Seismic Response Evaluation of Reinforced High Strength …scientiairanica.sharif.edu/article_4183_68fd1870e3c02103cd56925343... · Seismic Response Evaluation of Reinforced High

Scientia Iranica A (2018) 25(2), 579{589

Sharif University of TechnologyScientia Iranica

Transactions A: Civil Engineeringhttp://scientiairanica.sharif.edu

Seismic response evaluation of reinforced high strengthconcrete columns based on the modi�ed constitutivemodel

F. Vahid-Vahdattalaba, J. Mokari Rahmdelb, and E. Shafeib;�

a. Department of Structural Engineering, Urmia University of Technology.b. Faculty of Civil Engineering, Urmia University of Technology, Urmia, Iran.

Received 11 January 2016; received in revised form 13 September 2016; accepted 31 October 2016

KEYWORDSHigh strengthconcrete;Seismic assessment;Modi�ed strengthmodel;Cyclic loading;Second order forcee�ect;Reinforcement ratio.

Abstract. The current study deals with strength and seismic ductility assessment ofreinforced High-Strength Concrete (HSC) columns. We have studied the nonlinear responseof HSC columns with various reinforcement and axial force ratios subjected to cyclicloading. The study consists of primary veri�cation of mathematical nonlinear model andfurther calibration to ensure the required accuracy. The existing experimental work isassumed as veri�cation pilot that consists of four columns. Column members di�er inthe strength and axial force. Concrete has 63.1 MPa mean strength and 0.3% crushingstrain. The longitudinal and transverse reinforcements are based on ACI 318 regulations inexperiment. We have used the nonlinear �ber-element code in OpenSees environment forthe modeling and analysis of models. The existing proposed stress-strain curve is modi�edto ensure the validity of assessment. Calibration procedure has led to conclusion thatthe post-yield slope needs to be modi�ed in HSC model as the average value of ACI 363reference. We have developed twelve extra models to estimate the interaction of concretestrength, rebar ratio, and axial force e�ect on the seismic performance. Parametric studyof calibrated models reveals that the seismic energy dissipation in HSC members is thefunction of the provided longitudinal reinforcement ratio and lateral con�ning stirrupamount.© 2018 Sharif University of Technology. All rights reserved.

1. Introduction

Primarily, it is essential to have a short de�nition ofHSC according to valid regulations. ACI Committee363 [1] de�nes HSC as a concrete material with crush-ing strength (f 0c) higher than 41 MPa. HSC is usedin high-rise and special structures such as dams andhydropower substructures. Various research works areconducted in the �eld of HSC and its feasible potentialuse in civil structural systems. Sugano et al. [2]

*. Corresponding author. Tel.: +98 44 3372 8180E-mail address: [email protected] (E. Shafei)

doi: 10.24200/sci.2017.4183

conducted an e�ective research on the experimentalseismic behavior of HSC columns, which are laterallyreinforced with high strength steel bars. They revealedthat the use of high or ultra-high strength steel bars isquite e�ective in con�ning HSC with strength increaseup to 80 MPa. Therefore, they suggested the use ofhigh or ultrahigh strength lateral reinforcements forthe HSC columns subjected to axial compression. Xiaoand Martirossyan [3] conducted a broad research on theseismic performance evaluation of HSC columns witha focus on shear strengths. Results revealed that theACI 426 [4] relation overestimated the shear strengthof the HSC columns with a shear failure mode, but theACI 318 [5] relation estimated the shear strength with10% deviation.

