

60

40

20

0

Ki (k

Nm

m)

ndash10 0 10 20 30 40 50 60 70∆ (mm)

SC-1SC-2SC-3

SC-4SC-5SC-6

Figure 10 Stiffness degradation curves of specimens Stiffnessdegradation of the specimens is represented by secant stiffness Ki

10 Advances in Civil Engineering

As shown in Figure 12 the equivalent viscous dampingcoefficient (he) of the specimen and the displacement (Δ)curve of the column end were calculated for each specimenAt the initial stage of loading the energy consumption of thespecimen increased as the loading displacement increasedWhen the specimen was cracked stress redistribution oc-curred inside the specimen thereby impacting the stress anddeformation of the specimen and decreasing the energyconsumption As the loading displacement continued toincrease the crack continued opening and closing thusincreasing the energy consumption of the specimen Whenthe specimen yielded the internal longitudinal reinforce-ment of the specimen yielded and the stress redistributionoccurred again inside the specimen thus decreasing theenergy consumption of the specimen With continuousloading cracks of the specimen kept opening and closingand energy consumption continued increasing until thespecimen was destroyed (e equivalent viscous dampingcoefficient of each specimen increased as a whole whichindicated that the damage of the specimen increased as thehorizontal deformation increased during the loading pro-cess thereby increasing the energy consumption of thespecimen (Figure 12)

Cumulative energy consumption refers to the sum of allhysteresis loop areas generated from the beginning of theload application to the ultimate displacement point (elarger the value the stronger the energy dissipation capacityof the specimen and the better the seismic performance Asshown in Table 6 the cumulative energy dissipation wascalculated for each specimen

In contrast to SC-1 the cumulative energy consumptionof SC-2 increased by 37 indicating that the obliquehorizontal loading led to more serious cumulative damageand the consumption of more energy Compared to SC-2the accumulated energy consumption value of SC-3 de-creased by approximately 16 possibly due to the pre-mature failure of specimen and the increase of the axialpressure ratio which reduces the cumulative energy con-sumption capacity of specimen In contrast to specimen SC-3 the cumulative energy consumption values of specimensSC-4 SC-5 and SC-6 all improved with increase rates of222 278 and 412 respectively (is is because high-

strength stirrups with small spacing wound CFRP at the endof the column and steel plate mesh at the end of the columnlimit the shedding of concrete and thus increase the work ofthe concrete

37 OpenSees Finite Element Simulation (e open-sourcefinite element program OpenSees (Open System forEarthquake Engineering Simulation) was used as a platformto numerically simulate the experimental specimens (emodel used displacement-based nonlinear beam-columnelements (ree nodes along the height of the column wereused to form two units wherein the top node was free endand the bottom node was embedded (e P-Delta effectcaused by the vertical load was considered by the P-Del-taCrdTransf command (e fiber model was used to definethe relationship of the cross section restoring force at theunit integration point (e longitudinal reinforcement wasmodeled using the Reinforcing Steel uniaxial materialprovided in OpenSees which was based on the Chang-Mander uniaxial material model [21] and simulated theisotropic hardening behavior of steel bars (e concrete wassimulated by Concrete 02 provided by OpenSees (e ma-terial was based on the Kent-Scott-Park uniaxial material

A OG

D

B

C H Δ

P

Figure 11 PminusΔ hysteretic curve representing the energy-con-suming capacity of the specimen

Table 6 Accumulated dissipated energy (Ep) of all specimens

Specimen Ep (kNmiddotmm) Relative valueSC-1 49770 1SC-2 68307 137SC-3 41784 084SC-4 160490 322SC-5 187933 378SC-6 254794 512

SC-1SC-2SC-3

SC-4SC-5SC-6

004

006

008

010

012

014

016

018

020

022

024

he

0 10 20 30 40 50 60 70ndash10∆ (mm)

Figure 12 Viscous damping coefficient curves of each specimen(e equivalent viscous damping coefficient (he) of the specimenand the displacement (Δ) curve of the column end were calculatedfor each specimen

Advances in Civil Engineering 11

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

(a)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

(b)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

(c)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

(d)

Figure 13 Continued

12 Advances in Civil Engineering

model [22] (e model included the tensile mechanicalproperties of the concrete the stiffness degradation and theenergy dissipation behavior of the concrete during recip-rocating loading For the concrete in the core area theMander model [2324] was used to consider the restrainingeffect of stirrups on concrete Here the stress-strain rela-tionship of CFRP-constrained concrete was establishedusing the Concrete 02 material (e stress and strain at thepeak point were the same as the peak-point stress and strainof the concrete bound by the stirrup (e stress and strain atthe limit point were calculated using the peak-point stressand strain of the Lam-Teng model [2526] (ere was littleresearch on concrete columns reinforced by steel plate meshand no specific theoretical models Based on the existingsteel mesh reinforced concrete column the Concrete 02material in this study was used to establish the stress-strainrelationship of the steel plate mesh to the concrete equations(3) and (4) were used to calculate the peak concrete stress fccafter confinement [19] (e peak strain was 4 times that ofthe peak stress of unconstrained concrete the limit pointstress was twice that of the ultimate stress of unconstrainedconcrete the calculations of the remaining characteristicparameters were consistent with the calculation results of theunconstrained concrete

fcc 1 + 077λv( 1113857fck (3)

λv ρvfyv

fck

(4)

where fck is the axial compressive strength of the concrete λv isthe eigenvalue of the stirrup fyv is the yield strength of the steelplate mesh and ρv is the volumetric ratio of the steel plate mesh

(e vertical load was applied incrementally in 10 stepsusing the gravity loading module provided by OpenSees and

was held constant after the vertical load was completed (ehorizontal load was applied in time series and the loadingsystem was consistent with the experimental proceduresused in this study

(e hysteresis curves for SC-1 through SC-6 generatedby the OpenSees finite element analysis were compared tothe experimentally generated hysteresis curves as shown inFigure 13 (e curves generated by OpenSees are in goodagreement with the experimental results

4 Conclusion

Here six short concrete columns with high-strength lon-gitudinal reinforcements were subjected to low-cycle re-peated loading tests By comparing and analyzing the testresults based on observed test phenomena the followingconclusions are drawn

(1) Compared to the horizontally loaded test specimensthe strength of the diagonally loaded specimensdecreased and the stiffness degradation trendaccelerated this indicates that the effect of obliqueloading is unfavorable to the strength and stiffness ofthe specimens

(2) Under the action of oblique load as the axialcompression ratio increases the strength of thespecimen increases however the deformation ca-pacity becomes worse the stiffness becomes severelydegraded and the specimen is prone to shear brittlefailure

(3) Under the action of oblique load the reinforcementmeasures of the CFRP at the end of the columnimprove the strength and energy consumption of thespecimen however the higher axial compression

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(e)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(f)

Figure 13 OpenSees finite element simulations compared with the experimentally derived hysteresis curve for each specimen Resultscomparison of (a) SC-1 (b) SC-2 (c) SC-3 (d) SC-4 (e) SC-5 and (f) SC-6

Advances in Civil Engineering 13

ratio makes the CFRP more prone to damage anddoes not improve the deformation performance ofthe specimen However the local reinforcementmeasures of the steel plate mesh on the end of thecolumn not only increase the strength and energyconsumption of the specimen but also improve thedeformation ability of the specimen and the seismicperformance of the specimen

(4) In contrast to the unreinforced specimens theaddition of the high-strength stirrups with smallspacing column-end wound CFRP and column-end outer steel plate mesh all improve the strengthdeformation capacity and energy consumptioncapacity of the specimens (e addition of the high-strength stirrups with small spacing and the col-umn-end outer steel plate mesh both altered thefailure mode of the specimen transforming it fromshear failure to bending shear failure (is showsthat the above measures can effectively improve theseismic performance of the test specimen under theaction of oblique loads with a high axial com-pression ratio

(5) Under the action of a high axial pressure ratiooblique load by selecting the appropriate fiber unitand material constitutive relationship the OpenSeesprogram can obtain a simulation result that is ingood agreement with the test hysteresis curve (isverifies the validity of the numerical simulation andprovides a certain basis for subsequent and extendednumerical simulation analyses

Data Availability

All data or models used to support the findings of this studyare included within the article Some data or models thatsupport the findings of this study are available from thecorresponding author upon reasonable request

