behaviour of normal and high strength concrete-filled compact steel tube

Journal of Constructional Steel Research 62 (2006) 706–715www.elsevier.com/locate/jcsr

Behaviour of normal and high strength concrete-filled compact steel tubecircular stub columns

Ehab Ellobodya, Ben Youngb,∗, Dennis Lamc

a Department of Structural Engineering, Faculty of Engineering, Tanta University, Tanta, Egyptb Department of Civil Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong

c School of Civil Engineering, University of Leeds, Leeds, UK

Received 9 May 2005; accepted 2 November 2005

Abstract

This paper presents the behaviour and design of axially loaded concrete-filled steel tube circular stub columns. The study was conductedover a wide range of concrete cube strengths ranging from 30 to 110 MPa. The external diameter of the steel tube-to-plate thickness (D/t) ratioranged from 15 to 80 covering compact steel tube sections. An accurate finite element model was developed to carry out the analysis. Accuratenonlinear material models for confined concrete and steel tubes were used. The column strengths and load–axial shortening curves were evaluated.The results obtained from the finite element analysis were verified against experimental results. An extensive parametric study was conducted toinvestigate the effects of different concrete strengths and cross-section geometries on the strength and behaviour of concrete-filled compact steeltube circular stub columns. The column strengths predicted from the finite element analysis were compared with the design strengths calculatedusing the American, Australian and European specifications. Based on the results of the parametric study, it is found that the design strengthsgiven by the American Specifications and Australian Standards are conservative, while those of the European Code are generally unconservative.Reliability analysis was performed to evaluate the current composite column design rules.c© 2005 Elsevier Ltd. All rights reserved.

Keywords: Composite columns; Concrete; High strength; Steel tubes; Finite element; Modeling; Confinement; Structural design

1. Introduction

Concrete-filled steel tube columns have been increasinglyused in many modern structures. Their usage provides highstrength, high ductility, high stiffness and full usage ofconstruction materials. In addition to these advantages, the steeltubes surrounding the concrete columns eliminate permanentformwork which reduces construction time. Furthermore, steeltubes not only assist in carrying axial load, but also provideconfinement to the concrete. However, concrete confinementdepends on many factors such as the column diameter, thethickness of the steel tube, the concrete strength and the yieldstress of the steel tube.

Experimental research has been carried out to investigate thestrength and behaviour of concrete-filled steel tube columns.Schneider [1] studied the behaviour of short axially loaded

∗ Corresponding author. Tel.: +852 2859 2674; fax: +852 2559 5337.E-mail address: [email protected] (B. Young).

0143-974X/$ - see front matter c© 2005 Elsevier Ltd. All rights reserved.doi:10.1016/j.jcsr.2005.11.002

concrete-filled steel tube columns. Fourteen specimens weretested to investigate the effect of the tube shape and steeltube plate thickness on the composite column strength. Itwas concluded that circular steel tubes offer much morepost-yield axial ductility than square and rectangular tubesections. Like Schneider [1], Huang et al. [2] tested 17concrete-filled steel tube column specimens but with a highercolumn diameter-to-steel tube plate thickness ratio. The sameconclusion was achieved even for the higher column diameter-to-steel tube plate thickness ratio of 150. Sakino et al. [3]tested 114 specimens of centrally loaded concrete-filled steeltube short columns. In addition, Sakino et al. [3] studiedthe effect of steel tube tensile strength and concrete strengthon the behaviour of the composite columns. Giakoumelisand Lam [4] carried out 15 tests on circular concrete-filled tube columns. The effects of the steel tube platethickness, the bond between the steel tube and the concreteas well as the concrete confinement on the behaviour ofthese columns were studied. The test results were compared

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E. Ellobody et al. / Journal of Constructional Steel Research 62 (2006) 706–715 707

Nomenclature

Ac Cross-sectional area of concreteAs Cross-sectional area of steel tubeCP Correction factor in reliability analysisCOV Coefficient of variationD External diameter of steel tubeEcc Young’s modulus of confined concreteFm Mean value of fabrication factorf Equivalent uniaxial stressfc Unconfined compressive cylinder strength of

concretefcc Confined compressive strength of concretefcu Unconfined compressive cube strength of con-

cretefl Lateral confining pressurefsu Ultimate stress of steel tubefy Yield stress of steel tubeK Ratio of flow stress in triaxial tension to that in

compressionk1 Coefficient for confined concretek2 Coefficient for confined concretek3 Coefficient for confined concreteL Length of columnMm Mean value of material factorPACI/AS Ultimate load obtained from ACI/ASPEC4 Ultimate load obtained from EC4PFE Ultimate load obtained from finite element

analysisPm Mean value of tested-to-predicted load ratiosPTest Ultimate load obtained from testR Coefficient for confined concreteRE Coefficient for confined concreteRε Coefficient for confined concreteRσ Coefficient for confined concreter Reduction factor for confined concretet Plate thickness of steel tubeVF Coefficient of variation of fabrication factorVM Coefficient of variation of material factorVP Coefficient of variation of tested-to-predicted

load ratiosX Local x-coordinateY Local y-coordinateZ Local z-coordinateε Equivalent uniaxial strainεc Unconfined concrete strainεcc Confined concrete strainεsu Ultimate strain of steel tubeβ Material angle of frictionβ Reliability index (safety index)φ Resistance (capacity) factorυcc Poisson’s ratio of confined concreteη1, η2 Coefficients of confinement for concrete and steel

with column strengths calculated from current codes ofpractice.