580 F. Vahid-Vahdattalab et al./Scientia Iranica, Transactions A: Civil Engineering 25 (2018) 579{589

Ashour [6] conducted a research on the e�ect ofcompressive strength and tensile reinforcement ratioon exural behavior of HSC beams. The study re-vealed that for the same longitudinal reinforcement,the cracking moment increases as concrete compressivestrength increases. In addition, the increase in concretecompressive strength leads to an increase in the exuralrigidity of reinforced concrete beam. Bing et al. [7]conducted a research on the stress-strain curve of HSCcon�ned by ultrahigh and normal-strength transversereinforcements. The study revealed that the compres-sive strength of concrete determines the column duc-tility, particularly for strengths higher than 60 MPa.Regardless of the concrete compressive strength, a risein the con�nement ratio results in peak stress growth.In addition, results revealed that the enhancement inthe ultimate strain of lateral con�ning system resultsin a decrease in the slope of softening branch of stress-strain curve. Kabir and Shafei [8] conducted studies onthe lateral con�ning of HSC by FRP jackets subjectedto eccentric axial loading in advance. The acquiredresults revealed that FRP con�nement is also e�ectivein strength and ductility enhancements of high strengthcolumns. However, strengthening is much e�ectivein Normal Strength Concrete (NSC) than HSC, sinceconcrete does not exhibit adequate volumetric dilationto activate the FRP con�nement.

Woods et al. [9] conducted a research on thebending ductility of the rectangular HSC columns. Thestudy revealed that there is an interaction between theductility and transverse reinforcement spacing. Theynoted that for a given tie spacing, there is a rangeof transverse reinforcement ratio, which enhances thecolumn ductility. Ho et al. [10] conducted a researchon the a�ectivity of adding an additional con�ningsystem on the ductility improvement of HSC columns.The study presented that the stress-strain path ofthe concrete in con�ned columns is sensitive to theprovided con�ning system. In addition, the designparameters of the con�ned concrete are determinedby con�nement characteristics, which are necessaryfor initial proportioning of HSC members. Resultsrevealed that both of the balanced reinforcement ra-tio and ultimate axial force capacity increase whenthe con�ning pressure is increased, �nally improvingthe exural ductility of the con�ned column. Huiand Zhao [11] conducted a study on the empiricalstress-strain models of uncon�ned HSC under uniaxialcompression. Results con�rmed that the proposedempirical model could cover the existing experimentaldata for normal weight HSC materials e�ciently andrepresent the mean stress-strain curve.

Ozbakkaloglu [12] conducted a research on the be-havior of square and rectangular Ultra-High StrengthConcrete-Filled FRP Tube (UHSCFFT) columns un-der axial compression. It was revealed that su�ciently

con�ned square and rectangular columns could exhibita compressive behavior with high ductility. However,the behavior of members is highly sensitive to thecon�ning tube thickness. In other words, the tubeswith thin walls do not provide su�cient con�ningpressure in order to allow columns to maintain theirload-carrying capacity beyond the peak load. Inaddition, the crushing strength of HSC materialswith high strengths is more sensitive to the con�ningpressure than low strength ones. Kottb et al. [13]conducted a study on the behavior of HSC columnsunder eccentric axial loads. The study revealed thatusing normal longitudinal steel bar diameter in HSCcolumns is not adequate and leads to a catastrophiccollapse. They conducted analytical studies usingexisting semi-empirical material models of HSC withthe total assessment error of 17%, which con�rms theresults of the additional studies on the calibration ofmathematical models for HSC material behavior.

2. Research signi�cance

The main criteria in the seismic application feasibilityof HSC construction are stability and ductility levelsduring quake excitations. On the other hand, thedesign regulations obligate the designer to provide auni�ed material response curve for calculations andrequirement controls. Thus, there is an essential needto provide the preliminary material constitutive curvefor seismic excitation, besides the static loads. HSCcolumns are the primary members that resist quake-imposed energy during seismic action in moment-framesystems; therefore, they need to be designed in thedimension and material to do so. There is a serious lackin determination of initial design dimensions becausethere is no uni�ed regulation concerning the HSCmaterials. Seismic performance evaluation of suchmembers depends directly on calibrated de�nition ofstress-strain curve concerning the cyclic load protocols.

