Journal of Constructional Steel Research 77 (2012) 145–162

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Journal of Constructional Steel Research

Parameter study on composite frames consisting of steel beams and reinforcedconcrete columns

Wei Li a,⁎, Qing-ning Li b, Wei-shan Jiang b

a College of Architecture and Civil Engineering, Wenzhou University, Wenzhou 325035, PR Chinab School of Civil Engineering, Xi'an University of Architecture and Technology, Xi'an 710055, PR China

⁎ Corresponding author at: College of Architecture anUniversity, Chashan University Town, Wenzhou City, ZChina. Tel.: +86 57786689609.

E-mail address: lqn952@163.com (Q. Li).

0143-974X/$ – see front matter. Crown Copyright © 20doi:10.1016/j.jcsr.2012.04.007

a b s t r a c t

a r t i c l e i n f o

Article history:Received 20 August 2011Accepted 23 April 2012Available online 18 June 2012

Keywords:Composite frameHysteretic modelABAQUSFinite element analysisConfined concreteHigh-strength ties

A host of tests and numerical analyses for frames consisting of reinforced concrete columns and steel beams(RCS) have been conducted in the US and Japan over the past decades. Most results have revealed the superiorperformance of these structures relative to that of traditional concrete and steel frames. However, few studiescould be found about composite frame structures consisting of high-strength concrete columns confined bycontinuous compound spiral ties and steel beams (CCSTRCS), which requires the development of an accuratefinite element model of composite CCSTRCS frames. The validity of the proposed model is examined by com-paring with the test data presented in reference studies. With the proposed model, an extensive parametricstudy is carried out to investigate the behavior of composite CCSTRCS frames. Simplified hysteretic lateralload versus lateral displacement models are proposed for such composite frames.

Crown Copyright © 2012 Published by Elsevier Ltd. All rights reserved.

1. Introduction

It has been widely recognized that composite moment framesconsisting of RC columns and steel (S) beams, or the so-called RCSsystem, can provide cost-effective alternative to traditional steel orRC construction in seismic regions. As opposed to conventional steelor RC moment frames, the problems associated with connections aregreatly reduced, and the RCS frames are generally more economicalthan the purely steel or RC moment frames. The research programincluded extensive testing and finite element analyses of RCS beam-to-column connections and subassemblies, testing of reduced-scaleand full-scale RCSmoment frames and finite element analyses, seismicdesign studies and analyses of RCS moment frames and developmentof guidelines and recommendations for detailed design work [1].

Despite its potential benefits in construction speed and structuralexcellent ductility due to the use of CCSTRC column, research wasrarely conducted on compositemoment frames consistingof continuouscompound spiral tie reinforced concrete (CCSTRC) columns and com-posite steel beams. The experimental research on the CCSTRC columnand CCSTRC-steel (S) composite connection has been conducted andthe CCSTRC and steel (CCSTRCS) composite frames have great advantagedue to the use of high‐strength concrete column confined with high‐strength continuous compound spiral ties, which improves the strength

d Civil Engineering, Wenzhouhejiang Province, 325035, PR

12 Published by Elsevier Ltd. All rig

and ductility of the column and reduces the section size of column,thereby increasing effective building space. As an “undefined structuralsystem”, the composite CCSTRCS system cannot be easily adopted indesign and construction practice. However, they have become recog-nized by more and more researchers and practicing professionals inrecent years that though structural systems do not fully satisfy theprescriptive requirements of current building codes, they can providesatisfactory seismic performance. The desirable seismic characteristicsshould be validated by analyses and laboratory tests. However, since itis difficult to conduct a lot of experiments from an economical view-point, and due to unique features of the tested specimens and materialheterogeneity, it is also difficult to understand the complex seismicbehavior of beam–column connections and framed structures. Further-more, the effect of several influencing parameters such as plate thick-ness, axial load and the effect of confining cannot be varied in a limitednumber of tests. In order to quantify and make clear the influence ofcritical design parameters, it is necessary to develop a robust numericalmodel. Following this understanding, a series of finite element analysisfor composite structures was conducted by many researchers.

Liu and Foster [2] developed a finite element model to investi-gate the response of concentrically loaded columns with concretestrength up to 100 Mpa. Yu et al. 2010 [3,4] presented a modifiedDrucker-Prager (D-P)-type model and a Plastic-damage model andthen implemented it in ABAQUS. Hajjar et al. [5] proposed a 3Dmodelingof interior beam-to-column composite connections with angles bymeans of the ABAQUS code [6]. Salvatore et al. [7] studied seismic perfor-mance of exterior and interior partial-strength composite beam-to-column joints by using ABAQUS software. Hu et al. [8] proposed propermaterial constitutive models for concrete-filled tube (CFT) columns

hts reserved.

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and theywere verified by the nonlinear finite element programABAQUSagainst experimental data. Zhao and Li [9] studied the nonlinear me-chanical behavior and failure process of a bonded steel–concrete com-posite beam by using finite element program ABAQUS, The eight-nodebrick elements (C3D8) were employed to model the concrete slab andsteel beam. An adhesive layer was modeled by the eight-node three-dimensional cohesive elements (COH3D8). Bursi et al. [10] studied theseismic performance of moment-resisting frames consisting of steel–concrete composite beams with full and partial shear connection byusing the ABAQUS program. Han et al. [11] presented a finite elementmodeling of composite framewith concrete-filled square hollow section(SHS) columns to steel beam, the finite element program ABAQUS wasadopted. Wu et al. [12] studied the effect of wing plates numerically bysimulating H-beams in bolted beam–column connections as cantileverbeams using ABAQUS.

Set against this background, Li et al. [13] applied the finite elementprogram ABAQUS to simulate the behavior of composite CCSTRCSframes. The results show that continuous compound spiral high-strength ties can effectively improve the lateral deformation capacityof concrete, with a good constraint to the concrete in the core area,which increases the ultimate lateral bearing and deformation capacityof the composite CCSHRCS frame. However, the detailed influencefactors for composite CCSTRCS frames are not clear. Therefore, thispaper focuses on conducting an extensive parametric study on thebehaviors of composite CCSTRCS frames. Through parametric analysis,the simplified hysteretic lateral load versus lateral displacementmodels for such composite frames is proposed.

2. Finite element model

2.1. General descriptions

In order to accurately simulate the actual behavior of RCS framespecimen, themain six components of the frames need to bemodeled.They are the confined concrete columns, the interface and contactbetween the concrete in joint regions and the structural steel (e.g. facebearing plates, cover plates), the interface and contact between theshear connections of steel beam and concrete slab, the interaction ofreinforcement and concrete, the connection details betweenRC columnsand steel beam, and the steel beam. In addition to these parameters, thechoice of the element types, mesh sizes, boundary conditions and loadapplications that provide accurate and reasonable results are also impor-tant in simulating the behavior of structural frames.