Conflicts of Interest

(e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

(is work was supported by the Natural Science Foundationof Shandong Province under Grant nos ZR2015EQ017 andZR2018MEE044 and Off-Campus Development Project ofKey Laboratory of Beijing University of Technology underGrant no 2020B03 (e authors are grateful to the KeyLaboratory of Building Structural Retrofitting and Under-ground Space Engineering (Shandong Jianzhu University)Ministry of Education for accommodating the use of theequipment and facilities Professor Xingquan Zhao forproviding computer equipment for numerical simulation ofthe experiment and Editage (httpwwweditagecn) forEnglish language editing

References

[1] A Ghobarah and K Galal ldquoSeismic rehabilitation of shortrectangular RC columnsrdquo Journal of Earthquake Engineeringvol 8 no 1 pp 45ndash68 2004

[2] Y A Li T Y Huang and S J Hwang ldquoSeismic response ofreinforced concrete short columns failed in shearrdquo ACIStructural Journal vol 111 no 4 pp 945ndash954 2014

[3] H Takizawa and H Aoyama ldquoBiaxial effects in modellingearthquake response of RC structuresrdquo Earthquake Engi-neering amp Structural Dynamics vol 4 no 6 pp 523ndash5521976

[4] H Umehara and J O Jirsa ldquoShort rectangular RC columnsunder bidirectional loadingsrdquo Journal of Structural Engi-neering vol 110 no 3 pp 605ndash618 1984

[5] K A Woodward and J O Jirsa ldquoInfluence of reinforcementon RC short column lateral resistancerdquo Journal of StructuralEngineering vol 110 no 1 pp 90ndash104 1984

[6] K Maruyama H Ramirez and J O Jirsa ldquoShort RC columnsunder bilateral load historiesrdquo Journal of Structural Engi-neering vol 110 no 1 pp 120ndash137 1984

[7] H Rodrigues H Varum A Arede and A G CostaldquoBehaviour of reinforced concrete column under biaxial cyclicloadingmdashstate of the artrdquo International Journal of AdvancedStructural Engineering vol 5 no 1 pp 1ndash12 2013

[8] D Wang L Huang T Yu and Z Wang ldquoSeismic perfor-mance of CFRP-retrofitted large-scale square RC columnswith high axial compression ratiosrdquo Journal of Composites forConstruction vol 21 no 5 Article ID 04017031 2017

[9] J Yang and J Wang ldquoSeismic performance of shear-con-trolled CFRP-strengthened high-strength concrete squarecolumns under simulated seismic loadrdquo Journal of Compositesfor Construction vol 22 no 6 Article ID 04018061 2018

[10] X Zhou and J Liu ldquoSeismic behavior and shear strength oftubed RC short columnsrdquo Journal of Constructional SteelResearch vol 66 no 3 pp 385ndash397 2010

[11] H Ma J Xue Y Liu and X Zhang ldquoCyclic loading tests andshear strength of steel reinforced recycled concrete shortcolumnsrdquo Engineering Structures vol 92 pp 55ndash68 2015

[12] D Sokoli and W M Ghannoum ldquoHigh-strength reinforce-ment in columns under high shear stressesrdquo ACI StructuralJournal vol 113 no 3 pp 605ndash614 2016

[13] H Ding Y Liu C Han and Y Guo ldquoSeismic performance ofhigh-strength short concrete column with high-strengthstirrups constraintsrdquo Transactions of Tianjin Universityvol 23 no 4 pp 360ndash369 2017

[14] H O Shin Y S Yoon W D Cook and D Mitchell ldquoAxialload response of ultra-high-strength concrete columns andhigh-strength reinforcementrdquo Transactions of Tianjin Uni-versity vol 113 no 2 pp 325ndash336 216

[15] L A E Shehata M L A V Carneiro and L C D ShehataldquoStrength of short concrete columns confined with CFRPsheetsrdquo Materials and Structures vol 35 pp 50ndash58 2002

[16] F Colomb H Tobbi E Ferrier and P Hamelin ldquoSeismicretrofit of reinforced concrete short columns by CFRPmaterialsfit of reinforced concrete short columns by CFRPmaterialsrdquo Composite Structures vol 82 no 4 pp 475ndash4872008

[17] K Galal A Arafa and A Ghobarah ldquoRetrofit of RC squareshort columnsrdquo Engineering Structures vol 27 no 5pp 801ndash813 2005

[18] R Morshed and M T Kazemi ldquoSeismic shear strengtheningof RC beams and columns with expanded steel meshesrdquo

14 Advances in Civil Engineering

on the seismic performance of the specimens Here thesecant stiffness (Ki) was used to represent the stiffnessdegradation of the specimens (e secant stiffness Ki wascalculated as

Ki P

+i

11138681113868111386811138681113868111386811138681113868 + P

minusi

11138681113868111386811138681113868111386811138681113868

Δ+i

11138681113868111386811138681113868111386811138681113868 + Δminus

i

11138681113868111386811138681113868111386811138681113868 (1)

where Pi+ and Pminusi are the i-th positive and reverse peak loads

respectively and Δi+ and Δminusi are the i-th positive and reverse

peak displacements(e stiffness degradation curve of each test piece is

shown in Figure 10 As loading displacement increased thestiffness of each specimen gradually decreased (e stiffnessdegraded rapidly in the early stage and slowly in the laterstage (is could be due to the continuous cracking ofconcrete in the early stage of loading whereas no new crackswere generated in the late loading stages thus when thecumulative damage of the specimen reached a certain de-gree the slope of the stiffness degradation curve of thespecimen decreased Compared to specimen SC-1 thestiffness of specimen SC-2 degraded faster (is is becausethe oblique horizontal loading caused damage in the cornerof the specimen affecting each other In contrast to speci-men SC-2 the stiffness of specimen SC-3 decreased sharplyin the later stage of loading (is is due to the higher axialcompression ratio of the specimen which caused the con-crete to fall severely the stirrups to protrude and thelongitudinal bars to yield(e stiffness degradation curves ofSC-4 SC-5 and SC-6 had a slower downward trend and alonger curve extension compared to those of SC-3 (isindicates that the high-strength stirrups with small spacingthe column-end wound CFRP and the column-end outersteel plate mesh may have alleviated the damage degree ofthe specimen and thus slowed the degradation stiffnessdegradation of these specimens

36 Energy Dissipation (e energy dissipation capacity ofspecimens under earthquake action is an important indexfor evaluating their seismic performance Here the equiv-alent viscous damping coefficient (he) and cumulative energy

consumption (Ep) were used to characterize the energydissipation performance of the experimental specimens (eequivalent viscous damping coefficient characterizes theenergy dissipation performance of specimens at differentloading stages the cumulative energy consumption char-acterizes the overall energy dissipation capacity of specimensduring the whole loading process

As shown in Figure 11 the area of each hysteresis loop inthe hysteresis curve represents the energy-consuming ca-pacity of the specimens under this cycle When otherconditions are the same the larger the area of the hysteresisloop the better the energy consumption capability of thespecimen (e equivalent viscous damping coefficient he ofspecimens is calculated as

he 12π

timesSABC + SCDA

SODG + SOBH

(2)

Table 5 Experimentally derived characteristic loads and displacements for specimens SC-1 through SC-6

Specimen Loading direction Py (kN) Δy (mm) Pm (kN) Δm (mm) Pu (kN) Δu (mm) θμ () Relative value

SC-1 + 41650 986 49250 1820 46794 2500 417 1minus 40045 1205 47286 1819 46973 2500 417

SC-2 + 39470 938 46600 1817 41363 2500 417 1minus 38188 1066 45985 1820 44323 2500 417

SC-3 + 40820 850 47005 1820 44397 2000 333 080minus 41037 868 48192 1500 40963 2000 333

SC-4 + 43773 696 50493 1500 42919 3184 531 135minus 40828 972 48311 2500 41064 3595 599

SC-5 + 50121 917 57802 1820 49132 3223 761 134minus 43456 1113 51965 2800 48294 3500 798

SC-6 + 46587 1151 53813 2499 45741 4563 537 187minus 48357 1443 56164 3200 47739 4790 583

Note Py is the yield load Δy is the yield displacement Pm is the peak load Δm is the peak displacement Pu is the ultimate load Δu is the ultimate displacementand θμ is the deformation ability

100

80

60

40

20

0

Ki (k

Nm

m)

ndash10 0 10 20 30 40 50 60 70∆ (mm)