The HSC column ductility and its interaction withdemand seismic performance has not been speci�ed inrecent research works; therefore, the goal of the currentstudy is to evaluate the existing material models andmodify them, if required, in order to satisfy the designprerequisite performance levels. Primary target ofstudy is to assess the HSC compressive strength e�ecton the hysteretic load-de ection response and the dis-sipated energy under de�ned displacement protocols.Four square RC columns with HSC material, tested byXiao and Yun [14], are the basis of numerical simulationand should be calibrated according to the presentedexperimental data. The extended study on the presentresearch work is to evaluate the accuracy and validityof the existing stress-strain curves for HSC, whichalso considers the successive cracking and crushing ofconcrete.

F. Vahid-Vahdattalab et al./Scientia Iranica, Transactions A: Civil Engineering 25 (2018) 579{589 581

3. Response characterization

3.1. Experimental backgroundColumns accepted as the pilot experimental databaseare in full-scale size and have square of 510 mm cross-section with total height of 2032 mm; as tested byXiao and Yun, lateral loading point is elevated at1778 mm height at top of the footing. All columnsare reinforced with four no. 36 bars (d = 35:8 mm)plus four no. 29 bars (d = 28:7 mm), providing a exural reinforcement ratio of 2.6% [14]. The maintesting parameters selected as a parametric study werethe transverse reinforcement and axial load ratios. Theadditional y ash, silica fume, super-plasticizer, andlow water-to-cement ratio provide the design com-pressive strength from 34.5 MPa up to 64.1 MPa forHSC. Grade 420 steel rebar (fy = 469 MPa) is usedas longitudinal reinforcement for all members besidesboth grade 420 and 520 stirrups (fy = 524 MPa) astransverse reinforcement of each three-column group.The con�guration of HSC-RC columns tested by Xiaoand Yun is demonstrated in Figure 1. The details oftest members are reported by the studies in Table 1.

The base of all columns was anchored to a rigidbase using post-tensioning system, which is assumed asfull restraint in a numerical model. In an experimentalprocedure, due to restriction of axial load application,the value of vertical gravity load changes as columnis laterally displaced. However, this phenomenon

Figure 1. Detail of column specimens tested by Xiao andYun [14].

Figure 2. Lever arm system for axial loading andsecond-order e�ect detail in test [14].

is modeled exactly as occurring in real nature ofstructural columns, since vertical load does not haveany direction change in small drifts (lower than 6%).Therefore, the second-order e�ect of axial load (P ��)is expressed in an acceptable way in the simulation ofthe current study than as applied to the experiments.The experiment uses external apparatus to apply thecombined axial and vertical loading where the directionchange of vertical load has not been neglected inthe test. This case lowers the e�ect of the second-order load e�ect in the test. However, we keep thedirection of vertical load as constant and perpendicularto the foundation during the whole analysis, which isrealistic in structural problems. This case is shown inFigure 2. The axial load is constant over the periodof testing, although the lateral displacement has cyclicregime with increasing amplitudes. The time history ofapplied lateral relative displacement (�=L), i.e. drift,according to Figure 3, consists of six successive cycleswith a 0.5% drift increase, which is at �rst followed by1% of three drift cycles up to member rupture.

3.2. Material mathematical modelThe basic stress-strain constitutive curve assumed forHSC is the model proposed by Bing et al. [7], whichconsists of three continuous relations as follows. Theassumed model is based on classic uniaxial curve of

Table 1. Details of HSC column members tested by Xiao and Yun [13].

Specimens Longitudinalsteel

Transversesteel

Concrete strength(MPa)

Axial load(kN)

FHC-1

4�29 & 4�36

�16@100 64.1 3334FHC-2 �16@100 62.1 5373FHC-3 �16@100 62.1 3630FHC-4 �16@100 62.1 5240


Figure 3. Time history curve of lateral drift applied tocolumns [14].