Fig. 1. Uniaxial load cycle (tension–compression–tension) assuming d

2.2. Material modeling of concrete

In conventional concrete models, the behavior under compressivestresses is usually represented by the plasticity model, while thebehavior under tensile stresses is expressed by the smeared crackingmodel. The smeared cracking model, however, always encountersnumerical difficulties on analysis under cyclic load. To circumventthis situation, the concrete damaged plasticity model (Lee and Fenves1998) implemented in ABAQUS 2006 [6] is used herein.

By experimental observations on most of quasi-brittle materials,including concrete, when the load changes from the tension to com-pression, compression stiffness recovers with the closure of crack. Inaddition, when the load changes from compression to tension, oncethe crushed micro-cracks occur, and the stiffness in tension will notbe restored. This performance corresponds to the default valuewt=0 and wc=1 in ABAQUS. Fig. 1 describes the default propertiesunder uniaxial cyclic loading.

2.3. Material modeling of reinforcement and structural steel

In this paper, in order to simplify the problem in the analysis offinite element method, assuming that the ties and longitudinal rein-forcement in concrete columns are ideal elasto-plastic materials,regardless of the reinforcement service stage and Bauschinger effectin their stress–strain relations. The stress–strain curve is slopedbefore the steel yields, and it should be simplified to horizontal lineafter that, as shown in Fig. 2. The VonMises yield criterionwith isotropichardening model is adopted for structural steel.

2.4. Interactive modeling between concrete and reinforcement, concreteand structural steel

Since joints of steel beam and concrete column connect togetherby welding face bearing plate at the steel beam flange in the framestructure, beam–column and face bearing plate have a good confinedwith joint regions to make joint regions little slip. The details of theconnection of steel beam and reinforced concrete column are shownin Fig. 3a. It is shown that concrete and steel in the joint regions canstill work together until the destruction of the beam–column joint.Salvatore et al. [7] studied the seismic performance of exterior andinterior partial-strength composite beam-to-column joints by usingABAQUS software, a hardening elasto-plastic material is modeledusing discrete two-nodded beam elements, dimensionless bond-link

efault values for the stiffness recovery factors: wt=0and wc=1.

Fig. 2. Stress–strain relationship of reinforcement.

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elements are adopted to connect concrete and steel, friction betweenthe steel bars and the concrete slab is not modeled because it has littleinfluence on substructure responses. On the other hand, the jointadding bonding element, the analysis would become too complicated,so the bond-slip of the joint regions is not considered. In this paper,taking “Interaction” module “Constraint” command in ABAQUS asEmbedded region/embedded in the reinforced concrete columns. Inthis condition, there is no relative slip between the steel and concrete.

FBP

(a) The connection details

(b) Load modeling of a composite RCS frame

Fig. 3. The connection details and load modeling of a composite RCS frame.

Steel beam and concrete, face bearing plate and concrete in jointregions are directly constrained by the module “Tie” command inthe “Interaction” to make binding constraint, so there is no relativeslip between them.

2.5. Bounding conditions and loading

The boundary conditions and loading manners of RCS frame struc-tures are specific in this paper: concrete column foot is fixed constraint,axial load is imposed by the loading plate on top of the column, andlateral load is imposed on the beam. In the ABAQUS software, theboundary conditions are set as follows: three concrete columns withfixed boundary constraints, the steel beam and face bearing platesused the “Merge” command of the “Assembly” module to merge. Inthis case, steel beams and face bearing plate can be regarded as fixedconstraints. The loading plate and the interface of column cap are con-strained by the “Interaction” module “Tie” command. As shown inFig. 3b.

The loading of the frame divides into two categories: the axial loadat the top of the framed column and the lateral load at the end offramed beam. The two load steps are required in the ABAQUS code.The specific methods are as follows: at the top of the three framedcolumns respectively applied to the axial load. Firstly applied to interiorcolumn, and then to two other exterior columns, set it as a load step.When axial loading is completed, the lateral load should be loaded atboth ends of the framed beam, and displacement loading adopted inorder to obtain the load–displacement curves of frame, that is, displace-ment applied at the end of the beam (applied displacement boundaryconditions that known). In order to avoid stress concentration, the“Load” module “Pressure” of ABAQUS is adopted for the axial load andthe analysis will not stop until the selected displacement is reached.Fig. 3b is the loading model diagram of composite RCS frame.

2.6. The selection of element type and meshing

In order to simulate the detailed characteristics of steel beams-concrete columns joint, steel beams and concrete adopted a three-dimensional solid element with reduced integration eight-nodeformulation (C3D8R). Compared with the high-order isoparametricelement, although the accuracy of this element is slightly lower, itcan reduce to a lot of freedom degree, which can greatly reduce thecomputational cost. In order to understand the force characteristicsof reinforcement, the ties and longitudinal reinforcement in concretecolumns used a two‐node linear three-dimensional truss element(T3D2).

Fig. 4 shows the cross-section mesh diagram of the finite elementmodel for the concrete columns, steel, steel beams—the whole facebearing plate and beam–column joint region in this paper. Due tothe complexity of the beam-column joint regions, these regions aresubdivided to ensure the accuracy of the computational results.

3. Validity of FEM modeling

In order to validate the finite element model that developed in thispaper, the numerical results were compared with the test results inthe literature [14]. The detail sizing and reinforcement are shown inFig. 5. Details of the specimens are seen in Table 1, the correspondingmaterial properties are shown in Table 2.

In accordancewith the specific parameters of specimensmentioned,the finite element model of the specimen is developed by ABAQUS, asshown in Fig. 6. The frame specimenmodel consists of 18,511 elements,17,566 C3D8R solid elements and 945 T3D2 truss element. Since thebeam–column joint region is under a larger force, in order to avoiddistortions in the joint area, firstly, complex geometric models of jointregions are cut into simple geometric models, further element jointsare subdivided by geographical mesh.

(c) Steelbeam and FBP (d) beam-column joint

(a) Concrete column (b) Longitudinal reinforcementand tie

Fig. 4. Meshing sketch of section.

148 W. Li et al. / Journal of Constructional Steel Research 77 (2012) 145–162

3.1. The load–displacement relation for composite RCS frame

The relationship of the load–displacement for the RCS framedspecimen is obtained from calculation, and it is shown in Fig. 7, atthe initial of load for frame, when lateral displacement is within20 mm, the structure has not yet reached the ultimate bearing capacity,load–displacement curve has a nearly linear relationship. When thelateral displacement is more than 20 mm, with the increase of thedisplacement for the load–displacement curve, the load slowlyincreases until yielding to the destruction of the structure. In this condi-tion, the horizontal ultimate load and displacement are respectively797 kN and 77.8 mm. In addition, when adjusted to the test procedures,the ANSYS software is used for analysis on load–displacement relation-ship for framed specimens, and the ANSYS model is shown in Fig. 8a;and the comparison with that calculated by ABAQUS is shown inFig. 8b. The load–displacement curve calculated by ANSYS in Fig. 8bdoes not descend obviously and the load is more than 700 kN whilethe displacement is 15 mm. However, the ultimate load and displace-ment are 1021 kN and 47.6 mm, they are visibly higher than the calcu-lated values by ABAQUS. The load–displacement curve calculated byANSYS and ABAQUS is compared with the experimental results, andthey are shown in Fig. 9. The calculated results by ABAQUS agree wellwith the experimental value, while the calculated values by ANSYSare obviously higher than the experimental value, because the crushingand the stiffness degradation of concrete under compression of concreteconstitutive model in the ANSYS program haven't been considered,resulting in the calculated values being higher than the actual value.Table 3 shows the comparisonbetween the relation of load–displacementand the value calculated by ABAQUS. From that, the calculated values arein good agreement with the experimental values, it is indicated that theABAQUS software could simulate the load–displacement relations ofthis composite frame. However, it should note the load–displacementcurve in themodel that is influenced not only by the constitutive relation