Little success has been achieved so far in developingan accurate model due to the complexity in modeling theconcrete confinement. Schneider [1] developed a 3-D nonlinearfinite element model for concrete-filled steel tube circularcolumns. The ABAQUS program was used for the model. Theunconfined uniaxial stress–strain curve for concrete providedin the ABAQUS material library was used. Strain-hardeningwas not considered for the steel tube. Hu et al. [5] developeda nonlinear finite element model using the ABAQUS programto simulate the behaviour of concrete-filled steel tube columns.The concrete confinement was achieved by matching thenumerical results by trial and error via parametric study.

The main objective of this study is to develop an accuratefinite element model to simulate the behaviour of concrete-filled compact steel tube circular stub columns. The finiteelement program ABAQUS [6] was used in the analysis.The effects of concrete strength and concrete confinementwere considered in the analysis. A multi-linear stress–straincurve for the steel tube was used. The interface betweenconcrete and the steel tube was also modeled. The resultsobtained from the model were verified against the resultsof the tests conducted by Giakoumelis and Lam [4] andSakino et al. [3]. Parametric studies were performed toinvestigate the effect of concrete strength and cross-sectiongeometries on the behaviour of axially loaded concrete-filledcompact steel tube circular columns. The results obtained fromthe parametric study were compared with design strengthscalculated using Eurocode 4 [7], American Specifications [8,9]and Australian Standards [10,11] for concrete-filled steel tubecircular columns. The current composite column design ruleswere examined using reliability analysis.

2. Finite element modeling

2.1. General

In order to accurately simulate the actual behaviour ofconcrete-filled steel tube circular columns, the main threecomponents of these columns have to be modeled properly.These components are the confined concrete, the circular steeltube and the interface between the concrete and the steel tube.In addition to these parameters, the choice of the element typeand mesh size that provide accurate results with reasonablecomputational time is also important in simulating structureswith interface elements.

2.2. Finite element type and mesh

Different element types have been tried in order to find asuitable element to simulate the behaviour of concrete-filledsteel tube circular columns. Since it had been decided to modelonly the compact steel tubes, solid elements were found to bemore efficient in modeling both the steel tube and the concreteas well as the clearly defined boundaries of their elements.A fine mesh of three-dimensional eight-node solid elements

708 E. Ellobody et al. / Journal of Constructional Steel Research 62 (2006) 706–715

Fig. 1. Finite element mesh of concrete-filled steel tube circular column.

(C3D8) is used in this study. The efficiency of the elementswas first verified by modeling empty circular compact steeltubes and comparing the FE results with the results of the testsconducted by Giakoumelis and Lam [4] and Sakino et al. [3].Different mesh sizes were tried in order to find a reasonablemesh that provides both accurate results and less computationaltime. It is found that a mesh size of 1 (length):1 (width):2(depth), for most of the elements, can achieve accurate results.Fig. 1 shows the finite element mesh of a circular concrete-filledsteel tube of 5 mm plate thickness having an outer diameter of114 mm with a column length of 300 mm.

2.3. Boundary conditions and load application

Following the testing procedures conducted by Giakoumelisand Lam [4] and Sakino et al. [3], the top and bottom surfacesof the concrete-filled steel tube circular columns were fixedagainst all degrees of freedom except for the displacementat the loaded end, which is the top surface, in the directionof the applied load. Due to symmetry, only a quarter ofthe column was modeled, as shown in Fig. 1. The nodes onsymmetry surfaces 1 and 2 were prevented from displacing inX and Y directions, respectively, due to symmetry, as shown inFig. 1. The nodes on the column centreline are prevented fromdisplacing in both X and Y directions. Other nodes were free todisplace in any direction. The load was applied in incrementsusing the modified RIKS method available in the ABAQUSlibrary. The RIKS method is generally used to predict nonlinearcollapse of a structure such as in post-buckling analysis. Theload was applied as static uniform loads using the displacementcontrol at each node of the loaded top surface, which is identicalto the experimental investigation.