Mander et al. [15] for concrete compression. Model hasa quasi-linear pattern up to uncon�ned strength limit(f 0co) as in Eq. (1) which is 64.1 and 62.1 MPa for HSCcolumns tested by Xiao and Yun. High-strength na-ture of concrete leads to insensible transition betweenuncon�ned crushing strain ("co) and stirrup-con�nedcrushing strain ("cc) as expressed in Eq. (2). Finally,the strength-degrading branch of the curve is de�nedas in Eq. (3) with a linear descending up to 0:4 f 0ccstrength:

0 � "c � "co ! fc = Ec"c +(f 0co � Ec"co)

"co2 "c2; (1)

"co � "c � "cc ! fc=f 0cc� (f 0cc�f 0co)("cc�"co)2 � ("c�"cc)2;

(2)

"c>"cc ! fc=f 0cc�� f0cc"cc� ("c�"cc) � 0:4f 0cc; (3)

f 0cc=f 0co

"�0:413+1:413

s1+11:4

f 0lf 0co�2

f 0lf 0co

#: (4)

Con�ned concrete strength (f 0cc) depends on the

ratio of con�ning pressure (f 0l ) to uncon�ned crushingstrength (f 0co) as in Eq. (4). The parameters neededfor the above equations are elastic modules (Ec) asin Eq. (5) proposed by ACI committee 363 [1] andsoftening slope (�). One of the necessary stages incurve de�nition is an appropriate selection of � value.The relations proposing practical values for � are basedon Eqs. (6)-(8) sets:

Ec = 3320pf 0c + 6900; (5)

fyh � 550 MPaf 0co > 75 MPa

�! � = (0:048f 0co � 2:14)

� (0:098f 0co � 4:57)�f 0lf 0co

�1=3

(6)

fyh > 1200 MPaf 0co � 80 MPa

�! � = 0:07; (7)

fyh > 1200 MPaf 0co > 80 MPa

�! � = 0:1: (8)

Xiao and Yun reported on the basic experimentaldata and the initial calculated input values for HSCconcrete as shown in Table 2. These values are usedas preliminary data for the evaluation of model andneed further modi�cations. Based on the calculations,the input parameters for numerical model are alsoevaluated and reported in the same table.

3.3. Method and simulation procedureThe mathematical expression of governing responseexpressed in the previous section is de�ned usingOpenSees environment [16]. The nonlinear materialresponse is integrated into internal integration pointof elements, and then is assembled in nodal regionsconsidering geometrical nonlinearities. The member

Table 2. HSC stress-strain curve parameters and input values for numerical model.

Parameter Notation Values Unit

Elastic modulus Ec 33.481 33.063 GPaPoisson's ratio � 0.2 {Uncon�ned crushing strain "co 0.3 %Con�ned crushing strain "cc 0.8 0.8 %Uncon�ned crushing stress f 0co 64.1 62.1 MPaCon�ned crushing stress f 0cc 84.81 82.70 MPaDescending branch slope control � 0.16 0.15 {Lateral con�ning pressure f 0l 4.19 4.19 MPaOpenSees { Crushing stress fpc 84.81 82.70 MPaOpenSees { Crushing strain epsc0 0.8 0.8 %OpenSees { Failure stress fpcu 33.92 33.08 %OpenSees { Failure strain epsu 3.8 4 %


Figure 4. Calibration e�ect on compatibility of curves.

is modeled using three forced-based beam columnelements that have conjugate nodes in lateral displace-ment applied level and stirrup spacing change location.Characteristic of rebar and stirrup reinforcements isexpressed in STEEL02 uniaxial material code proposedby Menegotto [17] with a limitation on the ultimaterupture strain (material failure) implied by MINMAXoption. The elastic modules, initial yield strength,and post-yield hardening ratio are 200 GPa, 473 MPa,and 0.5%, respectively, as reported in the originalexperimental data. However, the transition from theelastic to plastic branches is calibrated using 40, 0.925,and 0.15 for R0, R1, and R2 coe�cients, respectively.It should be noted that higher R0 values would lead tothe smoother transition in yielding threshold.

