Behaviour of stiffened concrete-filled steel composite ( CFSC )

This paper investigates the behaviour of axially loaded stiffened concrete-filled steel composite (CFSC) stub columns using the finite element software LUSAS. Modelling accuracy is established by comparing results of the nonlinear analysis and the experimental test. The CFSC stub columns are extensively developed using different special arrangements, number, spacing, and diameters of bar stiffeners with various steel wall thicknesses, concrete compressive strengths, and steel yield stresses. Their effects on the columns behaviour are examined. Failure modes of the columns are also illustrated. It is concluded that the parameters have considerable effects on the behaviour of the columns. An equation is proposed based on the obtained results to predict the ultimate load capacity of the columns. Results are compared with predicted values by the design code EC4, suggested equation of other researchers, and proposed equation of this study which is concluded that the proposed equation can give closer predictions than the others.


INTRODUCTION
The strength and stiffness of concrete-filled steel composite (CFSC) columns are optimised by the location of steel and concrete in their cross-sections.Steel is situated at the outer perimeter where it acts most efficiently in tension and in withstanding bending moments.Also, the stiffness of CFSC columns is considerably increased since the steel lies farthest from the centroid, where it contributes the greatest to the moment of inertia.Concrete makes an ideal core to resist compressive loads [4].Inward buckling of the steel wall is prevented by the concrete core which leads to the delay of the local buckling of the steel wall.Whilst spalling of the concrete core is prevented by the steel wall.Also, the steel wall eliminates the need for the longitudinal and transverse reinforcements and it behaves as permanent formwork to the concrete core which results in reducing materials and labours costs [10].The steel consumption in CFSC columns is less than the steel columns leading to cost saving.On the other hand, CFSC columns have structural benefits such as high strength, large stiffness, and high ductility.Also, the surface of concrete is protected from damage by the steel wall in CFSC columns.Simple connections can be utilised between steel floor beams and CFSC columns and extra work is not required to make the columns stiffer in the area of the connection.In CFSC columns, deformations due to shrinkage are negligible and deformations owing to creep are about one third of their reinforced concrete counterparts.By the use of CFSC columns, several floors can be constructed and construction loadings can be supported before the concrete filling during the construction stage which highlights using CFSC columns as a cost effective structural element in multi-storey buildings.The cross-sectional area of CFSC columns can be reduced owing to higher strength of the columns.Steel plate thickness can be decreased which leads to more savings in weight and material.The use of CFSC columns increases the speed of the construction process of a building in the upper stories which is because of the point that steel elements of higher levels can be fabricated even if concrete has not been filled in the lower column [34].Moreover, CFSC columns have ecological benefits over reinforced concrete columns: reinforcement and formwork are not used in CFSC columns which brings about a clean construction site; high strength concrete in CFSC columns which does not possess reinforcement can be crushed easily and reutilised as aggregates when the building is demolished; and the steel wall that peels from the concrete core can be reused [32].The aforementioned advantages of CFSC columns have shown their priority over steel and reinforced concrete columns and have also resulted in their expanding usage in modern construction projects throughout the world.
A high fire resistance can be achieved for CFSC columns compared to hollow steel tubular columns [18].Although, steel is a highly thermal conductive material, it quickly loses its strength and stiffness under fire exposure [6].Bailey [3] noted that for steel tubular columns, different fire protection methods may be used to improve the fire resistance which are mostly expensive and do not strengthen the columns.Concrete-infill has been considered as an effective temperature sink which decreases the temperature in the steel wall during fire.Moreover, since the temperature of the concrete core is increased much slower than that of the steel wall, the concrete core can afford proper load capacity even when the steel wall has a high temperature.When a CFSC column is subjected to fire, the different thermal properties of steel and concrete, and the steel wall trapping the concrete core can lead to having higher temperature for the steel wall than the concrete core.The different thermal expansions in the steel wall and the concrete core decrease their interaction.In the initial stage of exposure to fire, the steel wall carries the load [40].Then, since the steel wall attains critical temperature it yields which is led to the significant decrease of its strength.Therefore, the load is transferred from the steel wall to the concrete core.The concrete core prevents the steel wall from inward buckling.But, after fire exposure, outward buckling can be occurred meaning the local separation of the steel wall and the concrete core, and finally the column fails [22].Since the fire resistance of CFSC columns is higher than that of hollow steel tubular columns, it is not needed to provide external protection in most cases [38].However, according to Lua et al. [29], there are several methods for further improvement of the fire resistance of CFSC columns such as using external fire insulation coating, utilising steel reinforcements in the concrete core and using high performance concrete ( [16], [22], [25]).Also, adding fibres to concrete is an effective method in order to obtain high performance concrete to attain higher fire resistance ( [23], [31]).