of concrete materials, but also by that of different materials. If the choiceof constitutive model of materials is inappropriate, it will result in largerdeviation for the calculated results, or it will lead to the serious distortionof the calculated results. Therefore, when using the numerical model, thesetting of each parameter should be grasped to make the model reflectthe actual situation, it is also necessary to master the computationalefficiency of the comprehensive computer.

4. Parametric analysis of composite CCSHRCS frame

4.1. Overview

The ABAQUS software has been used in the previous section toanalyze the performance of composite RCS frame, and the model isvalidated by the test results in the literature. A new finite elementmodel is developed using the same method in the previous section,and it is used to analyze the composite CCSTRCS frame structure, inorder to understand the influence of various parameters on the per-formance of composite CCSTRCS frame. The following parametersare analyzed: the ratio of longitudinal reinforcement of continuouscompound spiral ties concrete columns (ρs) and the strength of longitu-dinal reinforcement (fys), the volumetric ratio of ties (ρv) and thestrength of tie (fyv), compressive strength of concrete (fcu), the character-istic values of tie (λv), the yield strength of steel (fak), axial-load ratio (n),the linear stiffness ratio of the beam–column (K) and the slendernessof the column (λ). The calculation only changes one parameter whilekeeping other parameters unchanged.

4.2. Development of model for composite CCSTRCS frame

In order to investigate the behavior of composite CCSTRCS framestructure, the various parameters in composite CCSTRCS frame modelare changed. To take continuous compound spiral stirrups, a uniform

BeamColumn

Through beam type (TB) joint

Fig. 5. Specimens tested by Iizuka et al. 1997 [14].

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spacing with 50 mm was used to simplify the model. The model isshown in Fig. 10.

4.3. The ratio of longitudinal reinforcement (ρs)

The geometrical parameters are the same as that of the compositeRCS frame model in the previous section. The axial load for the exte-rior column is 242.1 kN, and the interior column is 484.2 kN. For thespecific parameters, see Table 4.

While keeping other parameters unchanged, just the ratio oflongitudinal reinforcement is different, Fig. 11 shows the lateral load–lateral displacement of composite CCSTRCS frame with different ratiosof longitudinal reinforcement. With the increase of the ratio of longitu-dinal reinforcement, the lateral stiffness of the frame at the elastic stageslightly increases. It can be seen that themaximum ratio of longitudinalreinforcement increases by 56% to that of theminimum longitudinal re-inforcement, but lateral stiffness at the yield stage doesn't improve.

Table 1Details and size of specimen.

Detailed parameters of the specimen

Column SectionLongitudinal reinforcementTieAxial load

Beam SectionBeam–column joints Tie

Lateral stiffness at post-yield stage slightly enhances. None of the curvesis descending, and lateral displacement is relatively large, it indicatesthat the frame has good ductility.

4.4. The strength of longitudinal reinforcement (fys)

To study the effect of the longitudinal reinforcement strength ofthe column on the behavior of the frame structures, the following lon-gitudinal reinforcement strengths were used: HRB335, HRB400, andHRB500. The diameter and uniform ratio of longitudinal reinforce-ment are taken as 12-D18 (3.39%). While keeping other parametersunchanged, just strength of longitudinal reinforcement is different;Fig. 12 shows the relationship of lateral load–lateral displacement ofcomposite CCSHRCS frame at different strength of longitudinal rein-forcement. With the increasing of the strength of longitudinal rein-forcement, the lateral stiffness of the frame at the elastic stagekeeps the same, lateral stiffness at the yield stage is almost the

b×h=300 mm×300 mm12-D19 (ρt=1.28%)4D-10@50 (ρw=1.9%)(Exterior column) 0.1BDσB=242100 N(interior column) 0.2BDσB=484200 N σB=26.9 N/mm2

BH-200×100×12×16 (mm)4D-6@50 (ρw=0.85%)

Table 2The properties of materials.

Specimen Compression strength(N/mm2)

Tensile strength(N/mm2)

Modulus of elasticity(104 N/mm2)

Column 26.9 1.91 2.21Foundation 29.4 2.62 2.19

Specimen Yield strength(N/mm2)

Tensile strength(N/mm2)

Modulus of elasticity(105 N/mm2)

Steel reinforcement D6 386 543.5 1.79D10 375.3 516.3 1.69D19 385.4 556 1.77

Steel plate 12 mm 312.4 463.9 1.9716 mm 299.8 425.4 1.95

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same, and the yield load remains unchanged. Lateral stiffness at post-yield stage increases slightly, it is indicated that ultimate load increaseswith the increasing of the strength of longitudinal reinforcement. Noneof the curves is descending, and lateral displacement is able to continueto increase, since the axial compression ratio of the columns is relativelysmall, and high-strength ties provide good constraints on the core con-crete, thus greatly increasing the large deformation of the framestructure.

4.5. The volume ratio of tie (ρv)

In order to study the influence of the volume ratio of tie of columnon the behaviors of the frame structures, high-strength ties withdiameters of 5 mm, 7 mm, 9 mm, respectively, were used. The yieldand tensile strength remain the same; longitudinal reinforcementwith HRB400 is adopted. While keeping other parameters unchanged,only the volume ratio of the tie is different. Fig. 13 shows the relation-ship of lateral load–lateral displacement of composite CCSHRCS frameat different volume ratios of tie. With the increase of the volume ratioof tie, the lateral stiffness of the frame at the elastic stage slightlyincreases, both the yield displacement and the yield load are increased,lateral stiffness at the yield stage increases, and lateral post-yield stiff-ness increases slightly. This indicates that the ultimate load increaseswith the increase of the volume ratio of tie. None of the curves isdescending, and lateral displacement is able to continue to increase.Since the axial compression ratio of the columns is relatively small,and high-strength ties provide good constraints on the core concrete,the large deformation of the frame structure thus greatly increases.

T3D2

C3D8R

Fig. 6. FEM model of framed specimen.