The physical model used for HSC material isassumed as CONCRETE01 proposed by Kent-Scottet al. [18], which is calibrated using compressive testdata. However, calculated values are the preliminarydata for analysis because HSC has lower ductility thanNSC, which leads to calibration of degrading slopein detail. Due to the lack of material test data inXiao and Yun research, the load-de ection curve ofcolumn is used for calibration of additional materialparameters. The elastic modulus (Ec), uncon�ned("co) and con�ned ("cc) crushing strains, con�ned axialstrength (f 0cc), descending branch slope control (�), andlateral con�ning pressure (f 0l ) are calculated based onthe subsequent load-de ection curve shown in Figure 4.This �gure shows the details of consecutive iterationsmade for primary calibration.

Geometric nonlinear response of column is to bemodeled exactly as applied to the experiment. For thispurpose, the second-order axial force (P-�) e�ect isconsidered by means of axial load equal to 0.2 and0.33 of nominal axial strength for FHC-1 and FHC-2 columns, respectively. Axial load is applied at thetop elevation of column in the numerical model andits time history is de�ned as constant over analysisdomain. Integration of internal forces for columnsection is conducted by a section �ber approach. The

current method discretizes the section into �nite areaswhere strain is calculated according to the de�ned uni-axial curve data and strain distribution along sectiondomain. The patches for reinforcement and concretevolume are de�ned separately according to dimensionalproperties of test members. Generated element ofHSC members is a nonlinear beam column with �veintegration points. Two types of data recorders fordisplacement in loading point (top) and base reaction(bottom) are generated. The load pattern of the lateraldisplacement is linear with respect to time and has acyclic regime. Loop calculation is de�ned for lateralload cycles, having displacement control theory forintegrator module and being repeated three times foreach drift ratio.

3.4. Simulation results and modi�cation ofmodel

Based on the primary numerical results, cyclic responseof FHC-1 and FHC-2 members is calculated, as shownin Figures 5 and 6. In order to compare the accuracyand validity of the developed models, the experimentaldata acquired by Xiao and Yun are plotted alongwith the results. Regarding the �gures, the post-peaksoftening of HSC members depends on post-yieldingslope of concrete material de�ned by � parameter.Due to the lack of material test data in the selectedexperimental pilot, member's response is analyzed withonly a change in � factor value, and stress-straincurve for each assumed value is generated. FHC-1curve has a con�rming estimation of peak resisted baseshear (Vf ) equal to 683.60 kN and 2.7% lateral drift;these parameters for FHC-2 are 748.00 kN and 2%,respectively. The current phenomenon shows that thestress-strain curve acquired by Eqs. (1) and (2) givesidentical results of HSC material. However, softeningcurve de�ned by Eq. (3) governs the backbone curveof members. Therefore, the ductility factor calculatedfor each assumed � factor needs to be analyzed andcompared to the existing experiment value.

The current study on � value shows that the


Figure 5. Hysteresis load-displacement curves of FHC-1 column with various � factors.

Figure 6. Hysteresis load-displacement curves of FHC-2 column with various � factors.

proposed relations as in Eqs. (6)-(8) do not cover allthe ranges of f 0c and fy. Bing et al. [7] also mentionedthis case in a study as the necessary investigation for� factor determination of HSC. The selected valuesfor � factor cover the range between minimum (0.07)

and maximum (0.25) for FHC-1, and the load curvefor each case is extracted using a numerical method.Furthermore, while minimum value for � is constantin FHC-2, maximum range changes to 0.22. Resultsshow a non-uniform variation of post-peak softening


Figure 7. Envelope load-displacement curves for allcolumns with various � factors.

with respect to � increase. Successive calculationsproposed � factor equal to 0.16 and 0.15 for FHC-1 and FHC-2, respectively. Within this assumption,acceptable accuracy is achieved which provides 7.3%ultimate drift and 470 kN force level, as reportedexactly in the experiment. According to various �values, stress-strain curves used in this research areshown in Figure 7. As the results show, within theincrement in � value, the concrete post-yield slopeincreases and this phenomenon controls the ductilityof HSC. This observation is reported in Table 3. Thestudy of the e�ect of � value on peak stress proved thatit does not have sensible impact on the peak stress.However, the deformation ductility has close relationwith the assumed � value.