A series of research works have been carried out on the behaviour of the CFSC columns.Uy and Patil [46] assessed the use of high strength concrete in steel box columns.22 high-strength rectangular concrete-filled steel hollow section stub columns with aspect ratios of 1, 1.5, and 2 were tested under axial concentric loading by Liu et al. [28].Han et al. [17] experimentally investigated 50 self-consolidating concrete-filled hollow structural steel stub columns subjected to an axial load.Tao et al. [42] carried out tests on concrete-filled steel tubular stub columns with inner and outer welded longitudinal steel stiffeners under axial compression.Tests on concrete-filled stiffened thin-walled steel tubular columns were performed by Tao et al. [41].Behaviour and design of axially loaded concrete-filled stainless steel columns were evaluated by Lam and Gardner [24].The data from 1819 tests on concrete-filled steel tube columns were summarised by Good and Lam [14] and the failure loads of the columns were also compared with the predictions of the code EC4 [11].The comparison with the code illustrated that the code can be confidently utilised and generally agrees well with the test results.32 concrete-filled steel tubular stub columns were experimentally studied under axially local compression by Han et al. [15].
Tests on concrete-filled composite columns were done by Liew and Xiong [26] to assess the effect of Latin American Journal of Solids and Structures 10(2013) 409 -440 preload on the axial capacity of the columns.Tao et al. [43] conducted experiments on concrete-filled stiffened thin-walled steel tubular columns under axial loading.Tests on concrete-filled double skin columns were carried out under compression by Uenaka et al. [45].Oliveira et al. [36] experimentally evaluated passive confinement effect of the steel tube in concrete-filled steel tubular columns.An experimental and analytical investigation on concrete-filled tubes with critical lengths ranging from 131 cm to 467 cm was performed by Muciaccia et al. [33].Uy et al. [47] tested short and slender concretefilled stainless steel tubular columns to investigate their performance under axial compression and combined action of axial force and bending moment.Nonlinear behaviour of concrete-filled steel composite slender columns was studied by Bahrami et al. [1] to evaluate and develop different shapes (V, T, L, Line, & Triangular) and number (1 on side & 2 on side) of longitudinal cold-formed steel sheeting stiffeners and also to assess their effects on the structural behaviour of the columns.However, research works on the behaviour of stiffened CFSC stub columns are limited.
This paper deals with the behaviour of the stiffened concrete-filled steel composite (CFSC) stub columns subjected to axial loading.Verification of the proposed three-dimensional (3D) finite element modelling is performed by comparison of the finite element result with the existing experimental result presented by Tao et al. [42].The verification demonstrates that the proposed finite element modelling of this study can accurately predict the behaviour of the columns.The CFSC stub columns are widely developed using different special arrangements, number, spacing, and diameters of bar stiffeners with various steel wall thicknesses, concrete compressive strengths, and steel yield stresses.Extensive parameters are considered in the nonlinear finite element analyses to investigate the behaviour of the columns.The main parameters are: (1) arrangements of bar stiffeners (C1 and C2); (2) number of bar stiffeners (2, 3, and 4); (3) spacing of bar stiffeners (from 50 mm to 150 mm); (4) diameters of bar stiffeners (from 8 mm to 12 mm); (5) steel wall thicknesses (from 2 mm to 3 mm); (6) concrete compressive strengths (from 30 MPa to 50.1 MPa), and (7) steel yield stresses (from 234.3 MPa to 450 MPa).Effects of different number and spacing of the bar stiffeners and also steel wall thicknesses on the ultimate load capacity and ductility of the columns are examined.In addition, effects of various arrangements and diameters of the bar stiffeners, concrete compressive strengths, and steel yield stresses on the ultimate load capacity of the columns are evaluated.Failure modes of the columns are assessed.An equation is also proposed based on the obtained results to predict the ultimate load capacity of the columns.The ultimate load capacities achieved from the nonlinear finite element analyses are compared with predicted values by the design code EC4 [11], equation of other researchers, and proposed equation of this study.