4.6. The strength of tie (fyv)

In order to study the influence of the volume ratio of tie of columnon the strength of tie of column on the behaviors of the frame struc-tures, tie as HRB335, HRB400, HRB500 respectively and prestressedconcrete steel barΦPC are used [16]. The diameter and uniform ratioof the longitudinal reinforcement are taken as 12-D18 (3.39%).While keeping other parameters unchanged, only the strength of thetie is different. Fig. 14 shows the relationship of lateral load–lateraldisplacement of composite CCSTRCS frame at different strengths oftie. With the increase of the strength of tie, the lateral stiffness of theframe at the elastic stage remains the same, the lateral stiffness atthe yield stage remains the same, and the lateral post-yield stiffnessalso almost remains the same. It indicates that ultimate load increaseswith the increase of the strength of tie. None of the curves is descending,and lateral displacement is able to continue to increase. Since the axialcompression ratio of the columns is relatively small and the space oftie is small, the result in the strength of tie has not been fully applied.In addition, high-strength ties provide good constraints on the core con-crete, thus greatly increasing large deformation of the frame structure.

4.7. The compressive strength of concrete (fcu)

In order to study the influence of the compressive strength of con-crete of column on the behaviors of the frame structures, concrete,C40, C60, C80 and C100 are used. The diameter and uniform ratioof longitudinal reinforcement are taken as 12-D18 (3.39%), and pres-tressed concrete steel bar ΦPC [15] is adopted.

While keeping other parameters unchanged, just not the samecompressive strength of concrete, Fig. 15 shows the relationship ofthe lateral load–lateral displacement of composite CCSTRCS frame atdifferent compressive strengths of concrete. With the increase ofthe compressive strength of concrete, the lateral stiffness of theframe at the elastic, yield, and post-yield stages increases slightly, itis indicated that yield and ultimate load increase with the increaseof the compressive strength of concrete. In a concrete strength fromC40 to C100, the elastic modulus also increases, but only little, so itonly has little effect on the lateral stiffness. None of the curves isdescending, and lateral displacement is able to continue to increase,it shows that a further increase of concrete strength has little effecton the bearing capacity of the frame structure, in the case that high-strength ties provide good constraints on the core concrete.

4.8. The characteristic values of tie (λv)

Reinforced concrete columns are the compression and bendingcomponent, the characteristic values of tie are vital to improve thedeformation properties of concrete. Previous sections have analyzedbehaviors of the composite CCSHRCS frame structures to be influencedon the volume ratio of tie, the strength of tie and the strength ofconcrete, the results show that the volume ratio of tie has an important

0 20 40 60 80

0

200

400

600

800

Displacement

Loa

d/kN

Displacement/mm

Load

Fig. 7. Relationship of load–displacement of framed specimen based on FEM.

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influence on lateral stiffness at yield and strengthening stages for thecomposite CCSTRCS frame structures, while the strength of tie and thestrength of concrete strength are less affected. To understand theperformance of these three combined effects of the frame, differentcharacteristic values of tie have been used to reflect the influence onbehaviors of composite CCSTRCS frame.

While keeping other parameters unchanged, Fig. 16 shows therelationship of lateral load–lateral displacement of composite CCSTRCSframe with different characteristic values of tie. With the increasing ofthe characteristic values of tie, the lateral stiffness of the frame at theelastic stage slightly increases. This is mainly because all the concreteused C60 in the model; ties have few effects on the lateral stiffness atthe elastic stage for composite CCSHRCS frame. The characteristic valuesof tie λv, which can be seen increasing from 0.308447 to 0.642598, therelationship of lateral load–lateral displacement of composite CCSTRCSframe descending from changing in circumstances, there is no drop-off situation, increasing the yield load, ultimate load has a largerincrease. Because when the characteristic values of tie λv is 0.308447,the column crushing due to no enough confined to the core concrete.In addition to characteristic values of tie λv 0.308447 under thedescending curve, none of the other curves descends, and the lateraldisplacement is relatively large. For rare earthquakes in more thanelastic–plastic story-drift ratio, the frame is also able to continue tobear the load and deformation. It shows that the frame has a good duc-tility. With the increasing of characteristic values of tie, lateral stiffnessat the yield stage increases slightly and lateral post-yield stiffnessincreases significantly, but when the characteristic values of the tiereach a certain level, there is no significant effect on the curve. And λv0.308447 compared to 0.642598, 1.645052 and 2.082019, respectively,under the ultimate load increases by 3.65% and 21.69%, and 24.52%. Itis indicated that the characteristic values of tie from small to large, theshape of the curve and the trends of lateral load–lateral displacementof frame are greatly influenced. When rising to a certain level, the effecton the curve decreases; it doesn't stabilize until the characteristic valuesof tie increase to a value.

4.9. The strength of steel beam (fak)

In order to study the influence of the strength of steel beam on thebehaviors of the frame structures, steels Q235, Q345, Q390, and Q420were used. Thediameter anduniform ratio of longitudinal reinforcement

are taken as 12-D18 (3.39%), and prestressed concrete steel barΦPC [15]is adopted.

While keeping other parameters unchanged, just not the samestrength of steel beam, Fig. 17 shows the relationship of lateralload–lateral displacement of composite CCSTRCS frame at differentstrengths of steel. With the increase of the strength of steel, the lateralstiffness of the frame at the elastic stage remains the same. Since theelastic modulus of the steel beam and its strength has little to do, it isindicated that the maximum yield strength of the steel beam thanminimum yield strength 78.72% increases, but the lateral stiffness ofthe frame at the yield stage almost remains the same. Because thehorizontal load of the yield load at the previous stage for RC columnis play early to the steel beam. The lateral post-yield stiffness in-creases significantly from Q235 to Q345; it is after the yielding ofthe beams that the horizontal load is greatly affected. None of the cur-ves is descending, and lateral displacement is relatively large, at theelastic–plastic story-drift ratio for the rare earthquake, the framealso can continue to carry load and deformation. It is shown thatthe frame has a good ductility. Compared with the Q235, Q345,Q390 and Q420, respectively, the ultimate load increased by 12.42%,13.80%, and 15.91%. However, the shape of the curve and trends oflateral load–lateral displacement of frame almost remain the same.

4.10. The axial-load ratio (n)

In order to study the influence of the axial-load ratio on the behav-iors of the frame structures, axial-load ratio with 0, 0.1, 0.3, 0.5, 0.7, 0.9and 1.05 was changed. The diameter and uniform ratio of longitudinalreinforcement are taken as 12-D18 (3.39%), and prestressed concretesteel bar ΦPC [15] is adopted. HRB400 is used in the longitudinalreinforcement.

While keeping other parameters unchanged, just not the sameaxial-load ratio, Fig. 18 shows the relationship of lateral load–lateraldisplacement of composite CCSTRCS frame at different axial-loadratios. With the increase of the axial-load ratio, the lateral stiffness ofthe frame at the elastic, yield and strengthening stages improves.None of the curves is descending, and lateral displacement is relativelylarge, mainly because the model calculation of slenderness of column isrelatively small, that at this time of the displacement ductility factor of isinfinite. In the axial-load ratio increases from 0 to 0.5, the lateral stiff-ness of the frame at the elastic and yield stages increases obviously.