SC-1SC-2SC-3

SC-4SC-5SC-6

Figure 10 Stiffness degradation curves of specimens Stiffnessdegradation of the specimens is represented by secant stiffness Ki

10 Advances in Civil Engineering

As shown in Figure 12 the equivalent viscous dampingcoefficient (he) of the specimen and the displacement (Δ)curve of the column end were calculated for each specimenAt the initial stage of loading the energy consumption of thespecimen increased as the loading displacement increasedWhen the specimen was cracked stress redistribution oc-curred inside the specimen thereby impacting the stress anddeformation of the specimen and decreasing the energyconsumption As the loading displacement continued toincrease the crack continued opening and closing thusincreasing the energy consumption of the specimen Whenthe specimen yielded the internal longitudinal reinforce-ment of the specimen yielded and the stress redistributionoccurred again inside the specimen thus decreasing theenergy consumption of the specimen With continuousloading cracks of the specimen kept opening and closingand energy consumption continued increasing until thespecimen was destroyed (e equivalent viscous dampingcoefficient of each specimen increased as a whole whichindicated that the damage of the specimen increased as thehorizontal deformation increased during the loading pro-cess thereby increasing the energy consumption of thespecimen (Figure 12)

Cumulative energy consumption refers to the sum of allhysteresis loop areas generated from the beginning of theload application to the ultimate displacement point (elarger the value the stronger the energy dissipation capacityof the specimen and the better the seismic performance Asshown in Table 6 the cumulative energy dissipation wascalculated for each specimen

In contrast to SC-1 the cumulative energy consumptionof SC-2 increased by 37 indicating that the obliquehorizontal loading led to more serious cumulative damageand the consumption of more energy Compared to SC-2the accumulated energy consumption value of SC-3 de-creased by approximately 16 possibly due to the pre-mature failure of specimen and the increase of the axialpressure ratio which reduces the cumulative energy con-sumption capacity of specimen In contrast to specimen SC-3 the cumulative energy consumption values of specimensSC-4 SC-5 and SC-6 all improved with increase rates of222 278 and 412 respectively (is is because high-

strength stirrups with small spacing wound CFRP at the endof the column and steel plate mesh at the end of the columnlimit the shedding of concrete and thus increase the work ofthe concrete

37 OpenSees Finite Element Simulation (e open-sourcefinite element program OpenSees (Open System forEarthquake Engineering Simulation) was used as a platformto numerically simulate the experimental specimens (emodel used displacement-based nonlinear beam-columnelements (ree nodes along the height of the column wereused to form two units wherein the top node was free endand the bottom node was embedded (e P-Delta effectcaused by the vertical load was considered by the P-Del-taCrdTransf command (e fiber model was used to definethe relationship of the cross section restoring force at theunit integration point (e longitudinal reinforcement wasmodeled using the Reinforcing Steel uniaxial materialprovided in OpenSees which was based on the Chang-Mander uniaxial material model [21] and simulated theisotropic hardening behavior of steel bars (e concrete wassimulated by Concrete 02 provided by OpenSees (e ma-terial was based on the Kent-Scott-Park uniaxial material

A OG

D

B

C H Δ

P

Figure 11 PminusΔ hysteretic curve representing the energy-con-suming capacity of the specimen

Table 6 Accumulated dissipated energy (Ep) of all specimens

Specimen Ep (kNmiddotmm) Relative valueSC-1 49770 1SC-2 68307 137SC-3 41784 084SC-4 160490 322SC-5 187933 378SC-6 254794 512

SC-1SC-2SC-3

SC-4SC-5SC-6

004

006

008

010

012

014

016

018

020

022

024

he

0 10 20 30 40 50 60 70ndash10∆ (mm)

Figure 12 Viscous damping coefficient curves of each specimen(e equivalent viscous damping coefficient (he) of the specimenand the displacement (Δ) curve of the column end were calculatedfor each specimen

Advances in Civil Engineering 11

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

(a)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

(b)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

(c)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

(d)

Figure 13 Continued

12 Advances in Civil Engineering

model [22] (e model included the tensile mechanicalproperties of the concrete the stiffness degradation and theenergy dissipation behavior of the concrete during recip-rocating loading For the concrete in the core area theMander model [2324] was used to consider the restrainingeffect of stirrups on concrete Here the stress-strain rela-tionship of CFRP-constrained concrete was establishedusing the Concrete 02 material (e stress and strain at thepeak point were the same as the peak-point stress and strainof the concrete bound by the stirrup (e stress and strain atthe limit point were calculated using the peak-point stressand strain of the Lam-Teng model [2526] (ere was littleresearch on concrete columns reinforced by steel plate meshand no specific theoretical models Based on the existingsteel mesh reinforced concrete column the Concrete 02material in this study was used to establish the stress-strainrelationship of the steel plate mesh to the concrete equations(3) and (4) were used to calculate the peak concrete stress fccafter confinement [19] (e peak strain was 4 times that ofthe peak stress of unconstrained concrete the limit pointstress was twice that of the ultimate stress of unconstrainedconcrete the calculations of the remaining characteristicparameters were consistent with the calculation results of theunconstrained concrete

fcc 1 + 077λv( 1113857fck (3)

λv ρvfyv

fck

(4)

where fck is the axial compressive strength of the concrete λv isthe eigenvalue of the stirrup fyv is the yield strength of the steelplate mesh and ρv is the volumetric ratio of the steel plate mesh

(e vertical load was applied incrementally in 10 stepsusing the gravity loading module provided by OpenSees and

was held constant after the vertical load was completed (ehorizontal load was applied in time series and the loadingsystem was consistent with the experimental proceduresused in this study

(e hysteresis curves for SC-1 through SC-6 generatedby the OpenSees finite element analysis were compared tothe experimentally generated hysteresis curves as shown inFigure 13 (e curves generated by OpenSees are in goodagreement with the experimental results

4 Conclusion

Here six short concrete columns with high-strength lon-gitudinal reinforcements were subjected to low-cycle re-peated loading tests By comparing and analyzing the testresults based on observed test phenomena the followingconclusions are drawn

(1) Compared to the horizontally loaded test specimensthe strength of the diagonally loaded specimensdecreased and the stiffness degradation trendaccelerated this indicates that the effect of obliqueloading is unfavorable to the strength and stiffness ofthe specimens

(2) Under the action of oblique load as the axialcompression ratio increases the strength of thespecimen increases however the deformation ca-pacity becomes worse the stiffness becomes severelydegraded and the specimen is prone to shear brittlefailure

(3) Under the action of oblique load the reinforcementmeasures of the CFRP at the end of the columnimprove the strength and energy consumption of thespecimen however the higher axial compression

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(e)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(f)

Figure 13 OpenSees finite element simulations compared with the experimentally derived hysteresis curve for each specimen Resultscomparison of (a) SC-1 (b) SC-2 (c) SC-3 (d) SC-4 (e) SC-5 and (f) SC-6

Advances in Civil Engineering 13

ratio makes the CFRP more prone to damage anddoes not improve the deformation performance ofthe specimen However the local reinforcementmeasures of the steel plate mesh on the end of thecolumn not only increase the strength and energyconsumption of the specimen but also improve thedeformation ability of the specimen and the seismicperformance of the specimen

(4) In contrast to the unreinforced specimens theaddition of the high-strength stirrups with smallspacing column-end wound CFRP and column-end outer steel plate mesh all improve the strengthdeformation capacity and energy consumptioncapacity of the specimens (e addition of the high-strength stirrups with small spacing and the col-umn-end outer steel plate mesh both altered thefailure mode of the specimen transforming it fromshear failure to bending shear failure (is showsthat the above measures can effectively improve theseismic performance of the test specimen under theaction of oblique loads with a high axial com-pression ratio

(5) Under the action of a high axial pressure ratiooblique load by selecting the appropriate fiber unitand material constitutive relationship the OpenSeesprogram can obtain a simulation result that is ingood agreement with the test hysteresis curve (isverifies the validity of the numerical simulation andprovides a certain basis for subsequent and extendednumerical simulation analyses

Data Availability

All data or models used to support the findings of this studyare included within the article Some data or models thatsupport the findings of this study are available from thecorresponding author upon reasonable request