2.4. Material modeling of steel tubes

The measured stress–strain curves presented by Giakoumelisand Lam [4] for circular steel tubes of 3.6 and 5.0 mm nominalplate thicknesses with 114 mm nominal external diameter have

been simulated as two multi-linear stress–strain curves. Theexperimental measured yield stresses ( fy) were 343 MPa and365 MPa for steel tubes with nominal plate thicknesses of3.6 mm and 5.0 mm, respectively, as summarized in Table 1.Tri-linear stress–strain curves were used to model the circularsteel tubes of 4.54 mm plate thickness with 238 and 360 mmnominal external diameters tested by Sakino et al. [3]. Themain defining parameters for the tri-linear stress–strain curvesare the experimental measured yield stresses ( fy), the ultimatestresses ( fsu) and the ultimate strains (εsu). The experimentalmeasured yield stresses ( fy) were 507 MPa and 525 MPa,the ultimate stresses ( fsu) were 531 MPa and 548 MPa, andthe ultimate strains were 0.0065 and 0.006 for steel tubeswith the nominal external diameters of 238 mm and 360 mm,respectively. The material behaviour provided by ABAQUS(using the *PLASTIC option) allows a multi-linear stress–straincurve to be used. The first part of the multi-linear curverepresents the elastic part up to the proportional limit stresswith a measured Young’s modulus of 205 GPa and Poisson’sratio equal to 0.3.

2.5. Material modeling of confined concrete

Concrete-filled steel tube circular columns with a highvalue of the D/t ratio provide inadequate confinement forthe concrete. This is attributed to the premature failure of thecolumns due to local buckling of steel tubes. On the other hand,concrete-filled steel tube circular columns with a small value ofthe D/t ratio provide remarkable confinement for the concrete.In this case, the concrete strength is considerably improved andthe confined concrete model can be taken as the concrete model.In this study, it is intended to develop a confined concretemodel and compare with experimental investigation. Fig. 2shows equivalent uniaxial presentations for the stress–straincurves of unconfined and confined concrete, where fc is theunconfined concrete cylinder compressive strength which isequal to 0.8( fcu) and fcu is the unconfined concrete cubecompressive strength. The corresponding unconfined strain(εc) is taken as 0.003. The confined concrete compressivestrength ( fcc) and the corresponding confined stain (εcc) canbe determined from Eqs. (1) and (2), respectively, proposed byMander et al. [12]:

fcc = fc + k1 fl (1)

εcc = εc

(1 + k2

fl

fc

)(2)

where fl is the lateral confining pressure imposed by thecircular steel tube. The lateral confining pressure ( fl) dependson the D/t ratio and the steel tube yield stress ( fy). Theapproximate value of ( fl) can be calculated from empiricalequations given by Hu et al. [5]. The equations were proposedfor a wide range of D/t ratios, from 21.7 to 150. Based onthese equations, the value of ( fl) has a significant effect for steeltubes with a small D/t ratio. On the other hand, a small value of( fl) is obtained for steel tubes with a high D/t ratio. The factors(k1) and (k2) are taken as 4.1 and 20.5, respectively, as givenby Richart et al. [13]. Knowing ( fl), (k1) and (k2), the values


Table 1Measured specimen dimensions and material properties

Specimen Dimensions Material properties Tested byD (mm) t (mm) D/t L (mm) L/D Concrete strength (MPa) Steel tube fy (MPa)

C1 114.0 3.87 29.4 298.9 2.62 – 343

Giakoumelis and Lam [4]

C2 115.0 5.02 22.9 300.0 2.61 – 365C7 114.9 4.91 23.4 300.5 2.61 34.7a 365C9 115.0 5.02 22.9 300.5 2.61 57.6a 365C8 115.0 4.92 23.4 300.0 2.61 104.9a 365C12 114.3 3.85 29.7 300.0 2.62 31.9a 343C11 114.3 3.75 30.5 300.0 2.62 57.6a 343C14 114.5 3.84 29.8 300.0 2.62 98.9a 343

CC6-C-0 238.0 4.54 52.4 714.0 3.0 – 507

Sakino et al. [3]

CC6-D-0 360.0 4.54 79.3 1080.0 3.0 – 525CC6-C-2 239.0 4.54 52.5 717.0 3.0 25.4b 507CC6-C-4-2 238.0 4.54 52.4 714.0 3.0 40.5b 507CC6-C-8 238.0 4.54 52.4 714.0 3.0 77.0b 507CC6-D-2 361.0 4.54 79.4 1083.0 3.0 25.4b 525CC6-D-4-1 361.0 4.54 79.4 1083.0 3.0 41.1b 525CC6-D-8 360.0 4.54 79.3 1080.0 3.0 85.1b 525

a fcu is the unconfined compressive cube strength of concrete.b fc is the unconfined compressive cylinder strength of concrete.

Fig. 2. Equivalent uniaxial stress–strain curves for confined and unconfinedconcrete.

of the equivalent uniaxial confined concrete strength ( fcc) andthe corresponding confined strain (εcc) can be determined usingEqs. (1) and (2).