FINITE ELEMENT MODELLING
The nonlinear 3D finite element modelling was conducted by the use of the finite element software LUSAS to simulate the CFSC stub columns.The stub column experiment carried out by Tao et al. [42] has been chosen for the nonlinear finite element modelling in this paper.The steel wall thickness (t) and cross-section of the column were 2.  In order to accurately simulate the actual behaviour of the columns, crucial parameters such as finite element type, mesh, concrete-steel interface, boundary conditions, and load application are needed to be taken into account in the simulation of the columns.Meanwhile, constitutive models of the steel wall, steel bar stiffeners, and concrete are important which should be suitably considered in the modelling.
2.1 Finite Element Type, Mesh, Concrete-Steel Interface, Boundary Conditions, and Load Application The element library of the finite element software LUSAS (Finite Element Analysis Ltd. [12]) was used to select the type of elements for the steel wall and concrete core of the columns in this study.The 6noded triangular shell element, TSL6, was used for modelling of the steel wall.This is a thin, doubly curved, isoparametric element which can be utilised to model 3D structures.This element can accommodate generally curved geometry with varying thickness and anisotropic and composite material properties.The element formulation takes account of both membrane and flexural deformations.The steel bar stiffeners were modelled by the 3-noded bar element type BRS3.This is an isoparametric bar element in 3D which can accommodate varying cross-sectional area.This element is suitable for modelling stiffening reinforcement with continuum elements.The 10-noded tetrahedral element, TH10, was utilised to model the concrete core.This is a 3D isoparametric solid continuum element capable of modelling curved boundaries.This type of element is a standard volume element of the LUSAS software.
Different finite element mesh sizes were tried to find a reasonable mesh size which can provide accurate results.Consequently, it was uncovered that the mesh size corresponding to 7713 elements can obtain exact results.Therefore, this mesh size was used in the nonlinear finite element analyses to accurately predict the behaviour of the columns.Figure 2 illustrates a typical finite element mesh used herein.
Latin American Journal of Solids and Structures 10(2013) 409 -440 Figure 2 A typical finite element mesh Slidelines were employed to represent the contact between the concrete core and steel (comprising steel wall and steel bar stiffeners).The slidelines are attributes which can be utilised to model contact surfaces in the finite element software LUSAS.The slideline contact facility is nonlinear and was used in the nonlinear analyses.Slave and master surfaces needed to be correctly selected to provide the contact between surfaces of steel and concrete.If a smaller surface is in contact with a larger surface, the smaller surface can be best selected as the slave surface.If it is not possible to distinguish this point, the body which possesses higher stiffness should be selected as the master surface.It needs to be highlighted that the stiffness of the structure should be considered not just the material.Although, the steel material is stiffer than the concrete material, steel may have less stiffness than the volume of the concrete core herein.As a result, the concrete core and steel surfaces were respectively selected as the master and slave surfaces.This process of choosing master and slave surfaces has been also stated by Dabaon et al. [5].The definition of properties such as friction coefficient is allowed in the slidelines.The friction between two surfaces, the concrete core and steel, is considered so that they can be in contact.The Coulomb friction coefficient in the slidelines was chosen as 0.25.The slidelines allow the concrete core and steel to separate or slide but not to penetrate each other.
Pin-ended supports of the corresponding experiment have been accurately simulated in the finite element modelling in this study.Accordingly, the rotations of the top and bottom surfaces of the columns in the X, Y, and Z directions were considered to be free.Also, the displacements of the top and bottom surfaces in the X and Z directions were restrained.On the other hand, the displacement of the bottom surface in the Y direction was restrained while that of the top surface, in the direction of the applied load and where the load was applied, was set to be free.The axial loading of the experiment has been appropriately simulated using incremental displacement load with an initial increment of 1 mm applied axially to the top surface of the columns in the negative Y direction.