Conflicts of Interest

(e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

(is work was supported by the Natural Science Foundationof Shandong Province under Grant nos ZR2015EQ017 andZR2018MEE044 and Off-Campus Development Project ofKey Laboratory of Beijing University of Technology underGrant no 2020B03 (e authors are grateful to the KeyLaboratory of Building Structural Retrofitting and Under-ground Space Engineering (Shandong Jianzhu University)Ministry of Education for accommodating the use of theequipment and facilities Professor Xingquan Zhao forproviding computer equipment for numerical simulation ofthe experiment and Editage (httpwwweditagecn) forEnglish language editing

References

[1] A Ghobarah and K Galal ldquoSeismic rehabilitation of shortrectangular RC columnsrdquo Journal of Earthquake Engineeringvol 8 no 1 pp 45ndash68 2004

[2] Y A Li T Y Huang and S J Hwang ldquoSeismic response ofreinforced concrete short columns failed in shearrdquo ACIStructural Journal vol 111 no 4 pp 945ndash954 2014

[3] H Takizawa and H Aoyama ldquoBiaxial effects in modellingearthquake response of RC structuresrdquo Earthquake Engi-neering amp Structural Dynamics vol 4 no 6 pp 523ndash5521976

[4] H Umehara and J O Jirsa ldquoShort rectangular RC columnsunder bidirectional loadingsrdquo Journal of Structural Engi-neering vol 110 no 3 pp 605ndash618 1984

[5] K A Woodward and J O Jirsa ldquoInfluence of reinforcementon RC short column lateral resistancerdquo Journal of StructuralEngineering vol 110 no 1 pp 90ndash104 1984

[6] K Maruyama H Ramirez and J O Jirsa ldquoShort RC columnsunder bilateral load historiesrdquo Journal of Structural Engi-neering vol 110 no 1 pp 120ndash137 1984

[7] H Rodrigues H Varum A Arede and A G CostaldquoBehaviour of reinforced concrete column under biaxial cyclicloadingmdashstate of the artrdquo International Journal of AdvancedStructural Engineering vol 5 no 1 pp 1ndash12 2013

[8] D Wang L Huang T Yu and Z Wang ldquoSeismic perfor-mance of CFRP-retrofitted large-scale square RC columnswith high axial compression ratiosrdquo Journal of Composites forConstruction vol 21 no 5 Article ID 04017031 2017

[9] J Yang and J Wang ldquoSeismic performance of shear-con-trolled CFRP-strengthened high-strength concrete squarecolumns under simulated seismic loadrdquo Journal of Compositesfor Construction vol 22 no 6 Article ID 04018061 2018

[10] X Zhou and J Liu ldquoSeismic behavior and shear strength oftubed RC short columnsrdquo Journal of Constructional SteelResearch vol 66 no 3 pp 385ndash397 2010

[11] H Ma J Xue Y Liu and X Zhang ldquoCyclic loading tests andshear strength of steel reinforced recycled concrete shortcolumnsrdquo Engineering Structures vol 92 pp 55ndash68 2015

[12] D Sokoli and W M Ghannoum ldquoHigh-strength reinforce-ment in columns under high shear stressesrdquo ACI StructuralJournal vol 113 no 3 pp 605ndash614 2016

[13] H Ding Y Liu C Han and Y Guo ldquoSeismic performance ofhigh-strength short concrete column with high-strengthstirrups constraintsrdquo Transactions of Tianjin Universityvol 23 no 4 pp 360ndash369 2017

[14] H O Shin Y S Yoon W D Cook and D Mitchell ldquoAxialload response of ultra-high-strength concrete columns andhigh-strength reinforcementrdquo Transactions of Tianjin Uni-versity vol 113 no 2 pp 325ndash336 216

[15] L A E Shehata M L A V Carneiro and L C D ShehataldquoStrength of short concrete columns confined with CFRPsheetsrdquo Materials and Structures vol 35 pp 50ndash58 2002

[16] F Colomb H Tobbi E Ferrier and P Hamelin ldquoSeismicretrofit of reinforced concrete short columns by CFRPmaterialsfit of reinforced concrete short columns by CFRPmaterialsrdquo Composite Structures vol 82 no 4 pp 475ndash4872008

[17] K Galal A Arafa and A Ghobarah ldquoRetrofit of RC squareshort columnsrdquo Engineering Structures vol 27 no 5pp 801ndash813 2005

[18] R Morshed and M T Kazemi ldquoSeismic shear strengtheningof RC beams and columns with expanded steel meshesrdquo

14 Advances in Civil Engineering

As shown in Figure 12 the equivalent viscous dampingcoefficient (he) of the specimen and the displacement (Δ)curve of the column end were calculated for each specimenAt the initial stage of loading the energy consumption of thespecimen increased as the loading displacement increasedWhen the specimen was cracked stress redistribution oc-curred inside the specimen thereby impacting the stress anddeformation of the specimen and decreasing the energyconsumption As the loading displacement continued toincrease the crack continued opening and closing thusincreasing the energy consumption of the specimen Whenthe specimen yielded the internal longitudinal reinforce-ment of the specimen yielded and the stress redistributionoccurred again inside the specimen thus decreasing theenergy consumption of the specimen With continuousloading cracks of the specimen kept opening and closingand energy consumption continued increasing until thespecimen was destroyed (e equivalent viscous dampingcoefficient of each specimen increased as a whole whichindicated that the damage of the specimen increased as thehorizontal deformation increased during the loading pro-cess thereby increasing the energy consumption of thespecimen (Figure 12)

Cumulative energy consumption refers to the sum of allhysteresis loop areas generated from the beginning of theload application to the ultimate displacement point (elarger the value the stronger the energy dissipation capacityof the specimen and the better the seismic performance Asshown in Table 6 the cumulative energy dissipation wascalculated for each specimen

In contrast to SC-1 the cumulative energy consumptionof SC-2 increased by 37 indicating that the obliquehorizontal loading led to more serious cumulative damageand the consumption of more energy Compared to SC-2the accumulated energy consumption value of SC-3 de-creased by approximately 16 possibly due to the pre-mature failure of specimen and the increase of the axialpressure ratio which reduces the cumulative energy con-sumption capacity of specimen In contrast to specimen SC-3 the cumulative energy consumption values of specimensSC-4 SC-5 and SC-6 all improved with increase rates of222 278 and 412 respectively (is is because high-

strength stirrups with small spacing wound CFRP at the endof the column and steel plate mesh at the end of the columnlimit the shedding of concrete and thus increase the work ofthe concrete

37 OpenSees Finite Element Simulation (e open-sourcefinite element program OpenSees (Open System forEarthquake Engineering Simulation) was used as a platformto numerically simulate the experimental specimens (emodel used displacement-based nonlinear beam-columnelements (ree nodes along the height of the column wereused to form two units wherein the top node was free endand the bottom node was embedded (e P-Delta effectcaused by the vertical load was considered by the P-Del-taCrdTransf command (e fiber model was used to definethe relationship of the cross section restoring force at theunit integration point (e longitudinal reinforcement wasmodeled using the Reinforcing Steel uniaxial materialprovided in OpenSees which was based on the Chang-Mander uniaxial material model [21] and simulated theisotropic hardening behavior of steel bars (e concrete wassimulated by Concrete 02 provided by OpenSees (e ma-terial was based on the Kent-Scott-Park uniaxial material

A OG

D

B

C H Δ

P

Figure 11 PminusΔ hysteretic curve representing the energy-con-suming capacity of the specimen

Table 6 Accumulated dissipated energy (Ep) of all specimens

Specimen Ep (kNmiddotmm) Relative valueSC-1 49770 1SC-2 68307 137SC-3 41784 084SC-4 160490 322SC-5 187933 378SC-6 254794 512

SC-1SC-2SC-3

SC-4SC-5SC-6

004

006

008

010

012

014

016

018

020

022

024

he

0 10 20 30 40 50 60 70ndash10∆ (mm)

Figure 12 Viscous damping coefficient curves of each specimen(e equivalent viscous damping coefficient (he) of the specimenand the displacement (Δ) curve of the column end were calculatedfor each specimen

Advances in Civil Engineering 11

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

(a)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

(b)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

(c)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

(d)