To define the full equivalent uniaxial stress–strain curve forconfined concrete as shown in Fig. 2, three parts of the curvehave to be identified. The first part is the initially assumedelastic range to the proportional limit stress. The value of theproportional limit stress is taken as 0.5( fcc) as given by Huet al. [5], while the initial Young’s modulus of confined concrete(Ecc) is reasonably well calculated using the empirical Eq. (3)given by ACI [8], and the Poisson’s ratio (υcc) of confinedconcrete is taken as 0.2:

Ecc = 4700√

fcc MPa (3)

The second part of the curve is the nonlinear portion startingfrom the proportional limit stress 0.5( fcc) and going to theconfined concrete strength ( fcc). This part of the curve can bedetermined from Eq. (4) which is a common equation proposedby Saenz [14]. This equation is used to represent the multi-dimensional stress and strain values for the equivalent uniaxialstress and strain values. The unknowns of the equation are the

uniaxial stress ( f ) and strain (ε) values defining this part of thecurve. The strain values (ε) are taken between the proportionalstrain, which is equal to (0.5 fcc/Ecc), and the confined strain(εcc), which corresponds to the confined concrete strength. Thestress values ( f ) can be easily determined from Eq. (4) byassuming the strain values (ε):

f = Eccε

1 + (R + RE − 2)(

εεcc

)− (2R − 1)

(ε

εcc

)2 + R(

εεcc

)3

(4)

where RE and R values are calculated from Eqs. (5) and (6),respectively:

RE = Eccεcc

fcc(5)

R = RE (Rσ − 1)

(Rε − 1)2− 1

Rε

(6)

while the constants Rσ and Rε are taken equal to 4 asrecommended by Hu and Schnobrich [15].

The third part of the confined concrete stress–strain curve isthe descending part from the confined concrete strength ( fcc)

to a value lower than or equal to rk3 fcc with the correspondingstrain of 11εcc. The reduction factor (k3) depends on the D/tratio and the steel tube yield stress ( fy). The approximate valueof k3 can be calculated from empirical equations given by Huet al. [5]. The equations were proposed for a wide range of D/tratios ranging from 21.7 to 150. The reduction factor (r) takesinto account the effect of the concrete strength. The equationsproposed by Hu et al. [5] for the factor (k3) were based onthe investigation of concrete cube strengths with a maximumvalue of 31.2 MPa. The experimental investigation conductedby Giakoumelis and Lam [4] showed that the value k3 proposedby Hu et al. [5] is workable only for concrete cube strength upto 30 MPa. It is also shown that even for the same D/t ratioand the same yield stress of the steel tube ( fy), the descending


of concrete is increased with increase of the concrete strengthabove 30 MPa. Since the main objective of this study is tointroduce an accurate confined concrete model, it is proposed tobase the reduction factor (r) on the experimental investigationcarried out by Giakoumelis and Lam [4]. The value of r istaken as 1.0 for concrete with the cube strength ( fcu) equal to30 MPa, while the value of r is taken as 0.5, as recommendedby Tomii [16], and Mursi and Uy [17], for concrete with fcugreater than or equal to 100 MPa, which is the maximumconcrete cube strength tested by Giakoumelis and Lam [4].Linear interpolation is used to determine the value of r forconcrete cube strength between 30 and 100 MPa.

The yielding part of the confined stress–strain curve forconcrete, which is the part after the proportional limit stress,is treated using the Drucker–Prager yield criterion modelavailable in the ABAQUS material library. The model isused to define yield surface and flow potential parametersfor materials subjected to triaxial compressive stresses.Two parameters (*DRUCKER PRAGER and *DRUCKERPRAGER HARDENING) are used to define the yield stageof confined concrete. The linear Drucker–Prager model is usedwith associated flow and the isotropic rule. The material angleof friction (β) and the ratio of flow stress in triaxial tensionto that in compression (K ) are taken as 20 degrees and 0.8,respectively, as recommended by Hu et al. [5].

2.6. Concrete–steel tube interface

The contact between the steel tube and the concrete ismodeled by interface elements. The interface elements consistof two matching contact faces of steel tube and concreteelements. The friction between the two faces is maintainedas long as the surfaces remain in contact. The coefficient offriction between the two faces is taken as 0.25 in the analysis.The interface element allows the surfaces to separate under theinfluence of a tensile force. However, the two contact elementsare not allowed to penetrate each other.