Constitutive Models
Materials used in the numerical analysis consist of steel wall, steel bar stiffener, and concrete.Constitutive models of the materials play a vital role in the behaviour of the columns and are presented in the following:

Steel Wall
Modelling of the steel wall has been carried out as an elastic-perfectly plastic material in both tension and compression.The stress-strain curve used for the steel wall is shown in Figure 3(a).The yield stress, modulus of elasticity, and Poisson's ratio of the steel wall have been respectively taken as 234.3 MPa, 208,000 MPa, and 0.247 that are identical to those in the corresponding experiment.Von Mises yield criterion, an associated flow rule, and isotropic hardening have been also utilised in the nonlinear material model.

Steel Bar Stiffener
The uniaxial behaviour of the steel bar stiffener is similar to that of the steel wall.Therefore, it can be simulated by the elastic-perfectly plastic material model (Figure 3(a)).The yield stress and modulus of elasticity of the steel bar stiffener have been considered as 400 MPa and 200,000 MPa, respectively.

Concrete
The compressive strength and modulus of elasticity of concrete have been respectively adopted as 50.1 MPa and 35,100 MPa which are the same as those in the corresponding experiment.Figure 3(b) shows the equivalent uniaxial stress-strain curves for concrete (Ellobody and Young [7,8]) which have been used in this study to model concrete.The unconfined concrete cylinder compressive strength f c = 0.8f cu in which f cu is the unconfined concrete cube compressive strength.In accordance with Hu et al. [19], the corresponding unconfined strain ε c is usually around the range of 0.002-0.003.They considered ε c as 0.002.The same value for ε c has been also taken in the analysis herein.When concrete is under laterally confining pressure, the confined compressive strength f cc and the corresponding confined strain ε cc are much greater than those of unconfined concrete.Equations ( 1) and ( 2) have been used to respectively obtain the confined concrete compressive strength f cc and the corresponding confined stain ε cc , as presented by Mander et al. [30]: where f 1 is the lateral confining pressure of the steel wall on the concrete core.The approximate value of f 1 can be interpolated from the values reported by Hu et al. [20].According to Richart et al. [37], the factors of k 1 and k 2 have been taken as 4.1 and 20.5, respectively.Since f 1 , k 1 and k 2 are known f cc and ε cc can be calculated by the use of Equations ( 1) and ( 2).The equivalent uniaxial stress-strain curve for confined concrete (Figure 3(b)) comprises three parts which are needed to be defined.The first part consists of the initially assumed elastic range to the proportional limit stress.The value of the proportional limit stress has been adopted as 0.5f cc , as recommended by Hu et al. [20].The empirical Equation (3) has been used to determine the initial Young's modulus of confined concrete E cc .The Poisson's ratio υ cc of confined concrete has been considered as 0.2. MPa. ( The second part includes the nonlinear portion which starts from the proportional limit stress 0.5f cc to the confined concrete strength f cc .The common Equation (4) presented by Saenz [39] can be used to determine this part.The values of uniaxial stress f and strain ε are the unknowns of the equation which define this part of the curve.The strain values ε have been considered between the proportional strain (0.5f cc /E cc ), and the confined strain ε cc which corresponds to the confined concrete strength.Equation ( 4) can be used to determine the stress values f by assuming the strain values ε. ( in which R E and R are: The constants R ε and R σ have been adopted as 4 in this study, as reported by Hu and Schnobrich [21].The third part of the curve is the descending part which is between f cc and rk 3 f cc with the corresponding strain of 11ε cc .k 3 is the reduction factor dependent on the H/t ratio.Empirical equations proposed by Hu et al. [20] can be utilised to determine the approximate value of k 3 .To consider the effect of different concrete strengths, the reduction factor r was introduced by Ellobody et al. [9] on the basis of the experimental study carried out by Giakoumelis and Lam [13].According to Tomii [44] and also Mursi and Uy [35], the value of r has been adopted as 1.0 for concrete with cube strength f cu equal to 30 MPa and as 0.5 for concrete with f cu greater than or equal to 100 MPa.The value of r for concrete cube strength between 30 MPa and 100 MPa has been calculated by the use of linear interpolation.