Figure 13 Continued

12 Advances in Civil Engineering

model [22] (e model included the tensile mechanicalproperties of the concrete the stiffness degradation and theenergy dissipation behavior of the concrete during recip-rocating loading For the concrete in the core area theMander model [2324] was used to consider the restrainingeffect of stirrups on concrete Here the stress-strain rela-tionship of CFRP-constrained concrete was establishedusing the Concrete 02 material (e stress and strain at thepeak point were the same as the peak-point stress and strainof the concrete bound by the stirrup (e stress and strain atthe limit point were calculated using the peak-point stressand strain of the Lam-Teng model [2526] (ere was littleresearch on concrete columns reinforced by steel plate meshand no specific theoretical models Based on the existingsteel mesh reinforced concrete column the Concrete 02material in this study was used to establish the stress-strainrelationship of the steel plate mesh to the concrete equations(3) and (4) were used to calculate the peak concrete stress fccafter confinement [19] (e peak strain was 4 times that ofthe peak stress of unconstrained concrete the limit pointstress was twice that of the ultimate stress of unconstrainedconcrete the calculations of the remaining characteristicparameters were consistent with the calculation results of theunconstrained concrete

fcc 1 + 077λv( 1113857fck (3)

λv ρvfyv

fck

(4)

where fck is the axial compressive strength of the concrete λv isthe eigenvalue of the stirrup fyv is the yield strength of the steelplate mesh and ρv is the volumetric ratio of the steel plate mesh

(e vertical load was applied incrementally in 10 stepsusing the gravity loading module provided by OpenSees and

was held constant after the vertical load was completed (ehorizontal load was applied in time series and the loadingsystem was consistent with the experimental proceduresused in this study

(e hysteresis curves for SC-1 through SC-6 generatedby the OpenSees finite element analysis were compared tothe experimentally generated hysteresis curves as shown inFigure 13 (e curves generated by OpenSees are in goodagreement with the experimental results

4 Conclusion

Here six short concrete columns with high-strength lon-gitudinal reinforcements were subjected to low-cycle re-peated loading tests By comparing and analyzing the testresults based on observed test phenomena the followingconclusions are drawn

(1) Compared to the horizontally loaded test specimensthe strength of the diagonally loaded specimensdecreased and the stiffness degradation trendaccelerated this indicates that the effect of obliqueloading is unfavorable to the strength and stiffness ofthe specimens

(2) Under the action of oblique load as the axialcompression ratio increases the strength of thespecimen increases however the deformation ca-pacity becomes worse the stiffness becomes severelydegraded and the specimen is prone to shear brittlefailure

(3) Under the action of oblique load the reinforcementmeasures of the CFRP at the end of the columnimprove the strength and energy consumption of thespecimen however the higher axial compression

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(e)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(f)

Figure 13 OpenSees finite element simulations compared with the experimentally derived hysteresis curve for each specimen Resultscomparison of (a) SC-1 (b) SC-2 (c) SC-3 (d) SC-4 (e) SC-5 and (f) SC-6

Advances in Civil Engineering 13

ratio makes the CFRP more prone to damage anddoes not improve the deformation performance ofthe specimen However the local reinforcementmeasures of the steel plate mesh on the end of thecolumn not only increase the strength and energyconsumption of the specimen but also improve thedeformation ability of the specimen and the seismicperformance of the specimen

(4) In contrast to the unreinforced specimens theaddition of the high-strength stirrups with smallspacing column-end wound CFRP and column-end outer steel plate mesh all improve the strengthdeformation capacity and energy consumptioncapacity of the specimens (e addition of the high-strength stirrups with small spacing and the col-umn-end outer steel plate mesh both altered thefailure mode of the specimen transforming it fromshear failure to bending shear failure (is showsthat the above measures can effectively improve theseismic performance of the test specimen under theaction of oblique loads with a high axial com-pression ratio

(5) Under the action of a high axial pressure ratiooblique load by selecting the appropriate fiber unitand material constitutive relationship the OpenSeesprogram can obtain a simulation result that is ingood agreement with the test hysteresis curve (isverifies the validity of the numerical simulation andprovides a certain basis for subsequent and extendednumerical simulation analyses

Data Availability

All data or models used to support the findings of this studyare included within the article Some data or models thatsupport the findings of this study are available from thecorresponding author upon reasonable request

Conflicts of Interest

(e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

(is work was supported by the Natural Science Foundationof Shandong Province under Grant nos ZR2015EQ017 andZR2018MEE044 and Off-Campus Development Project ofKey Laboratory of Beijing University of Technology underGrant no 2020B03 (e authors are grateful to the KeyLaboratory of Building Structural Retrofitting and Under-ground Space Engineering (Shandong Jianzhu University)Ministry of Education for accommodating the use of theequipment and facilities Professor Xingquan Zhao forproviding computer equipment for numerical simulation ofthe experiment and Editage (httpwwweditagecn) forEnglish language editing

References

[1] A Ghobarah and K Galal ldquoSeismic rehabilitation of shortrectangular RC columnsrdquo Journal of Earthquake Engineeringvol 8 no 1 pp 45ndash68 2004

[2] Y A Li T Y Huang and S J Hwang ldquoSeismic response ofreinforced concrete short columns failed in shearrdquo ACIStructural Journal vol 111 no 4 pp 945ndash954 2014

[3] H Takizawa and H Aoyama ldquoBiaxial effects in modellingearthquake response of RC structuresrdquo Earthquake Engi-neering amp Structural Dynamics vol 4 no 6 pp 523ndash5521976

[4] H Umehara and J O Jirsa ldquoShort rectangular RC columnsunder bidirectional loadingsrdquo Journal of Structural Engi-neering vol 110 no 3 pp 605ndash618 1984

[5] K A Woodward and J O Jirsa ldquoInfluence of reinforcementon RC short column lateral resistancerdquo Journal of StructuralEngineering vol 110 no 1 pp 90ndash104 1984

[6] K Maruyama H Ramirez and J O Jirsa ldquoShort RC columnsunder bilateral load historiesrdquo Journal of Structural Engi-neering vol 110 no 1 pp 120ndash137 1984

[7] H Rodrigues H Varum A Arede and A G CostaldquoBehaviour of reinforced concrete column under biaxial cyclicloadingmdashstate of the artrdquo International Journal of AdvancedStructural Engineering vol 5 no 1 pp 1ndash12 2013

[8] D Wang L Huang T Yu and Z Wang ldquoSeismic perfor-mance of CFRP-retrofitted large-scale square RC columnswith high axial compression ratiosrdquo Journal of Composites forConstruction vol 21 no 5 Article ID 04017031 2017

[9] J Yang and J Wang ldquoSeismic performance of shear-con-trolled CFRP-strengthened high-strength concrete squarecolumns under simulated seismic loadrdquo Journal of Compositesfor Construction vol 22 no 6 Article ID 04018061 2018

[10] X Zhou and J Liu ldquoSeismic behavior and shear strength oftubed RC short columnsrdquo Journal of Constructional SteelResearch vol 66 no 3 pp 385ndash397 2010

[11] H Ma J Xue Y Liu and X Zhang ldquoCyclic loading tests andshear strength of steel reinforced recycled concrete shortcolumnsrdquo Engineering Structures vol 92 pp 55ndash68 2015

[12] D Sokoli and W M Ghannoum ldquoHigh-strength reinforce-ment in columns under high shear stressesrdquo ACI StructuralJournal vol 113 no 3 pp 605ndash614 2016

[13] H Ding Y Liu C Han and Y Guo ldquoSeismic performance ofhigh-strength short concrete column with high-strengthstirrups constraintsrdquo Transactions of Tianjin Universityvol 23 no 4 pp 360ndash369 2017

[14] H O Shin Y S Yoon W D Cook and D Mitchell ldquoAxialload response of ultra-high-strength concrete columns andhigh-strength reinforcementrdquo Transactions of Tianjin Uni-versity vol 113 no 2 pp 325ndash336 216

[15] L A E Shehata M L A V Carneiro and L C D ShehataldquoStrength of short concrete columns confined with CFRPsheetsrdquo Materials and Structures vol 35 pp 50ndash58 2002

[16] F Colomb H Tobbi E Ferrier and P Hamelin ldquoSeismicretrofit of reinforced concrete short columns by CFRPmaterialsfit of reinforced concrete short columns by CFRPmaterialsrdquo Composite Structures vol 82 no 4 pp 475ndash4872008

[17] K Galal A Arafa and A Ghobarah ldquoRetrofit of RC squareshort columnsrdquo Engineering Structures vol 27 no 5pp 801ndash813 2005

[18] R Morshed and M T Kazemi ldquoSeismic shear strengtheningof RC beams and columns with expanded steel meshesrdquo

14 Advances in Civil Engineering

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

(a)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

(b)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

(c)

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

(d)