3. Verification of finite element model

3.1. Experimental results

Recent experimental investigations on concrete-filled steeltube circular columns conducted by Giakoumelis and Lam [4]and Sakino et al. [3] were used to verify the FE modeldeveloped in this study. Table 1 summarizes the measureddimensions and material properties of the tested specimens.The specimens used in the tests conducted by Giakoumelis andLam [4] had nominal outer diameter (D) and nominal length(L) of 114 mm and 300 mm, respectively. The specimens C1and C2 were circular steel tube columns without concrete infillhaving the nominal plate thicknesses of 3.6 mm and 5.0 mm,respectively. Specimens C7, C9 and C8 had the same steeltube with nominal plate thickness of 5.0 mm but with nominalconcrete cube strengths of 30 MPa, 60 MPa and 100 MPa,respectively, while specimens C12, C11 and C14 had the samenominal plate thickness of 3.6 mm but with nominal concrete

cube strengths of 30 MPa, 60 MPa and 100 MPa respectively.The tests were conducted on concrete-filled steel tube circularcolumns compressed between fixed ends. The yield stresses ofthe steel tubes were 343 MPa and 365 MPa for the nominalplate thicknesses of 3.6 mm and 5.0 mm, respectively. Thenominal length-to-external diameter (L/D) ratio was 2.63 forall columns. The external diameter-to-thickness (D/t) ratioof the steel tubes was 31.7 and 22.8 for the steel tubes withnominal plate thicknesses of 3.6 mm and 5.0 mm, respectively.

Circular concrete-filled steel tube specimens for the testsconducted by Sakino et al. [3] had a steel tube plate thicknessof 4.54 mm and a length of 3D. Two nominal diameters of238 mm and 360 mm were used with the D/t ratios of 52.4and 79.3, respectively. Specimens CC6-C-0 and CC6-D-0 wereempty steel tubes with diameters of 238 mm and 360 mm,respectively. Specimens CC6-C-2, CC6-C-4-2 and CC6-C-8were concrete-filled steel tubes with the nominal diameter of238 mm and the concrete cylinder strengths of 25.4 MPa,40.5 MPa and 77.0 MPa, respectively. Specimens CC6-D-2,CC6-D-4-1 and CC6-D-8 were concrete-filled steel tubes withthe nominal diameter of 360 mm and the concrete cylinderstrengths of 25.4 MPa, 41.1 MPa and 85.1 MPa, respectively.The yield stresses of the steel tubes were 507 MPa and 525 MPafor diameters of 238 mm and 360 mm, respectively.

3.2. Comparison of finite element results with experimentalresults

In order to verify the finite element model, a comparisonbetween the experimental results and finite element resultswas carried out. The ultimate loads obtained from the tests(PTest) and finite element analysis (PFE) as well as theload–axial shortening curves and deformed shapes after failurehave been investigated. Table 2 shows a comparison of theultimate loads of the concrete-filled steel tube circular columnsobtained experimentally and numerically using the finiteelement model. It can be seen that good agreement has beenachieved between the two sets of results for most of thecolumns. A maximum difference of 7% was observed betweenexperimental and numerical results for column specimens C9and C11. The mean value of the PTest/PFE ratios is 0.98 withthe corresponding coefficient of variation (COV) of 0.037 asshown in Table 2.

The experimental load–axial shortening curves werecompared with the numerical results, and good agreement hadbeen achieved. Fig. 3 plots the load–axial shortening curvesfor the columns without concrete infill specimens C1 andC2. It can be seen that the finite element model successfullypredicted the ultimate load of the columns and the load–axialshortening behaviour. The buckling behaviour of the columnswithout concrete infill was verified very well when usingthe mesh of C3D8 elements in the finite element model.The verification ensures that the material model of the steeltube efficiently represented the experimental investigation ofthe steel tube material properties. Fig. 4 plots the load–axialshortening behaviour of concrete-filled steel tube specimens C9and C11. The specimens had the same nominal concrete cube


Table 2Comparison between test and finite element analysis of concrete-filled steeltube column strengths

Specimen PTest (kN) PFE (kN) PTestPFE

C1 539.0 534.9 1.01C2 805.8 801.0 1.01C7 1 380.0 1 364.0 1.01C9 1 413.0 1 511.5 0.93C8 1 787.0 1 805.6 0.99C12 998.0 1 015.9 0.98C11 1 067.0 1 144.0 0.93C14 1 359.0 1 419.3 0.96CC6-C-0 1 768.0 1 764.0 1.00CC6-D-0 2 778.0 2 772.0 1.00CC6-C-2 3 035.0 3 228.0 0.94CC6-C-4-2 3 647.0 3 820.0 0.95CC6-C-8 5 578.0 5 280.0 1.06CC6-D-2 5 633.0 6 000.0 0.94CC6-D-4-1 7 260.0 7 440.0 0.98CC6-D-8 11 505.0 11 640.0 0.99

Mean – – 0.98COV – – 0.037

Fig. 3. Comparison of experimental and finite element analysis load–axialshortening curves for specimens C1 and C2.

strength of 60 MPa, the same nominal diameter of 114 mm butwith different steel tube nominal plate thicknesses of 5.0 mmand 3.6 mm, respectively. It can be shown that there is goodagreement between experimental and numerical load–axialshortening behaviour. The column strengths predicted using thefinite element model for both columns were 7% greater thanthat observed from the tests.