Table 3. E�ect of � value on ultimate ductility.

Specimens Procedure � �u=�y

FHC-1 Numerical 0.16 2.67Experimental | 2.44

FHC-2 Numerical 0.16 2.0Experimental | 2.1

4. Parametric study

4.1. Axial force e�ectOne of the important parameters in the assessment ofenergy dissipation is the axial force ratio. In orderto estimate the energy-dissipation capacity of columnsand their hysteretic behavior, variable axial force valuesare applied with respect to section nominal strength(Pn) that is estimated as 13950 kN in the researchof Xiao and Yun. The relative value of these loadsbegins from 10% up to 50% of the section strengthwith 0:1Pn rise step. For the accurate and betterevaluation of the column behavior, authors applied acollapse criterion based on the strength decay as 20%of ultimate shear force (0:2Vn). The extracted datacurves are demonstrated in Figure 8 with respect to theaxial force increase. In the �rst step, the peak resistedbase shear is 563 kN for 2% lateral drift in the columnwith 0:1Pn axial force, and the column is also stablefor further lateral drift values. The ultimate dissipatedenergy for this case is 1418 kN.m without any strengthloss up to 8% drift.

Figure 8. Axial load e�ect on hysteretic behavior of HSC columns (� = 0:16).


A further increase in axial load up to 0:2Pnleads to 658 kN shear capacity of column at 2.4%lateral drift. Here, the axial load increases the load-carrying capacity and ductility of HSC column by thesimultaneous concrete crushing and rebar yielding. Inthis case, column starts to dissipate 1394 kN.m energylevel with a slight strength decrease due to the second-order axial force e�ect. In advance, a further increasein axial force value up to 0:3Pn results in the apparentdecrease in energy dissipation of member to 840 kN.mand the ultimate drift to 6%, although the shearstrength is increased up to 720 kN. Additional increaseof the axial force to 0:4Pn and 0:5Pn just leads to theshear capacity of 760 kN and 790 kN, respectively,along with a dissipated energy decrease to 480 kN.mand 470 kN.m, respectively. It is observed that axialload increase a�ects the energy dissipation capabilityof HSC members in a major manner; therefore, suchmembers are sensitive to the second-order e�ect. Thedrop ratios of absorbed energy value are 0:3Pn, 0:4Pn,and 0:5Pn; consequently, axial force ratios are 40%,60%, and 70% with respect to 0:1Pn case. In order toanalyze the sensitivity of HSC columns to rebar ratioand axial force value, further numerical models aregenerated and compared to the analogous case withNSC columns along with 30 MPa concrete crushingstrength in advance.

4.2. Rebar ratio and crushing strength e�ectsIn order to have a better understanding of the e�ect of

concrete strength on the hysteresis behavior, additionaldata with normal strength concrete is provided. NSCmodels obey the proposed model of Mander et al. [15]for stress-strain curve as expressed in Eq. (9):

f 0cc = f 0co

"�1:254 + 2:254

s1 + 7:94

f 0lf 0co� 2

f 0lf 0co

#:(9)

The longitudinal reinforcement ratio (�) is also consid-ered as 1.3%, 2.6%, and 3.9% values in order to considerthe interaction of concrete and steel strengths in thecalculation of the shear capacity and feasible energydissipation. In addition, the axial force ratio is consid-ered as 0:24Pn and 0:38Pn values in the dimensionlessform, not the same as the considered values in theprevious section, to investigate the ductility sensitivityof HSC and NSC columns.

The extracted data for the assumed parametersare plotted in Figure 9 for the shear strength historyof HSC and NSC columns versus lateral cyclic drifts.Data are reported in Table 4 considering various con-crete strengths, rebar ratios, and axial force ratio. ForNSC and HSC columns with 0:24Pn axial force ratio(1600 kN and 3300 kN, respectively), it was detectedthat the NSC column with the same rebar ratio asHSC member has a better energy-dissipation thanthe HSC column. In addition, the pinching of HSCcolumn's hysteresis curve is increased which approvesthe lower energy dissipation of the member. Rebar

Figure 9. Shear force versus lateral drift curves as function of concrete strength, axial load level, and rebar ratio.