Figure 13 Continued

12 Advances in Civil Engineering

model [22] (e model included the tensile mechanicalproperties of the concrete the stiffness degradation and theenergy dissipation behavior of the concrete during recip-rocating loading For the concrete in the core area theMander model [2324] was used to consider the restrainingeffect of stirrups on concrete Here the stress-strain rela-tionship of CFRP-constrained concrete was establishedusing the Concrete 02 material (e stress and strain at thepeak point were the same as the peak-point stress and strainof the concrete bound by the stirrup (e stress and strain atthe limit point were calculated using the peak-point stressand strain of the Lam-Teng model [2526] (ere was littleresearch on concrete columns reinforced by steel plate meshand no specific theoretical models Based on the existingsteel mesh reinforced concrete column the Concrete 02material in this study was used to establish the stress-strainrelationship of the steel plate mesh to the concrete equations(3) and (4) were used to calculate the peak concrete stress fccafter confinement [19] (e peak strain was 4 times that ofthe peak stress of unconstrained concrete the limit pointstress was twice that of the ultimate stress of unconstrainedconcrete the calculations of the remaining characteristicparameters were consistent with the calculation results of theunconstrained concrete

fcc 1 + 077λv( 1113857fck (3)

λv ρvfyv

fck

(4)

where fck is the axial compressive strength of the concrete λv isthe eigenvalue of the stirrup fyv is the yield strength of the steelplate mesh and ρv is the volumetric ratio of the steel plate mesh

(e vertical load was applied incrementally in 10 stepsusing the gravity loading module provided by OpenSees and

was held constant after the vertical load was completed (ehorizontal load was applied in time series and the loadingsystem was consistent with the experimental proceduresused in this study

(e hysteresis curves for SC-1 through SC-6 generatedby the OpenSees finite element analysis were compared tothe experimentally generated hysteresis curves as shown inFigure 13 (e curves generated by OpenSees are in goodagreement with the experimental results

4 Conclusion

Here six short concrete columns with high-strength lon-gitudinal reinforcements were subjected to low-cycle re-peated loading tests By comparing and analyzing the testresults based on observed test phenomena the followingconclusions are drawn

(1) Compared to the horizontally loaded test specimensthe strength of the diagonally loaded specimensdecreased and the stiffness degradation trendaccelerated this indicates that the effect of obliqueloading is unfavorable to the strength and stiffness ofthe specimens

(2) Under the action of oblique load as the axialcompression ratio increases the strength of thespecimen increases however the deformation ca-pacity becomes worse the stiffness becomes severelydegraded and the specimen is prone to shear brittlefailure

(3) Under the action of oblique load the reinforcementmeasures of the CFRP at the end of the columnimprove the strength and energy consumption of thespecimen however the higher axial compression

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(e)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(f)

Figure 13 OpenSees finite element simulations compared with the experimentally derived hysteresis curve for each specimen Resultscomparison of (a) SC-1 (b) SC-2 (c) SC-3 (d) SC-4 (e) SC-5 and (f) SC-6

Advances in Civil Engineering 13

ratio makes the CFRP more prone to damage anddoes not improve the deformation performance ofthe specimen However the local reinforcementmeasures of the steel plate mesh on the end of thecolumn not only increase the strength and energyconsumption of the specimen but also improve thedeformation ability of the specimen and the seismicperformance of the specimen

(4) In contrast to the unreinforced specimens theaddition of the high-strength stirrups with smallspacing column-end wound CFRP and column-end outer steel plate mesh all improve the strengthdeformation capacity and energy consumptioncapacity of the specimens (e addition of the high-strength stirrups with small spacing and the col-umn-end outer steel plate mesh both altered thefailure mode of the specimen transforming it fromshear failure to bending shear failure (is showsthat the above measures can effectively improve theseismic performance of the test specimen under theaction of oblique loads with a high axial com-pression ratio

(5) Under the action of a high axial pressure ratiooblique load by selecting the appropriate fiber unitand material constitutive relationship the OpenSeesprogram can obtain a simulation result that is ingood agreement with the test hysteresis curve (isverifies the validity of the numerical simulation andprovides a certain basis for subsequent and extendednumerical simulation analyses

Data Availability

All data or models used to support the findings of this studyare included within the article Some data or models thatsupport the findings of this study are available from thecorresponding author upon reasonable request

Conflicts of Interest

(e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

(is work was supported by the Natural Science Foundationof Shandong Province under Grant nos ZR2015EQ017 andZR2018MEE044 and Off-Campus Development Project ofKey Laboratory of Beijing University of Technology underGrant no 2020B03 (e authors are grateful to the KeyLaboratory of Building Structural Retrofitting and Under-ground Space Engineering (Shandong Jianzhu University)Ministry of Education for accommodating the use of theequipment and facilities Professor Xingquan Zhao forproviding computer equipment for numerical simulation ofthe experiment and Editage (httpwwweditagecn) forEnglish language editing

References

[1] A Ghobarah and K Galal ldquoSeismic rehabilitation of shortrectangular RC columnsrdquo Journal of Earthquake Engineeringvol 8 no 1 pp 45ndash68 2004

[2] Y A Li T Y Huang and S J Hwang ldquoSeismic response ofreinforced concrete short columns failed in shearrdquo ACIStructural Journal vol 111 no 4 pp 945ndash954 2014

[3] H Takizawa and H Aoyama ldquoBiaxial effects in modellingearthquake response of RC structuresrdquo Earthquake Engi-neering amp Structural Dynamics vol 4 no 6 pp 523ndash5521976

[4] H Umehara and J O Jirsa ldquoShort rectangular RC columnsunder bidirectional loadingsrdquo Journal of Structural Engi-neering vol 110 no 3 pp 605ndash618 1984

[5] K A Woodward and J O Jirsa ldquoInfluence of reinforcementon RC short column lateral resistancerdquo Journal of StructuralEngineering vol 110 no 1 pp 90ndash104 1984

[6] K Maruyama H Ramirez and J O Jirsa ldquoShort RC columnsunder bilateral load historiesrdquo Journal of Structural Engi-neering vol 110 no 1 pp 120ndash137 1984

[7] H Rodrigues H Varum A Arede and A G CostaldquoBehaviour of reinforced concrete column under biaxial cyclicloadingmdashstate of the artrdquo International Journal of AdvancedStructural Engineering vol 5 no 1 pp 1ndash12 2013

[8] D Wang L Huang T Yu and Z Wang ldquoSeismic perfor-mance of CFRP-retrofitted large-scale square RC columnswith high axial compression ratiosrdquo Journal of Composites forConstruction vol 21 no 5 Article ID 04017031 2017

[9] J Yang and J Wang ldquoSeismic performance of shear-con-trolled CFRP-strengthened high-strength concrete squarecolumns under simulated seismic loadrdquo Journal of Compositesfor Construction vol 22 no 6 Article ID 04018061 2018

[10] X Zhou and J Liu ldquoSeismic behavior and shear strength oftubed RC short columnsrdquo Journal of Constructional SteelResearch vol 66 no 3 pp 385ndash397 2010

[11] H Ma J Xue Y Liu and X Zhang ldquoCyclic loading tests andshear strength of steel reinforced recycled concrete shortcolumnsrdquo Engineering Structures vol 92 pp 55ndash68 2015

[12] D Sokoli and W M Ghannoum ldquoHigh-strength reinforce-ment in columns under high shear stressesrdquo ACI StructuralJournal vol 113 no 3 pp 605ndash614 2016

[13] H Ding Y Liu C Han and Y Guo ldquoSeismic performance ofhigh-strength short concrete column with high-strengthstirrups constraintsrdquo Transactions of Tianjin Universityvol 23 no 4 pp 360ndash369 2017

[14] H O Shin Y S Yoon W D Cook and D Mitchell ldquoAxialload response of ultra-high-strength concrete columns andhigh-strength reinforcementrdquo Transactions of Tianjin Uni-versity vol 113 no 2 pp 325ndash336 216

[15] L A E Shehata M L A V Carneiro and L C D ShehataldquoStrength of short concrete columns confined with CFRPsheetsrdquo Materials and Structures vol 35 pp 50ndash58 2002

[16] F Colomb H Tobbi E Ferrier and P Hamelin ldquoSeismicretrofit of reinforced concrete short columns by CFRPmaterialsfit of reinforced concrete short columns by CFRPmaterialsrdquo Composite Structures vol 82 no 4 pp 475ndash4872008