(a)

(b)

0 10 20 30 40 50 60 70 80 900

100

200

300

400

500

600

700

800

900

1000

1100

ANSYS

ABAQUS

Loa

d/kN

Displacement/mm

Fig. 8. Relationship of load–displacement of framed specimen based on ANSYS and ABAQUS.

0 20 40 60 80displacement (mm)

0

200

400

600

800

1000

1200

P (k

N)

ANSYS

ABAQUSExpeirment

Fig. 9. ABAQUS and ANSYS versus experimental relationship of load–displacement offramed specimen.

152 W. Li et al. / Journal of Constructional Steel Research 77 (2012) 145–162

From 0.7 to 1.05, the lateral stiffness of the frame at the elastic and yieldstage remains almost the same. The lateral post-yield stiffness of theframe increases slightly. The yield load in axial-load ratio increasesfrom 0 to 0.5 than increases from 0.5 to 1.05 is more significant.Ultimate load also increases, but the ductility decreases.

Table 3Load-drift based on calculated and experiment.

Experimentalresults

Calculatedresults

Calculated/experimental

Load(kN) Interior column Interior column

Locationof yield

Column footat the first story

639 658.015 1.0301/113 1/114.17 0.990

Column cap thesecond story

787 776.45 0.9861/25 1/28.50 0.877

Steel beam atthe second story

885 797 0.9011/33 1/30.64 1.078

Fig. 10. The FEM model of CCSH.

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4.11. The linear stiffness ratio of beam–column (K)

In order to study the influence of linear stiffness ratio of beam–

column on the behaviors of the frame structures, taking into accountthe convenience for model, the calculation input parameters remainthe same, just changing the model in the modulus of elasticity ofthe steel beam to achieve the purposes of changing the linear stiffnessratio of the beam–column. The modulus of elasticity of steel beamsis taken, 2.06×105Mpa, 4.12×105Mpa, 8.25×105Mpa, and 1.37×106Mpa, respectively.

While keeping other parameters unchanged, just not the samelinear stiffness ratio of beam–column, Fig. 19 shows the relation-ship of the lateral load–lateral displacement of compositeCCSTRCS frame at different linear stiffness ratios of beam–column.With the increasing of the linear stiffness ratio of beam–column,the lateral stiffness of the frame at the elastic stage increases.With the increase of the linear stiffness ratio of beam–column,beam‐to‐column constraints are also increasing. However, in-creasing the ratio of its lateral stiffness increases not only blindly,but also by a significant difference. The degree of increasing forlateral stiffness at the elastic stage is a decreasing trend with theincrease of linear stiffness ratio of beam–column. Especiallywhen linear stiffness ratio of beam–column from K=1.49 to2.64, the lateral stiffness increases to a lower extent. It is observedthat none of curves is descending, and lateral displacement is rel-atively large. At the elastic–plastic story-drift ratio for the rareearthquake, the frame also can continue to carry load and defor-mation. It is shown that the frame has a good ductility. With theincrease of the linear stiffness ratio of beam–column, the yieldload and ultimate load also increase. Compared with K=0.396,K=0.793, K=1.59 and K=2.64, respectively, the ultimate loadincreases by 8.42%, 13.52%, and 16.27%. The reason for the linear stiff-ness ratios of beam–column has an influence on the bearing capacityof the frame is that the effective length of framed column changes. Thelinear stiffness ratio of the beam–column reflects the level of constraintthat beam to column, and the linear beam-column stiffness ratios at theend of a beam-column affect the capacity for lateral deformation of a

Table 4The properties of materials.

Specimen Compression strength(N/mm2)

Column 26.9

Steel Yie(N

Reinforcement Tie ΦPC 10Longitudinal reinforcement HRB400 4

Steel plate 12 mm 316 mm 2

rotational framed column. Thus, the effective length of the framed col-umns is directly affected, leading to changes in the bearing capacity ofa given frame.

4.12. The slenderness of column (λ)

In the member of flexure and compression, in general according tothe different slenderness of column, are divided into short columnsand long columns. Columns in the loading process, its second-ordereffects can be ignored; long columns in the course of its second-order effect cannot be ignored. Whether the lateral deformation atthe end of columns, the second-order effects are very different. TheACI 318R-08 code [16] divides the column into without lateral swayandwith lateral sway. For non-sway frames, because there is no lateralsway at both ends of the columns, the second-order effects only con-tain P–δ effect, the column buckles on its own, when both ends ofthe additional moment is zero. For sway frames, which include theP–δ effect and the P–Δ effect, the P–δ effect is the relation of the loadand bending deformation, and the P–Δ effect is load, bending andlateral deformation, not only the additional bending moment at bothends of column is not zero, but also relatively large. This model canconsider the constraint at both ends of the sway frames.

Therefore, in order to more accurately study the influence of theslenderness of column on the behaviors of the frame structures, theAmerican Concrete Specification ACI 318R-08 [16] equations wasused to determine the effective length of framed columns, thus deter-mining the slenderness of the column. To facilitate the modelingcalculations, other parameters in themodel are the same, only the lengthof the framed columns is changed to achieve the purpose of changingthe slenderness of the column. To this end, the clear height of thecolumn, respectively, is designed for 900 mm, 1800 mm, 3600 mmand 4500 mm.

While keeping other parameters unchanged, just not the sameslenderness of column, Fig. 20 shows the relationship of lateralload–lateral displacement of composite CCSHRCS frame at differentslenderness of column. With the increase of the slenderness of col-umn, the lateral stiffness of the frame at the elastic stage reduces.

Tensile strength(N/mm2)

Modulus of elasticity(104 N/mm2)

1.91 2.21

ld strength/mm2)

Tensile strength(N/mm2)

Modulus of elasticity(105 N/mm2)

00 1200 2.000 540 2.012.4 463.9 1.9799.8 425.4 1.95

0 20 40 60 80 100 120 140 160 1800

200

400

600

800

1000

1200

Loa

d/kN

Displacement/mm

Fig. 11. The relationship of load–displacement of composite CCSHRCS frame during the different ratios of longitudinal reinforcement.

154 W. Li et al. / Journal of Constructional Steel Research 77 (2012) 145–162

The larger slenderness of column is more prone to tensile failure,leading to the premature yield of longitudinal reinforcement andconcrete crushing. The lateral stiffness and bearing capacity at theyield stage significantly reduce, and that at post-yield stage also sig-nificantly reduces; this is due to the local instability of concrete col-umns. Although none of the curves is descending, and lateraldisplacement is relatively large, at this time the yield and ultimateload remain almost unchanged, it is indicated that the overall struc-ture imminently fails. With the increase of the slenderness of col-umn, the yield load and ultimate load decrease significantly. Andλ=23.0 compared to λ=35.1, λ=57.3 and λ=67.7, respectively,under the ultimate load decreases 1.38, 2.15, and 2.82 times. It isshown that the slenderness of the column is more than 57.3, the

0

200

400

600

800

1000

1200

Loa

d/kN

0 20 40 60 80Displac

Fig. 12. The relationship of load–displacement of composite CCSHRCS f

overall frame instability due to the formation of institutions. There-fore, it is a good engineering design to control the slenderness ofcolumn.