The deformed shapes of the columns after failure observedfrom the tests were also compared with the finite elementanalysis prediction. The ABAQUS viewer [6] has been usedto plot the deformed shapes for all columns. Good agreementwas found between the experimental and numerical deformedshapes of the columns. Fig. 5 shows a comparison between thedeformed shapes of the column observed experimentally andnumerically for specimen C14. The concrete-filled steel tubecircular column C14 had a nominal diameter of 114 mm, a steeltube plate thickness of 3.6 mm and a column length of 300 mm.The column had a yield stress of the steel tube of 343 MPa anda concrete cube strength of 100 MPa.

Fig. 4. Comparison of experimental and finite element analysis load–axialshortening curves for specimens C9 and C11.

(a) Experimental. (b) FE analysis.

Fig. 5. Comparison of experimental and finite element analysis failure modesof specimen C14.

4. Parametric study and discussion

A total of 40 columns were analyzed in the parametric studyand the dimensions and material properties of the columnsare summarized in Table 3. The columns were divided into 8groups with different (D/t) ratios which is different from theapproach used in the experimental investigations conducted byGiakoumelis and Lam [4] and Sakino et al. [3]. The first fourgroups of columns G1, G2, G3 and G4 had the same overalllength of 300 mm and the same diameter of 114 mm whichare the same length and diameter as the specimens in the testsconducted by Giakoumelis and Lam [4] had. The steel tubeplate thicknesses of the first four groups of columns G1, G2,G3 and G4 were 7.60 mm, 2.85 mm, 2.07 mm and 1.63 mm,respectively. The diameter-to-steel tube plate thickness (D/t)ratio was 15, 40, 55 and 70 for groups G1, G2, G3 and G4,respectively. The slenderness ratio (D/t) was chosen less thana value of 125/( fy/250) which is equal to 91.1 in this casebased on the Bradford et al. [18] findings, to prevent localbuckling. The five columns investigated in each group hadconcrete cube strengths of 30, 50, 70, 90 and 110 MPa. The


Table 3Specimen dimensions and material properties for the parametric study

Group Specimen Dimensions Material propertiesL (mm) D (mm) t (mm) D/t Concrete fcu (MPa) Steel tube fy (MPa)

G1

S1 300 114 7.60 15 30 343S2 300 114 7.60 15 50 343S3 300 114 7.60 15 70 343S4 300 114 7.60 15 90 343S5 300 114 7.60 15 110 343

G2

S6 300 114 2.85 40 30 343S7 300 114 2.85 40 50 343S8 300 114 2.85 40 70 343S9 300 114 2.85 40 90 343S10 300 114 2.85 40 110 343

G3

S11 300 114 2.07 55 30 343S12 300 114 2.07 55 50 343S13 300 114 2.07 55 70 343S14 300 114 2.07 55 90 343S15 300 114 2.07 55 110 343

G4

S16 300 114 1.63 70 30 343S17 300 114 1.63 70 50 343S18 300 114 1.63 70 70 343S19 300 114 1.63 70 90 343S20 300 114 1.63 70 110 343

G5

S21 714 238 11.90 20 30 507S22 714 238 11.90 20 50 507S23 714 238 11.90 20 70 507S24 714 238 11.90 20 90 507S25 714 238 11.90 20 110 507

G6

S26 714 238 3.97 60 30 507S27 714 238 3.97 60 50 507S28 714 238 3.97 60 70 507S29 714 238 3.97 60 90 507S30 714 238 3.97 60 110 507

G7

S31 1080 360 8.00 45 30 525S32 1080 360 8.00 45 50 525S33 1080 360 8.00 45 70 525S34 1080 360 8.00 45 90 525S35 1080 360 8.00 45 110 525

G8

S36 1080 360 6.55 55 30 525S37 1080 360 6.55 55 50 525S38 1080 360 6.55 55 70 525S39 1080 360 6.55 55 90 525S40 1080 360 6.55 55 110 525

measured stress–strain curve of a steel tube with a nominal platethickness of 3.6 mm having a yield stress of 343 MPa was usedin the finite element model for G1, G2, G3 and G4.

The concrete-filled steel tube columns of groups G5 and G6had a diameter of 238 mm as used in the tests conducted bySakino et al. [3] and plate thicknesses of 11.9 mm and 3.97 mm,respectively. The (D/t) ratio was 20 and 60 for groups G5 andG6, respectively. The slenderness ratio (D/t) was also chosenless than a value of 125/( fy/250) which is equal to 61.6 inthis case, to prevent local buckling. A tri-linear stress–straincurve for specimen CC6-C-0 having a yield stress of 507 MPawas used in the material model for groups G5 and G6. Theconcrete-filled steel tube columns of groups G7 and G8 hada diameter of 360 mm, which is the same diameter as thespecimens used in the tests conducted by Sakino et al. [3] had,and plate thicknesses of 8 mm and 6.55 mm respectively. The

(D/t) ratios were 45 and 55 for groups G7 and G8, respectively.The slenderness ratio (D/t) was chosen less than a value of125/( fy/250) which is equal to 59.5. A tri-linear stress–straincurve for specimen CC6-D-0 having a yield stress of 525 MPawas used in the finite element model for groups G7 and G8.