Table 4. Calculated response parameters of NSC and HSC column members.

Specimens Axial force ratio Rebar ratio Shear capacity Peak drift Dissipated energy(%) (kN) (%) (kN.m)

HSC-1 0.24 1.3 458.4 2.4 365.2HSC-2 0.24 2.6 635.4 2.7 711.9HSC-3 0.24 3.9 811.5 3.0 1736.4HSC-4 0.38 1.3 542.0 1.8 202.6HSC-5 0.38 2.6 691.0 2.0 391.8HSC-6 0.38 3.9 843.1 2.4 1045.0NSC-1 0.24 1.3 321.2 2.4 600.2NSC-2 0.24 2.6 501.1 3.0 1164.2NSC-3 0.24 3.9 677.4 3.2 1704.6NSC-4 0.38 1.3 357.7 2.7 355.33NSC-5 0.38 2.6 520.6 3.0 1136.6NSC-6 0.38 3.9 679.3 3.6 1669.2

Figure 10. Shear strength of HSC and NSC columnswith respect to axial load and rebar ratios.

ratios are 1.3%, 2.6%, and 3.9%. Considering the e�ectof rebar ratio in the study, it was seen that rebar ratiois one of the signi�cant parameters in HSCs. Thisresult explains that we need to increase the maximumrebar ratio (�max) of HSC members with respect tothe limit which is de�ned for the normal strengthelements. Since the high-strength concrete has morebrittle response than the normal strength concrete,we need further rebar ratio to provide the demandductility in high strength concrete elements. Hence, incontrast to the idea that the maximum rebar ratio isalmost constant to the column elements, the designersof high strength members should extend the rebar ratioin order to provide the required energy dissipationduring the earthquake excitation. Rebar ratio e�ectis shown in Figure 9 regarding hysteresis response andin Figure 10 regarding the ultimate resisted shear force.

Ultimate shear strength (Vn), peak lateral drift(�), and total dissipated seismic energy (UI) areplotted in Figures 10-12, respectively, versus concrete

Figure 11. Peak lateral drift of HSC and NSC columnswith respect to axial load and rebar ratios.

grade (NSC and HSC), axial force ratio (P=Pn), andthe rebar ratio (�). As shown in Figure 9, the shearstrength of column is increased when we change theconcrete grade from NSC to HSC. In the next stage,within the raise of the axial force ratio, it was seen thatthe shear strength of column is increased. However, thee�ect of axial force ratio is more intuitive for the lowrebar ratios, meaning that within the increase in theaxial force ratio of the low rebar amount, columns havebetter seismic performance and energy dissipation. Inthe �nal stage, the shear strength of column is increasedwhen we increase the rebar ratio. However, the HSCcolumns are more sensitive to the rebar ratio parameterthan NSC ones. In other words, HSC columns needhigher reinforcement ratio than NSC ones in order toprovide the required strength and energy dissipationdemand.

We have plotted the variation of the peak lateraldrift versus the aforementioned factors in Figure 11.


Figure 12. Absorbed seismic energy of HSC and NSCcolumns with respect to axial load and rebar ratios.

In the �rst stage, it was seen that for a constant rebarratio, the NSC column has better performance thanHSC one. In addition, it was seen that the peaklateral drift in the HSC columns is decreasing when weincrease the axial force ratio. However, this observationis in the reverse order for NSC columns. Finally, theincrease in the rebar ratio results in the increase ofthe peak lateral drift in both of the concrete types.We have the maximum resisted lateral drift for 3.9%rebar ratio. We investigated the dissipated energylevel versus the aforementioned parameters in Figure 12for conclusion improvement in advance. Primarily, itwas seen that the energy absorption is decreasing forconcrete strength increase. However, this observation isnot true for 3.9% rebar ratio. It means that we need toprovide higher reinforcement ratio for HSC columns todissipate higher energy than NSC ones. The absorbedenergy decreases, while the axial force level increases;this is more apparent in HSC columns than the NSCones. Analogous to the conclusion made for the peaklateral drift parameter, the absorbed energy increaseswhen we provide high rebar ratio. Overall conclusion isthe requirement of higher rebar ratio for HSC column inorder to provide better energy dissipation and ductilitywith respect to NSC columns.