5. The load–displacement backbone curve of composite CCSTRCSframe structure

5.1. The development for load–displacement backbone curve of compositeCCSTRCS frame structure

The relationship of the lateral load–lateral displacement of com-posite CCSTRCS frame is based on the above parameters. The bilinearmodel and trilinear model are adopted to simulate non-descending

HRB400HRB500

HRB335

100 120 140 160 180ement/mm

rame during the different strengths of longitudinal reinforcement.

0

200

400

600

800

1000

Loa

d/kN

v =1.96%

v=3.85%v =6.36%

0 20 40 60 80 100 120 140 160 180Displacement/mm

Fig. 13. The relationship of load–displacement of composite CCSHRCS frame during the different volume ratios of ties.

155W. Li et al. / Journal of Constructional Steel Research 77 (2012) 145–162

and descending curves of the lateral load–lateral displacement of thecomposite CCSTRCS frame.

The bilinear model represents skeleton curves of lateral load–lateral displacement with non-descending, as shown in Fig. 21.

Where, Ke, Ks, represent the elastic stiffness, stiffness at the post-yield stage of frame structures, respectively; Py is the yield load, Δy isthe displacement corresponding to Py, that is the yield displacement.

It can be seen that once the elastic stiffness Ke, the yield load Pyand stiffness at the strengthening stage Ks are determined, skeletoncurves of lateral load–lateral displacement with non-descending forcomposite CCSTRCS frame are developed.

Finite element analysis results show that the axial-load ratio n, linearstiffness ratio of beam–column K and the slenderness of column λ have

0

200

400

600

800

1000

Loa

d/kN

0 20 40 60 80Displ

Fig. 14. The relationship of load–displacement of composite

an important influence on the elastic stiffness of composite CCSTRCSframe, and it can be obtained by regression analysis, the empirical for-mula of the elastic stiffness Ke is,

Ke ¼ 6:93þ 39:66n−40:35n2� � 1

β3

3EcI0l3

ð1Þ

Where, n is the design axial-load ratio; β coefficient of effectivelength of column, their calculation formula see ACI 318R-08 [16];l is the length of the framed column.

The lateral stiffness at the post-yield stage of composite CCSTRCSframe is influenced by the following key factors: the characteristicvalues of tie (λv), yield strength of steel (fak), axial-load ratio (n),

HRB500

HRB400

HRB335

pc

100 120 140 160 180acement/mm

CCSHRCS frame during the different strengths of ties.

0

200

400

600

800

1000

C100L

oad/

kN

C40

C60

C80

0 20 40 60 80 100 120 140 160 180Displacement/mm

Fig. 15. The relationship of load–displacement of composite CCSHRCS frame during the different concrete strengths.

156 W. Li et al. / Journal of Constructional Steel Research 77 (2012) 145–162

and the slenderness of column (λ). The empirical formula for stiffnessat the post-yield stage Ks can be obtained by regression analysis,

Ks ¼−0:05407þ 0:003829λv þ 0:001255λv

2

þ0:098253f ak.

235−0:03136 f ak

.235

� �2

−0:05936nþ 0:098943n2

0BB@

1CCA3EcI0

l3ð2Þ

Where, l is the length of framed column; λv is the characteristicvalues of tie; fak is standard value for the strength of steel; λ is theslenderness of the column; n is the axial-load ratio; Ec is the modulusof elasticity of concrete; and I0 is the moment of inertia of grossconcrete column section about centroidal axis.

Though analysis on the frame of this model shows 12 indeterminatenumbers, under lateral load, there are 12 plastic hinges; the plastic

0

100

200

300

400

500

600

700

800

900

1000

1100

1200

Loa

d/kN

0 20 40 60 80

Displ

Fig. 16. The relationship of load–displacement of composite CCS

hinge distribution is shown in Fig. 22. Therefore, the lateral ultimateload is obtained,

Pu ¼ 12Ms

lð3Þ

Where, Ms is the plastic limit moment of the beam section; l is thelength of framed column.

According to the method in literature [17], if λ>35 or n>np,then,

Py ¼ Pu 1− 2NKelþ N

� �ð4Þ

=2.082019=1.645025

=0.642598

=0.308447

100 120 140 160 180

acement/mm

HRCS frame during the different characteristic values of tie.

0

200

400

600

800

1000

Q420

Q390

Q345

Loa

d/kN

Q235

0 20 40 60 80 100 120 140 160Displacement/mm

Fig. 17. The relationship of load–displacement of composite CCSHRCS frame during the different strengths of steel beam.

157W. Li et al. / Journal of Constructional Steel Research 77 (2012) 145–162

If λ≤35 or n≤np, then,

Py ¼ Pu ð5Þ

Where, N is the axial compressive load; l is the length of framedcolumn; Ke is the elastic stiffness; np=1.05−0.024279λ.

The trilinear model represents the skeleton curves of the lateralload–lateral displacement with descending, as shown in Fig. 23.

Where, OA is at the elastic stage, AB is at the post-yield stage, BC isat the descending stage, Ke, Ks, and Kc, are elastic stiffness, post-yieldstiffness and degradation stiffness, respectively. Py is the yield load, Δy

is the displacement corresponding to Py, that is the yield displace-ment, ΔB is the peak displacement corresponding to the ultimateload Pu, the lateral load of A is based on the method in the literature[18], that is Py=0.6 Pu, Pu obtained by Eq. (3).

0

200

400

600

800

1000

1200

1400

Loa

d/kN

0 20 40 60 80Displ

Fig. 18. The relationship of load–displacement of composite

It can be seen that once the elastic stiffness Ke, the yield load Py,the ultimate load Pu, post-yield stiffness Ks, degradation stiffness Kc

and the peak displacement ΔB are determined, the skeleton curvesof lateral load–lateral displacement with descending for compositeCCSTRCS frame will be developed. The empirical formula of the elasticstiffness can be obtained by regression analysis,

Ke ¼ −5:75107−1:58967λ−0:06849λ2� �3EcI0

l31β3 ð6Þ

Where, l is the length of the framed column; λ is the slendernessof column; Ec is the modulus of elasticity of concrete; I0 is the momentof inertia of gross concrete column section about centroidal axis, β isthe coefficient of effective length of column, and its equation is seenin ACI 318R-08 [16].

n=0.7n=0.9

n=0.1

n=0.3

n=1.05

n=0.5

n=0

100 120 140 160 180acement/mm

CCSHRCS frame during the different axial-load ratios.

0

100

200

300

400

500

600

700

K=2.64K=1.59K=0.793

Loa

d/kN

K=0.396

0 20 40 60 80 100 120 140 160 180Displacement/mm

Fig. 19. The relationship of load–displacement of composite CCSHRCS frame during the different linear stiffness ratios of beam–column.