The strength of the concrete-filled steel tube circularcolumns and the load–axial shortening behaviour were obtainedfrom the parametric study. Table 4 summarizes the columnstrengths analyzed in the parametric study using the finiteelement model. For groups G1, G2, G3 and G4 having the samediameter of 114 mm, it can be clearly seen that the columnstrength increases due to the decrease of the D/t ratio up to55. The column strength slightly increases for D/t ratios of55 and 70. It is also shown that the relationship between thecolumn strengths and the concrete cube strengths increasesapproximately linearly as the concrete strength increases, as


Table 4Comparison of column strengths obtained from parametric study and design calculation

Group Specimen Analysis Design ComparisonPFE (kN) PEC4 (kN) PACI/AS (kN) PFE/PEC4 PFE/PACI/AS

G1

S1 1 560.0 1 554.2 1 028.2 1.00 1.52S2 1 664.0 1 670.4 1 132.5 1.00 1.47S3 1 760.0 1 786.9 1 236.8 0.98 1.42S4 1 848.0 1 903.6 1 341.1 0.97 1.38S5 1 936.0 2 020.7 1 445.4 0.96 1.34

G2

S6 757.5 798.5 529.5 0.95 1.43S7 877.3 939.6 654.8 0.93 1.34S8 1 009.7 1 081.6 780.1 0.93 1.29S9 1 155.5 1 224.0 905.5 0.94 1.28S10 1 290.8 1 366.9 1 030.8 0.94 1.25

G3

S11 567.9 654.3 443.2 0.87 1.28S12 700.1 800.4 572.2 0.87 1.22S13 847.1 947.3 701.2 0.89 1.21S14 992.8 1 094.9 830.1 0.91 1.20S15 1 140.2 1 242.8 959.1 0.92 1.19

G4

S16 491.3 459.1 329.7 1.07 1.49S17 641.1 612.5 463.4 1.05 1.38S18 791.1 766.7 597.2 1.03 1.32S19 938.1 921.4 730.9 1.02 1.28S20 1 085.6 1 076.4 864.7 1.01 1.26

G5

S21 7 360.0 7 782.3 5 206.5 0.95 1.41S22 7 920.0 8 455.1 5 819.4 0.94 1.36S23 8 520.0 9 130.4 6 432.2 0.93 1.32S24 9 080.0 9 808.1 7 045.1 0.93 1.29S25 9 600.0 10 488.1 7 657.9 0.92 1.25

G6

S26 2 932.0 3 694.8 2 540.9 0.79 1.15S27 3 580.0 4 487.8 3 247.9 0.80 1.10S28 4 240.0 5 286.1 3 954.8 0.80 1.07S29 4 880.0 6 088.4 4 661.8 0.80 1.05S30 5 520.0 6 893.8 5 368.7 0.80 1.03

G7

S31 8 440.0 10 391.5 7 017.3 0.81 1.20S32 9 880.0 12 150.5 8 598.0 0.81 1.15S33 11 360.0 13 920.7 10 178.6 0.82 1.12S34 12 800.0 15 699.9 11 759.2 0.82 1.09S35 14 280.0 17 486.3 13 339.9 0.82 1.07

G8

S36 7 200.0 9 127.1 6 231.0 0.79 1.16S37 8 680.0 10 924.5 7 838.4 0.79 1.11S38 10 160.0 12 733.9 9 445.8 0.80 1.08S39 11 600.0 14 552.4 11 053.2 0.80 1.05S40 13 080.0 16 378.1 12 660.6 0.80 1.03

Mean, Pm – – – 0.90 1.24COV, VP – – – 0.096 0.111Reliability index, β – – – 2.22 3.38

shown in Fig. 6. The load–axial shortening curves of theconcrete-filled steel tube circular columns obtained from theparametric study were plotted for all groups. Figs. 7 and 8 showthe load–axial shortening curves of groups G2 (D = 114 mmand D/t = 40) and G5 (D = 238 mm and D/t = 20),respectively. It can be seen that the ductility of the columns isdecreased as the concrete strength increases.

5. Comparison with design rules

The ultimate axial strengths of concrete-filled steel tubecircular columns obtained from the parametric study werecompared with the design strengths predicted by the Eurocode

4 (EC4) [7], American Specifications (ACI) [8] and (AISC) [9]and Australian Standards (AS3600) [10] and (AS4100) [11]. Incalculating the design strengths, the unity material partial safetyfactors were used. The EC4 provides design rules for concreteencased as well as partially encased steel sections and concrete-filled sections with or without reinforcement. The code takesinto account the concrete confinement by the circular steelhollow sections. The EC4 equation for ultimate axial capacity(PEC4) of a concrete-filled steel tube circular column is given as

PEC4 = As fyη2 + Ac fc

(1 + η1

t

D

fy

fc

)(7)


Fig. 6. Column strength and concrete cube strength relationships obtained fromparametric study.