[17] K Galal A Arafa and A Ghobarah ldquoRetrofit of RC squareshort columnsrdquo Engineering Structures vol 27 no 5pp 801ndash813 2005

[18] R Morshed and M T Kazemi ldquoSeismic shear strengtheningof RC beams and columns with expanded steel meshesrdquo

14 Advances in Civil Engineering

model [22] (e model included the tensile mechanicalproperties of the concrete the stiffness degradation and theenergy dissipation behavior of the concrete during recip-rocating loading For the concrete in the core area theMander model [2324] was used to consider the restrainingeffect of stirrups on concrete Here the stress-strain rela-tionship of CFRP-constrained concrete was establishedusing the Concrete 02 material (e stress and strain at thepeak point were the same as the peak-point stress and strainof the concrete bound by the stirrup (e stress and strain atthe limit point were calculated using the peak-point stressand strain of the Lam-Teng model [2526] (ere was littleresearch on concrete columns reinforced by steel plate meshand no specific theoretical models Based on the existingsteel mesh reinforced concrete column the Concrete 02material in this study was used to establish the stress-strainrelationship of the steel plate mesh to the concrete equations(3) and (4) were used to calculate the peak concrete stress fccafter confinement [19] (e peak strain was 4 times that ofthe peak stress of unconstrained concrete the limit pointstress was twice that of the ultimate stress of unconstrainedconcrete the calculations of the remaining characteristicparameters were consistent with the calculation results of theunconstrained concrete

fcc 1 + 077λv( 1113857fck (3)

λv ρvfyv

fck

(4)

where fck is the axial compressive strength of the concrete λv isthe eigenvalue of the stirrup fyv is the yield strength of the steelplate mesh and ρv is the volumetric ratio of the steel plate mesh

(e vertical load was applied incrementally in 10 stepsusing the gravity loading module provided by OpenSees and

was held constant after the vertical load was completed (ehorizontal load was applied in time series and the loadingsystem was consistent with the experimental proceduresused in this study

(e hysteresis curves for SC-1 through SC-6 generatedby the OpenSees finite element analysis were compared tothe experimentally generated hysteresis curves as shown inFigure 13 (e curves generated by OpenSees are in goodagreement with the experimental results

4 Conclusion

Here six short concrete columns with high-strength lon-gitudinal reinforcements were subjected to low-cycle re-peated loading tests By comparing and analyzing the testresults based on observed test phenomena the followingconclusions are drawn

(1) Compared to the horizontally loaded test specimensthe strength of the diagonally loaded specimensdecreased and the stiffness degradation trendaccelerated this indicates that the effect of obliqueloading is unfavorable to the strength and stiffness ofthe specimens

(2) Under the action of oblique load as the axialcompression ratio increases the strength of thespecimen increases however the deformation ca-pacity becomes worse the stiffness becomes severelydegraded and the specimen is prone to shear brittlefailure

(3) Under the action of oblique load the reinforcementmeasures of the CFRP at the end of the columnimprove the strength and energy consumption of thespecimen however the higher axial compression

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(e)

ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0∆ (mm)

10 20 30 40 50 60 70

Black = experimentally derivedRed = finite element

700600500400300200100

0ndash100ndash200ndash300ndash400ndash500ndash600ndash700

P (k

N)

(f)

Figure 13 OpenSees finite element simulations compared with the experimentally derived hysteresis curve for each specimen Resultscomparison of (a) SC-1 (b) SC-2 (c) SC-3 (d) SC-4 (e) SC-5 and (f) SC-6

Advances in Civil Engineering 13

ratio makes the CFRP more prone to damage anddoes not improve the deformation performance ofthe specimen However the local reinforcementmeasures of the steel plate mesh on the end of thecolumn not only increase the strength and energyconsumption of the specimen but also improve thedeformation ability of the specimen and the seismicperformance of the specimen

(4) In contrast to the unreinforced specimens theaddition of the high-strength stirrups with smallspacing column-end wound CFRP and column-end outer steel plate mesh all improve the strengthdeformation capacity and energy consumptioncapacity of the specimens (e addition of the high-strength stirrups with small spacing and the col-umn-end outer steel plate mesh both altered thefailure mode of the specimen transforming it fromshear failure to bending shear failure (is showsthat the above measures can effectively improve theseismic performance of the test specimen under theaction of oblique loads with a high axial com-pression ratio

(5) Under the action of a high axial pressure ratiooblique load by selecting the appropriate fiber unitand material constitutive relationship the OpenSeesprogram can obtain a simulation result that is ingood agreement with the test hysteresis curve (isverifies the validity of the numerical simulation andprovides a certain basis for subsequent and extendednumerical simulation analyses

Data Availability

All data or models used to support the findings of this studyare included within the article Some data or models thatsupport the findings of this study are available from thecorresponding author upon reasonable request

Conflicts of Interest

(e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

(is work was supported by the Natural Science Foundationof Shandong Province under Grant nos ZR2015EQ017 andZR2018MEE044 and Off-Campus Development Project ofKey Laboratory of Beijing University of Technology underGrant no 2020B03 (e authors are grateful to the KeyLaboratory of Building Structural Retrofitting and Under-ground Space Engineering (Shandong Jianzhu University)Ministry of Education for accommodating the use of theequipment and facilities Professor Xingquan Zhao forproviding computer equipment for numerical simulation ofthe experiment and Editage (httpwwweditagecn) forEnglish language editing

References

[1] A Ghobarah and K Galal ldquoSeismic rehabilitation of shortrectangular RC columnsrdquo Journal of Earthquake Engineeringvol 8 no 1 pp 45ndash68 2004

[2] Y A Li T Y Huang and S J Hwang ldquoSeismic response ofreinforced concrete short columns failed in shearrdquo ACIStructural Journal vol 111 no 4 pp 945ndash954 2014

[3] H Takizawa and H Aoyama ldquoBiaxial effects in modellingearthquake response of RC structuresrdquo Earthquake Engi-neering amp Structural Dynamics vol 4 no 6 pp 523ndash5521976

[4] H Umehara and J O Jirsa ldquoShort rectangular RC columnsunder bidirectional loadingsrdquo Journal of Structural Engi-neering vol 110 no 3 pp 605ndash618 1984

[5] K A Woodward and J O Jirsa ldquoInfluence of reinforcementon RC short column lateral resistancerdquo Journal of StructuralEngineering vol 110 no 1 pp 90ndash104 1984

[6] K Maruyama H Ramirez and J O Jirsa ldquoShort RC columnsunder bilateral load historiesrdquo Journal of Structural Engi-neering vol 110 no 1 pp 120ndash137 1984

[7] H Rodrigues H Varum A Arede and A G CostaldquoBehaviour of reinforced concrete column under biaxial cyclicloadingmdashstate of the artrdquo International Journal of AdvancedStructural Engineering vol 5 no 1 pp 1ndash12 2013

[8] D Wang L Huang T Yu and Z Wang ldquoSeismic perfor-mance of CFRP-retrofitted large-scale square RC columnswith high axial compression ratiosrdquo Journal of Composites forConstruction vol 21 no 5 Article ID 04017031 2017

[9] J Yang and J Wang ldquoSeismic performance of shear-con-trolled CFRP-strengthened high-strength concrete squarecolumns under simulated seismic loadrdquo Journal of Compositesfor Construction vol 22 no 6 Article ID 04018061 2018

[10] X Zhou and J Liu ldquoSeismic behavior and shear strength oftubed RC short columnsrdquo Journal of Constructional SteelResearch vol 66 no 3 pp 385ndash397 2010

[11] H Ma J Xue Y Liu and X Zhang ldquoCyclic loading tests andshear strength of steel reinforced recycled concrete shortcolumnsrdquo Engineering Structures vol 92 pp 55ndash68 2015

[12] D Sokoli and W M Ghannoum ldquoHigh-strength reinforce-ment in columns under high shear stressesrdquo ACI StructuralJournal vol 113 no 3 pp 605ndash614 2016

[13] H Ding Y Liu C Han and Y Guo ldquoSeismic performance ofhigh-strength short concrete column with high-strengthstirrups constraintsrdquo Transactions of Tianjin Universityvol 23 no 4 pp 360ndash369 2017

[14] H O Shin Y S Yoon W D Cook and D Mitchell ldquoAxialload response of ultra-high-strength concrete columns andhigh-strength reinforcementrdquo Transactions of Tianjin Uni-versity vol 113 no 2 pp 325ndash336 216