5. Conclusions

The current research work deals with the seismiccharacteristics of the high strength concrete columnsubjected to lateral displacement cycles. We haveprovided the numerical models for initial validationof the existing experimental results, and then revisedthe governing stress-strain curve in order to improvethe validity and accuracy of the developed nonlinearmodels. Results recommend that softening slope of thehigh strength concrete materials should be modi�ed inorder to approve the experimentally recorded ductility

and energy dissipation. In addition, we extended themodels for normal strength and high strength concretecolumns with variable axial force and reinforcementratios in order to investigate the response sensitivity.The general conclusions made from the current researchwork can be mentioned as in the following topics:

1. The increase in the concrete grade and axial forceratio results in shear strength enhancement of col-umn. However, the peak lateral drift and dissipatedseismic energy decrease. Therefore, it is requiredto provide higher reinforcement ratio than code-de�ned value in HSC to con�rm the responseperquisite;

2. The increase of rebar ratio results in the improve-ment of ultimate shear strength, peak lateral drift,ductility and absorbed energy in HSC columns;

3. HSC columns can be an appropriate choice forspecial structures only if the lateral drift andabsorbed energy are controlled by the existing coderegulations;

4. Assuming analogous rebar ratio for HSC and NSCcolumns, NSC members can be more e�cient thanHSC in high-risk seismic zones;

5. The current study proposes a new modi�ed concretestress-strain curve, considering linear interpolationbetween � factors presented in the previous researchworks for intermediate-strength HSC materials.

Nomenclature

d Rebar diameterfy Yield stress

f 0co; f 0c Uncon�ned Concrete compressivestrength

P Axial force"co Uncon�ned concrete strain"cc Con�ned concrete strainEc Concrete modules of elasticity� Descending sloop controlf 0l Lateral con�ning pressuref 0cc Con�ned concrete compressive strengthVf Peak resisted base shearPn Section nominal strength�max Maximum rebar ratioVn Ultimate shear strength� Longitudinal reinforcement ratio� Poisson ratio� Peak lateral driftL Elevation between lateral force point

and foundation surface


R0; R1; R2 Transition from elastic to plasticbranch coe�cient

UI Dissipated seismic energy

References

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2. Sugano, S., Nagashima, T., Kimura, H. and Tamura,H. \Experimental studies on seismic behavior of highstrength concrete columns laterally reinforced withhigh strength steel bars", Proceedings of the 9thWCEE, Tokyo, Kyoto (1988).

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Biographies

Farzin Vahid-Vahdattalab received his MSc degreein Structural Engineering from the Urmia Universityof Technology, Urmia, Iran, in 2015. Presently, heis working on the high strength reinforced concretecolumns under supervision of Dr. Erfan Shafei and Dr.Javad Mokari Rahmdel with focus on the nonlineardynamic characteristics.

Javad Mokari Rahmdel received his PhD degreein Earthquake Engineering from the International In-stitute of Earthquake Engineering and Seismology,Tehran, Iran, in 2009. Since then, he has beenwith Urmia University of Technology as an AssistantProfessor in Civil Engineering Department, where heis currently the Administrative and Support specialist.

Erfan Shafei received his PhD degree in StructuralEngineering from the Amirkabir University of Tech-nology (Tehran Polytechnic), Tehran, Iran, in 2013.Since then, he has been with the Urmia University ofTechnology as an Assistant Professor in Civil Engineer-ing Department, where he is currently the Director ofCivil Engineering Department. His research interestis on the nonlinear response assessment of semi-brittlematerials.

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