Modelling Verification
Verification of the finite element modelling was carried out by comparison of the modelling result with the experimental result reported by Tao et al. [42].Figure 4 demonstrates that the load-normalised axial shortening curves obtained from the modelling and corresponding experiment agree well with each other.The obtained ultimate load capacity from the finite element analysis is 3325 kN while that from the experiment is 3230 kN.Accordingly, their difference is only 2.9% which uncovers the accuracy of the modelling.As a consequence, the proposed 3D finite element modelling can accurately predict the behaviour of the columns herein.Because the accuracy of the proposed 3D finite element modelling of this study was demonstrated, the method was used for the nonlinear analysis of stub columns of same size and cross-section as that tested by Tao et al. [42] but with bar stiffeners.Each of the CFSC stub columns was accurately modelled based on the described modelling features.Figure 5 illustrates details of the stiffened CFSC stub columns which were analysed by the use of nonlinear finite element method.As can be seen from Figure 5 (a, b), 2 different special arrangements of the bar stiffeners namely C1 and C2 are considered in this study.Also, various number (2, 3, and 4) and spacing of the bar stiffeners (50 mm, 100 mm, and 150 mm) are adopted in the columns in which 2 typical elevations are shown in Figure 5 (c, d).In addition, typical finite element meshes of the stiffened CFSC columns are illustrated in Figure 6.Table 1 summarises specifications and obtained ultimate load capacities of the analysed CFSC stub columns.C1 and C2 in the column labels represent the columns with different special arrangements of the bar stiffeners as illustrated in Figure 5 (a, b).The first four numbers following C1 and C2 respectively denote the steel wall thickness t (mm), diameter of bar stiffener D (mm), steel wall yield stress f y (MPa), and concrete compressive strength f c (MPa).Also, the number before the parentheses is the number of the bar stiffeners and the number in the parentheses represents the centre-to-centre spacing (mm) between the bar stiffeners.Moreover, the load eccentricity (e) for those eccentrically loaded columns is added to the columns labels as the last number after the parentheses, i.e. 30 and 60 respectively stand for the load eccentricities of 30 mm and 60 mm.Effects of various parameters on the behaviour of the columns are presented in the following sections.The CFSC stub columns with two different special arrangements of bar stiffeners, C1 and C2, (Figure 5(a, b)) and various number of the bar stiffeners (2, 3, and 4) were analysed to investigate their effects on the behaviour of the columns.These effects on the ultimate load capacity are illustrated in Figure 7. Table 1 also summarises the corresponding ultimate load capacity values of the curves.
As can be seen from the figure and table, the use of the bar stiffeners increases the ultimate load capacity of the unsiffened CFSC stub column.As an example, the ultimate load capacity of the unstiffened column is 3325 kN which increases to 3760 kN by the use of 4C1 bar stiffeners (C1-2.5-10-234-50-4(50)),an improvement of 13.1%.Also, using 4C2 bar stiffeners (C2-2.5-10-234-50-4(50))leads to the ultimate load capacity of 3668 kN which is 10.3% higher than that of the unstiffened column.Therefore, the use of C1 bar stiffeners uncovered to be more effective on the increase of the ultimate load capacity of the unstiffened CFSC columns than C2 bar stiffeners.Moreover, as the number of the bar stiffeners is enhanced the ultimate load capacity is improved.For instance, the ultimate load capacity of the column with 2C1 bar stiffeners and spacing of 100 mm is 3424 kN (C1-2.5-10-234-50-2(100))which is enhanced to 3656 kN (C1-2.5-10-234-50-4(100))by the use of 4C1 bar stiffeners and the same bar spacing, an increase of 6.8%.