[15] L A E Shehata M L A V Carneiro and L C D ShehataldquoStrength of short concrete columns confined with CFRPsheetsrdquo Materials and Structures vol 35 pp 50ndash58 2002

[16] F Colomb H Tobbi E Ferrier and P Hamelin ldquoSeismicretrofit of reinforced concrete short columns by CFRPmaterialsfit of reinforced concrete short columns by CFRPmaterialsrdquo Composite Structures vol 82 no 4 pp 475ndash4872008

[17] K Galal A Arafa and A Ghobarah ldquoRetrofit of RC squareshort columnsrdquo Engineering Structures vol 27 no 5pp 801ndash813 2005

[18] R Morshed and M T Kazemi ldquoSeismic shear strengtheningof RC beams and columns with expanded steel meshesrdquo

14 Advances in Civil Engineering

ratio makes the CFRP more prone to damage anddoes not improve the deformation performance ofthe specimen However the local reinforcementmeasures of the steel plate mesh on the end of thecolumn not only increase the strength and energyconsumption of the specimen but also improve thedeformation ability of the specimen and the seismicperformance of the specimen

(4) In contrast to the unreinforced specimens theaddition of the high-strength stirrups with smallspacing column-end wound CFRP and column-end outer steel plate mesh all improve the strengthdeformation capacity and energy consumptioncapacity of the specimens (e addition of the high-strength stirrups with small spacing and the col-umn-end outer steel plate mesh both altered thefailure mode of the specimen transforming it fromshear failure to bending shear failure (is showsthat the above measures can effectively improve theseismic performance of the test specimen under theaction of oblique loads with a high axial com-pression ratio

(5) Under the action of a high axial pressure ratiooblique load by selecting the appropriate fiber unitand material constitutive relationship the OpenSeesprogram can obtain a simulation result that is ingood agreement with the test hysteresis curve (isverifies the validity of the numerical simulation andprovides a certain basis for subsequent and extendednumerical simulation analyses

Data Availability

All data or models used to support the findings of this studyare included within the article Some data or models thatsupport the findings of this study are available from thecorresponding author upon reasonable request

Conflicts of Interest

(e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

(is work was supported by the Natural Science Foundationof Shandong Province under Grant nos ZR2015EQ017 andZR2018MEE044 and Off-Campus Development Project ofKey Laboratory of Beijing University of Technology underGrant no 2020B03 (e authors are grateful to the KeyLaboratory of Building Structural Retrofitting and Under-ground Space Engineering (Shandong Jianzhu University)Ministry of Education for accommodating the use of theequipment and facilities Professor Xingquan Zhao forproviding computer equipment for numerical simulation ofthe experiment and Editage (httpwwweditagecn) forEnglish language editing

References

[1] A Ghobarah and K Galal ldquoSeismic rehabilitation of shortrectangular RC columnsrdquo Journal of Earthquake Engineeringvol 8 no 1 pp 45ndash68 2004

[2] Y A Li T Y Huang and S J Hwang ldquoSeismic response ofreinforced concrete short columns failed in shearrdquo ACIStructural Journal vol 111 no 4 pp 945ndash954 2014

[3] H Takizawa and H Aoyama ldquoBiaxial effects in modellingearthquake response of RC structuresrdquo Earthquake Engi-neering amp Structural Dynamics vol 4 no 6 pp 523ndash5521976

[4] H Umehara and J O Jirsa ldquoShort rectangular RC columnsunder bidirectional loadingsrdquo Journal of Structural Engi-neering vol 110 no 3 pp 605ndash618 1984

[5] K A Woodward and J O Jirsa ldquoInfluence of reinforcementon RC short column lateral resistancerdquo Journal of StructuralEngineering vol 110 no 1 pp 90ndash104 1984

[6] K Maruyama H Ramirez and J O Jirsa ldquoShort RC columnsunder bilateral load historiesrdquo Journal of Structural Engi-neering vol 110 no 1 pp 120ndash137 1984

[7] H Rodrigues H Varum A Arede and A G CostaldquoBehaviour of reinforced concrete column under biaxial cyclicloadingmdashstate of the artrdquo International Journal of AdvancedStructural Engineering vol 5 no 1 pp 1ndash12 2013

[8] D Wang L Huang T Yu and Z Wang ldquoSeismic perfor-mance of CFRP-retrofitted large-scale square RC columnswith high axial compression ratiosrdquo Journal of Composites forConstruction vol 21 no 5 Article ID 04017031 2017

[9] J Yang and J Wang ldquoSeismic performance of shear-con-trolled CFRP-strengthened high-strength concrete squarecolumns under simulated seismic loadrdquo Journal of Compositesfor Construction vol 22 no 6 Article ID 04018061 2018

[10] X Zhou and J Liu ldquoSeismic behavior and shear strength oftubed RC short columnsrdquo Journal of Constructional SteelResearch vol 66 no 3 pp 385ndash397 2010

[11] H Ma J Xue Y Liu and X Zhang ldquoCyclic loading tests andshear strength of steel reinforced recycled concrete shortcolumnsrdquo Engineering Structures vol 92 pp 55ndash68 2015

[12] D Sokoli and W M Ghannoum ldquoHigh-strength reinforce-ment in columns under high shear stressesrdquo ACI StructuralJournal vol 113 no 3 pp 605ndash614 2016

[13] H Ding Y Liu C Han and Y Guo ldquoSeismic performance ofhigh-strength short concrete column with high-strengthstirrups constraintsrdquo Transactions of Tianjin Universityvol 23 no 4 pp 360ndash369 2017

[14] H O Shin Y S Yoon W D Cook and D Mitchell ldquoAxialload response of ultra-high-strength concrete columns andhigh-strength reinforcementrdquo Transactions of Tianjin Uni-versity vol 113 no 2 pp 325ndash336 216

[15] L A E Shehata M L A V Carneiro and L C D ShehataldquoStrength of short concrete columns confined with CFRPsheetsrdquo Materials and Structures vol 35 pp 50ndash58 2002

[16] F Colomb H Tobbi E Ferrier and P Hamelin ldquoSeismicretrofit of reinforced concrete short columns by CFRPmaterialsfit of reinforced concrete short columns by CFRPmaterialsrdquo Composite Structures vol 82 no 4 pp 475ndash4872008

[17] K Galal A Arafa and A Ghobarah ldquoRetrofit of RC squareshort columnsrdquo Engineering Structures vol 27 no 5pp 801ndash813 2005

[18] R Morshed and M T Kazemi ldquoSeismic shear strengtheningof RC beams and columns with expanded steel meshesrdquo

14 Advances in Civil Engineering

Structural Engineering and Mechanics vol 21 no 3pp 333ndash350 2005

[19] Z Li X Wang Y Xie and C Yu ldquoExperimental study ofseismic behavior of high-strength concrete columns withexpanded metal lathrdquo Journal of North China University ofScience and Technology (Natural Science Edition) Chinavol 40 no 4 pp 51ndash58 2018

[20] Z Li C Yu Y Xie H Ma and Z Tang ldquoSize effect on seismicperformance of high-strength reinforced concrete columnssubjected to monotonic and cyclic loadingrdquo EngineeringStructures vol 183 no 15 pp 206ndash219 2019

[21] S K Kunnath Y Heo and J F Mohle ldquoNonlinear uniaxialmaterial model for reinforcing steel barsrdquo Journal of Struc-tural Engineering vol 135 no 4 pp 335ndash343 2009

[22] B D Scott R Park and M J N Priestley ldquoStress-strainbehavior of concrete confined by overlapping hoops at lowand high strain ratesrdquo ACI Journal vol 79 no 1 pp 13ndash271982

[23] J B Mander M J N Priestley and R Park ldquo(eoreticalstress-strain model for confined concreterdquo Journal of Struc-tural Engineering vol 114 no 8 pp 1804ndash1826 1988

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

[25] L Lam and J Teng ldquoDesign-oriented stress-strain model forFRP-confined concreterdquo Construction and BuildingMaterialsvol 17 no 7 pp 471ndash489 2003

[26] L Lam and J G Teng ldquoDesign-Oriented stress-strain modelfor FRP-confined concrete in rectangular columnsrdquo Journal ofReinforced Plastics and Composites vol 22 no 13pp 1149ndash1186 2003

Advances in Civil Engineering 15