0

200

400

600

800

1000

1200

=67.7

=57.3

=35.1

=23.0

Loa

d/kN

0 20 40 60 80 100 120 140 160 180Displacement/mm

Fig. 20. The relationship of load–displacement of composite CCSHRCS frame during the different slenderness of column.

Fig. 21. Bilinear model.

158 W. Li et al. / Journal of Constructional Steel Research 77 (2012) 145–162

The post-yield stiffness:

Ks ¼ −1:2923þ 0:099319λ−0:001619λ2 þ 0:8313n−1:9011n2� �3EcI0

l3

ð7Þ

Where, l is the length of framed column; λ is the slenderness ofcolumn; n is the axial-load ratio; Ec is the modulus of elasticity of con-crete; and I0 is the moment of inertia of gross concrete column sectionabout centroidal axis.

The degradation stiffness of frame structures:

Kc ¼ −0:7292−4:4809λv þ 11:9856λv2 þ 3:8491n−3:2449n2

� �3EcI0l3

ð8Þ

Fig. 22. The distribution of plastic hinge of frame under lateral load.

159W. Li et al. / Journal of Constructional Steel Research 77 (2012) 145–162

Where, l is the length of framed column; λv is the characteristicvalues of stirrup; n is the axial-load ratio; Ec is themodulus of elasticityof concrete; and I0 is the moment of inertia of gross concrete columnsection about centroidal axis.

Fig. 23 shows the geometric relationship:

Ks ¼Pu−Py

ΔB−Δyð9Þ

Hence:

ΔB ¼ Pu−Py

Ksþ Δy ¼

Pu−0:6Pu

Ksþ Δy ¼

0:4Pu

Ksþ Δy ð10Þ

5.2. The validation for load–displacement backbone curve of compositeCCSTRCS frame structure

5.2.1. The validation for non-descending skeleton curve modelFig. 24 shows the comparison of the skeleton curves of the lateral

load–lateral displacement by the finite element method and simplifiedmodel conducted by the Technical Research and Development Institute,Nishimatsu Construction in 1997, for steel beam–concrete columnframe specimens [14]. It is shown that the elastic stiffness and post-yield stiffness agree well with them, but the yield load is larger thanthe FEA results, since the yield load of the simplified model is basedon the determination of the ideal rigid-plastic limit analysis theory,and in the actual process frame stiffness of the structure will havedegraded.

In order to study the simplified model in a wider scope of applica-bility, a two-story and two-bay composite CCSHRCS frame is selected

Fig. 23. Trilinear model with deterioration.

to compared different parameters, the comparison for calculatedresults are shown in Fig. 25, it shows good agreement with elastic stiff-ness, slightly higher than the yield load of finite element analysis,strengthening stage is lower than the stiffness of the finite elementcalculation. As a simplifiedmodel, however, the overall good agreementbetween the two can meet general engineering requirements.

5.2.2. The validation for descending skeleton curve modelFig. 26 is the comparison of the finite element analysis and the

simplified model, good agreement with elastic stiffness, yield load isslightly less than the finite element method, and stiffness at thepost-yield stage of the simplified model is lower than that of the finiteelement method, degradation stiffness is in good agreement. As asimplified model, however, the overall good agreement between thetwo can also meet the general engineering requirements.

6. Summary and concluding remarks

In this paper, the ABAQUS software is applied to analyze the influ-ence of different parameters on behaviors of composite CCSTRCSframe structures. These parameters are as follow: the ratio of longitudi-nal reinforcement (ρs) and the volume ratio of tie (ρv), the strength oflongitudinal reinforcement (fys) and the strength of tie (fyv), the com-pressive strength of cubic concrete (fcu), characteristic values of tie(λv), the yield strength of steel (fak), axial-load ratio (n), the linear stiff-ness ratio of beam–column (K) and the slenderness of column (λ).

The results show that the above parameters have a correspondingeffect on lateral load–lateral displacement of the composite CCSTRCSframe. In which, the axial-load ratio(n), the linear stiffness ratio of

N N N

P

0 20 40 60 800

200

400

600

800

1000

P/k

N

/mm

FEM

simplified model

Fig. 24. Comparisons of load–displacement backbone curve of CCSHRCS tested framebetween FEM and simplified model.

P

NNN

2345 / , 2.082

23, 0.5, 0.128vkaf N mm

n K

0 20 40 60 80 1000

200

400

600

800

1000

1200

Simplified model

P/k

N

FEM

/mm

0 20 40 60 80 100

/mm

0 20 40 60 80 100

/mm

0 20 40 60 80 100

/mm

0 20 40 60 80 100/mm

2345 / , 0.5484

35.1, 0.5, 0.396vkaf N mm

n K

P

NNN

0

100

200

300

400

500

simplified model

P/kN

FEM

2345 / , 2.1285

35.1, 0.5, 0.793vkaf N mm

n K

P

NNN

0

100

200

300

400

500

600

P/kN

FEM

Simplified model

2345 / , 2.1285

35.1, 0.5, 1.59vkaf N mm

n K

P

NNN

0

100

200

300

400

500

600

P/kN

FEM

Simplified model

2345 / , 2.1285

23, 0.1, 0.128vkaf N mm

n K

P

NNN

0

200

400

600

800

1000

P/kN

FEM

Simplified model

(a)

(c)

(e)

(d)

(b)

Fig. 25. Comparisons of backbone curve of composite CCSHRCS frame between FEM and the simplified model.

160 W. Li et al. / Journal of Constructional Steel Research 77 (2012) 145–162

beam–column (K) and the slenderness of column (λ) have a signifi-cant influence on elastic stiffness; and the characteristic values of tie(λv), the yield strength of steel (fak), axial-load ratio (n) and the slen-derness of column (λ) have a significant influence on the post-yieldstiffness. When the characteristic value of tie is more than 0.362,P–Δ curves are not descending; if less than 0.362, P–Δ curves aredescending. Other conditions are the same, with the decrease of thecharacteristic value of tie, elastic stiffness is invariable, post-yieldstiffness and ultimate load reduce, so is the degradation stiffness;when the axial-load ratio increases, the elastic stiffness changes little,post-yield stiffness and ultimate load significantly reduce, degrada-tion stiffness also significantly reduces.

The relationship of the lateral load–lateral displacement of com-posite CCSTRCS frame is based on the above parameters, the bilinearmodel and trilinear model are adopted to simulate non-descendingand descending curves of lateral load–lateral displacement of compositeCCSTRCS frame.