Effect of Spacing of Bar Stiffeners on Ultimate Load Capacity
To investigate the effect of spacing of bar stiffeners on the behaviour of the CFSC stub columns, three different bar spacing of 50 mm, 100 mm, and 150 mm were considered in the analyses.Figure 8 indicates this effect on the ultimate load capacity of the columns.In accordance with the figure and Table 1, the ultimate load capacity is increased by the decrease of spacing of the bar stiffeners.For example, by the decrease of spacing of the bar stiffeners from 150 mm to 50 mm with the same number of the bar stiffeners the ultimate load capacity is enhanced from 3486 kN (C1-2.5-10-234-50-3(150)) to 3661 kN (C1-2.5-10-234-50-3(50)),an increase of 5%.
Latin American Journal of Solids and Structures 10(2013) 409 -440 Three different diameters of bar stiffeners (8 mm, 10 mm, and 12 mm) were used in the analyses to uncover the effect of diameter of the bar stiffeners on the ultimate load capacity of the CFSC stub columns.Figure 10 illustrates the results.According to the figure and Table 1, larger diameter of the bar stiffeners results in higher ultimate load capacity.For instance, if the diameter of the bar stiffeners is enhanced from 8 mm to 12 mm for the same number and spacing of the bar stiffeners, the ultimate load capacity is increased from 3505 kN (C2-2.5-8-234-50-3(50)) to 3661 kN (C2-2.5-12-234-50-3(50)),an enhancement of 4.5%.In order to assess the ductility of the columns, a ductility index (DI) defined by Lin and Tsai [27] has been utilised in this paper.Equation ( 5) is the ductility index: (5) where ε 85% is the nominal axial shortening (∆/L) corresponding to the load which falls to its 85% of the ultimate load capacity and ε y is ε 75% /0.75 in which ε 75% is the nominal axial shortening corresponding Latin American Journal of Solids and Structures 10(2013) 409 -440 to the load that obtains 75% of the ultimate load capacity.The values of ε 85% and ε y can be taken from  The ductility of the unstiffened column can be determined as 2.85 from Figure 4 and using Equation ( 5).The use of 4C1 bar stiffeners (C1-2.5-10-234-50-4(50))and 4C2 bar stiffeners (C2-2.5-10-234-50-4(50)) in the unstiffened column improves the ductility of the column from 2.85 to 3.447 and 3.325 (Figure 11) respectively, which represent the maximum ductility increases of 20.9% and 16.7%, respectively.