Fig. 7. Load–axial shortening curves for different concrete strengths forcolumns of group G2.

Fig. 8. Load–axial shortening curves for different concrete strengths forcolumns of group G5.

where As is the cross-sectional area of the steel tube, Ac is thecross-sectional area of the concrete and η1 and η2 are coeffi-cients of confinement for concrete and steel tube, respectively.In the calculation of column strengths using EC4, the effectivelength of the column is taken as one-half of the column length.

The American Specifications and Australian Standards(ACI/AS) use similar formulas for calculating the ultimateaxial capacity of the concrete-filled columns. Neither ofthese specifications takes into consideration the concreteconfinement. The ACI/AS equation for ultimate axial capacity

(PACI/AS) of a concrete-filled circular column is given as

PACI/AS = 0.85Ac fc + As fy (8)

Table 4 shows the comparison of the column strengthsobtained from the parametric study with the design strengthscalculated from Eqs. (7) and (8) for EC4 and ACI/AS,respectively. It can be seen that the American Specifications andAustralian Standards ACI/AS are conservative in calculatingthe design strengths for all columns. The reason is that theACI/AS does not take into consideration the confinement of theconcrete by the steel tubes, which has a very significant effecton concrete-filled compact steel columns. For example columnstrengths predicted by the ACI/AS (PACI/AS) for groups G6 andG8 are less than that predicted from the FE model (PFE) by3 to 16% for different concrete strengths. On the other hand,the column strengths PACI/AS of group G1 are considerablyless than PFE, by 34% to 52% for different concrete strengths.The mean value of the PFE/PACI/AS ratio is 1.24 with thecorresponding coefficient of variation (COV) of 0.111.

The design strengths predicted by EC4 are generallyunconservative, except for the specimens in group G4 (D/t =70) and specimen S1. The EC4 design strengths were close tothat of the FE model prediction for groups G1, G5, G2 and G4having the D/t ratios of 15, 20, 40 and 70, respectively, witha maximum deviation of 8%. The mean value of the PFE/PEC4ratio is 0.9 with the corresponding COV of 0.096.

6. Reliability analysis

The reliability of the column design rules is evaluatedusing reliability analysis. The reliability index (β) is a relativemeasure of the safety of the design. In general, a larger valueof β reflects that the design is more reliable. The resistancefactor (φ) of 0.85 was used in the reliability analysis. A loadcombination of 1.2 DL + 1.6 LL as specified in the AmericanSociety of Civil Engineers Standard (ASCE) [19] was used inthe reliability analysis, where DL is the dead load and LL isthe live load. The statistical parameters Mm = 1.10, Fm =1.00, VM = 0.10 and VF = 0.05 were used, which are themean values and coefficients of variation for material propertiesand fabrication factors. The statistical parameters Pm and VPare the mean value and coefficient of variation for the columndesign rules, as shown in Table 4. A correction factor CPin the reliability analysis was also used to account for theinfluence of the small number of tests as suggested by Pekozand Hall [20], and Tsai [21]. Reliability analysis is detailed inthe commentaries of the AISC Specification [9] and the NASSpecification [22]. The reliability index of 3.38 was obtainedfor the American Specifications and Australian Standards, buta smaller value of the reliability index of 2.22 was obtained forthe Eurocode 4, as shown in Table 4. Hence, the column designrules in the American Specifications and Australian Standardsare considered to be more reliable than those in the Eurocode 4.

7. Conclusions

An accurate nonlinear finite element model for the analysisof normal and high strength concrete-filled compact steel


tube circular stub columns has been presented. The confinedconcrete model has been accurately introduced. The measuredstress–strain curves for steel tubes were used to simulate theactual material of the steel tubes. The comparison betweenthe finite element results and the experimental results forthe columns with different concrete strengths and differentgeometric dimensions showed good agreement in predicting thebehaviour of the columns. The column strengths, load–axialshortening curves and deformed shapes of the columns havebeen predicted using the finite element model and comparedwell with the experimental results. A parametric study of40 concrete-filled compact steel tube circular columns withdifferent external diameters of the steel tube-to-plate thickness(D/t) ratio ranging from 15 to 70 and different concretecube strengths ranging from 30 to 110 MPa was performedusing the finite element analysis. The results of the parametricstudy showed that the column design rules specified inthe American Specifications and Australian Standards areconservative. However, the design strengths predicted by theEurocode 4 are generally unconservative. The column designrules in the American Specifications and Australian Standardsare capable of producing reliable limit state design whencalibrated with the resistance factor φ = 0.85 for theaxially loaded concrete-filled compact steel tube circular stubcolumns.

Acknowledgments

The authors are grateful to Professor Brian Uy, Departmentof Civil, Mining and Environmental Engineering, University ofWollongong, Australia, for his useful comments.

References

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behaviour of normal and high strength concrete-filled compact steel tube

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