The parameters of the simplified model of P–Δ curve with descend-ing and non-descending for composite CCSTRCS frame are derived bymultiple linear regressions. Comparing the simplified model with finiteelement results, it shows that for the case of non-descending, elasticstiffness is of good agreement, yield load is slightly higher and post-yield stiffness is lower than that of the finite element method. For thedescending case, elastic stiffness is also of good agreement, yield load

2345 / , 0.362

35.1, 0.9, 0.396vkaf N mm

n K

P

NNN

0 20 40 60 80 1000

50

100

150

200

250

300

350

400P/

kN

/mm

0 20 40 60 80 100

/mm

0 20 40 60 80 100

/mm

0 20 40 60 80 100

/mm

0 20 40 60 80 100

/mm

FEM

simplified model

2345 / , 0.362

23, 0.9, 0.128vkaf N mm

n K

P

NNN

0

100

200

300

400

500

600

700

P/kN

FEM

simplified model

2345 / , 0.362

23, 0.7, 0.128vkaf N mm

n K

P

NNN

0

100

200

300

400

500

600

700

800

P/kN

FEM

simplified model

2345 / , 0.2142

35.1, 0.8, 0.396vkaf N mm

n K

P

NNN

0

50

100

150

200

250

300

350

400

P/kN

FEM

simplified model

2345 / , 0.2142

35.1, 0.5, 0.396vkaf N mm

n K

P

NNN

0

50

100

150

200

250

300

350

400

P/kN

FEM

simplified model

(a)

(c)

(e)

(b)

(d)

Fig. 26. Comparisons of load–displacement backbone curve of composite CCSHRCS frame between FEM and the simplified model.

161W. Li et al. / Journal of Constructional Steel Research 77 (2012) 145–162

is slightly less and post-yield stiffness is lower than that of the finiteelement method. The degradation stiffness also agrees well with eachother. As a simplified model, the overall agree well between the two,and they are able to meet the general engineering requirements.

In addition, if ties with high-strength and small spacing areadopted, the characteristic value of tie is generally greater than0.362. Therefore, the P–Δ curves for high-strength concrete columnconfined with continuous compound spiral ties-steel beam framestructure, even when the axial-load ratio is more than 1.0, the curvesare still not descending. Ductility coefficient is infinite in theory.

However, in practical engineering, it is necessary to consider the slen-derness of column and axial-load ratio to ensure the ductility of thecolumns.

Acknowledgments

The authors would like to express their appreciation to Xi'AnUniversity of Architecture & Technology and their classmates. Simul-taneously we thank the beneficial material provided by theArchitectural Institute of Japan.

162 W. Li et al. / Journal of Constructional Steel Research 77 (2012) 145–162

Thewriterswould like to acknowledge the help ofMei Li andXiao-leiLi; they translated and revised the part of this paper. In addition, thewriters appreciate the reviewers for their valuable comments andsuggestions.

References

[1] Goel SC. United States–Japan Cooperative Earthquake Engineering Research Pro-gram on Composite and Hybrid Structures [J]. J Struct Eng ASCE 2004;130(2):157–8.

[2] Liu J, Foster SJ. Finite element model for confined concrete columns[J]. J Struct EngASCE 1998;124(9):1011–7.

[3] Yu T, Teng JG, Wong YL, Dong SL. Finite element modeling of confined concrete-I:Drucker–Prager type plasticity model [J]. Eng Struct 2010;32:665–79.

[4] Yu T, Teng JG, Wong YL, Dong SL. Finite element modeling of confined concrete-II:Plastic-damage model [J]. Eng Struct 2010;32:680–91.

[5] Hajjar J, Leon R, Gustafson M, Shield C. Seismic response of compositemoment-resisting connections. II: Behavior[J]. J Struct Eng ASCE 1998;124(8):877–85.

[6] ABAQUS user's manual—version 6.8.1. Pawtucket, RI: Hibbit, Karlsson & Sorenson;2006.

[7] Salvatore W, Bursi OS, Lucchesi D. Design, testing and analysis of high ductilepartial-strength steel-concrete composite beam-to-column joints[J]. ComputStruct 2005;83:2334–52.

[8] Hu HT, Huang CS, Wu MH, Wu YM. Nonlinear Analysis of Axially LoadedConcrete-Filled Tube Columns with Confinement Effect[J]. J Struct Eng ASCE2003;129(10):1322–9.

[9] Zhao GZ, Li A. Numerical study of a bonded steel and concrete composite beam[J].Comput Struct 2008;86:1830–8.

[10] Bursi OS, Sun FF, Postal S. Non-linear analysis of steel–concrete composite frameswith full and partial shear connection subjected to seismic loads[J]. J Constr SteelRes 2005;61:67–92.

[11] Han LH, WangWD, Zhao XL. Behavior of steel beam to concrete-filled SHS columnframes: Finite element model and verifications [J]. Eng Struct 2008;30:1647–58.

[12] Wu LY, Chung LL, Wang MT, Huang GL. Numerical study on seismic behavior ofH-beams with wing plates for bolted beam–column connections [J]. J ConstrSteel Res 2009;65:97–115.

[13] Li W, Li QN, Jiang WS. Nonlinear finite element analysis of behaviors of steelbeam-continuous compound spiral stirrups reinforced concrete column framestructures [J]. The Structural Design of Tall and Special Buildings. http://dx.doi.org/10.1002/tal.758,2012.

[14] Li W, Li QN, Jiang WS, Jiang L. Seismic performance of composite reinforced con-crete and steel moment frame structures-state-of-the-art[J]. Compos B2011;42(2):190–206.

[15] Technical specification for confined concrete structures and hybrid structures ofconcrete and steel (DB13(J)/T83-2009[S]. Shijiazhuang: Engineering ConstructionStandard in Hebei Province; 2009 [in Chinese].

[16] ACI Committee 318. Building code requirements for structural concrete, ACI318-08,and commentary, ACI R318-08[S]. Farmington Hills, Michigan: American ConcreteInstitute; 2008.

[17] Zhong ST, Jiang WS, Liu WY. The theory and practice of steel and concrete com-posite structures [M]. Beijing: China Architecture and Building Press; 2008 [inChinese].

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Nomenclature

C: grade of compressive strength of concreteHPB: hot rolled steel reinforcing barsfcu: specified compressive strength of concrete cubesρs: ratio of longitudinal reinforcement ρs ¼ As

bhfys: specified yield strength of longitudinal reinforcementρv: volumetric ratio of tiefyv: specified yield strength of tiefc: design compressive strength of concreteλv: characteristic values of tie λv ¼ ρv

f yvf c

fak: specified yield strength of steel beamK: linear stiffness ratio of beam–columnλ: slenderness of columnn: axial-load ratio n ¼ N

f cAnp: peak axial-load ratio np ¼ Np

f cAKe: elastic stiffness of frame structuresKs: post-yield stiffness of frame structuresKc: degradation stiffness of frame structuresPy: yield loadPu: ultimate load△y: yield displacement△B: peak displacement corresponding to ultimate loadEc: modulus of elasticity of concretel: unsupported length of framed columnβ: effective length coefficient of framed columnI0: moment of inertia of gross concrete column section about centroidal axisMs: plastic limit moment of beam sectionN: axial compressive load

Wei Li (1981―), male, ethnic Han, native of Wannian, Jiangxi Province, born inNovember 1981. PhD, interested in the research of high-rise building structures andcomposite steel and concrete structures.

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