Effects of Thickness of Steel Wall on Ductility
Equation (5) of the section 4.5 has been also used to evaluate the effect of steel wall thickness on the ductility of the columns.Figure 12 indicates this effect on the ductility of the columns.The ductility is improved by the increase of the steel wall thickness (Figure 12).As an example, the enhancement of the steel wall thickness from 2 mm to 3 mm enhances the ductility of the column C2-2-10-234-50-2(50) from 2.979 to 3.225 (C2-3-10-234-50-2(50)), an improvement of 8.3%.Two different load eccentricities of 30 mm and 60 mm were taken in the nonlinear analyses of the columns with C1-4(50) and C1-4(100) bar stiffeners to examine the effect of load eccentricity on the ultimate load capacity of the columns.Figure 13 illustrates this effect and Table 1 summarises its ultimate load capacity values.As it is evident from the figure and table, the load eccentricity increase adversely affects the ultimate load capacity.For example, enhancement of the load eccentricity from 30 mm (C1- The effect of various concrete compressive strengths (30 MPa, 40 MPa, and 50.1 MPa) on the ultimate load capacity of the columns is shown in Figure 14 along with their corresponding values in Table 1.It is obvious from the figure and table that the higher concrete compressive strength leads to higher ultimate load capacity of the columns.For example, as the concrete compressive strength is increased from 30 MPa to 50.1 MPa, the ultimate load capacity of the column C2-2.5-10-234-30-3(50) is enhanced from 2446 kN to 3583 kN (C2-2.5-10-234-50-3(50)),an enhancement of 46.5%.As can be seen from the figures, the failure modes of the columns were identified as concrete crushing about their mid-height where local buckling of the steel wall was induced.Also, the in-filled concrete prevented the steel wall from the buckling inward.Also, it can be noted that the increase of the ultimate load capacity and ductility due to the use of the bar stiffeners, increase of the number of the bar stiffeners, decrease of spacing of the bar stiffeners, enhancement of the steel wall thickness, or increase of diameter of the bar stiffeners can be owing to the enhancement of the confinement effect of the steel wall on the concrete core.This EC4 [11] is one of the popular international standards in composite construction which is used throughout the world.According to EC4 [11], the ultimate load capacity of a square or rectangular CFSC stub column can be calculated from Equation ( 6): N pl,Rd = A a f yd + A c f cd (6) where A a and A c are cross-sectional areas of steel and concrete respectively, and also f yd and f cd are yield stress of the steel wall and compressive strength of the concrete core, respectively.The predicted ultimate load capacities based on EC4 [11], N pl,Rd , are listed in Table 2 and compared with the values obtained from the nonlinear analyses of the columns, N u .SD and COV in  Increasing number of the bar stiffeners and/or steel wall thickness enhances the ultimate load capacity and ductility of the columns.The increase of the diameter of the bar stiffeners increases the ultimate load capacity.As spacing of the bar stiffeners decreases the ultimate load capacity and ductility are improved.The use of the bar stiffeners, increase of the number of the bar stiffeners, decrease of spacing of the bar stiffeners, enhancement of the steel wall thickness, or increase of diameter of the bar stiffeners enhances the confinement effect of the steel wall on the concrete core and delays the local buckling of the steel wall which leads to the increased ultimate load capacity and ductility.Enhancement of the load eccentricity decreases the ultimate load capacity of the columns.Also, if the concrete compressive strength is enhanced, the ultimate load capacity is increased because the use of higher concrete compressive strength significantly increases the bond strength of the columns with the stiffeners.Moreover, the higher steel yield stress results in higher ultimate load capacity.The improved ultimate load capacity of the columns owing to the increase of the concrete compressive strength and/or steel yield stress of the columns leads to utilising smaller column size and enhancing the usable floor space in a structure.The smaller size of CFSC columns results in more savings in weight and material of the structure.Meanwhile, the columns failed due to concrete crushing about their mid-height where the steel wall locally buckled.The inward buckling of the steel wall was prevented by the in-filled concrete.Based on the obtained results, an equation was also proposed to predict the ultimate load capacity of the columns.Furthermore, the ultimate load capacities of the columns were predicted based on EC4 [11], the equation of Baig et al. [2] and the proposed equation of this study and also compared with those obtained values from the nonlinear analyses.These comparisons revealed that the equations of EC4 [11] and Baig et al. [2] could respectively estimate the ultimate load capacities with 5.1% underestimation and 3% overestimation.On the other hand, the comparisons demonstrated that the proposed equation of this study could give a very close prediction of the ultimate load capacities with only 0.8% underestimation.
5 mm and 249 mm × 250.4 mm, respectively, as shown in Figure 1.The length of the column was 750 mm.

Figure 4
Figure 4 Load versus normalised axial shortening curves for the CFSC stub columns 3 NUMERICAL ANALYSIS

Figure 5
Figure 5 Details of the stiffened CFSC stub columns: (a) arrangement of C1 bar stiffener in the column, (b) arrangement of C2 bar stiffener in the column, (c) typical elevation of the column with 3C1 bar stiffeners and spacing of 100 mm, (d) typical elevation of the column with 3C2 bar stiffeners and spacing of 100 mm; (unit: mm)

Figure 6
Figure 6 Typical finite element meshes of the stiffened CFSC stub columns: (a) column with 4C1 bar stiffeners and spacing of 150 mm, (c) column with 4C2 bar stiffeners and spacing of 150 mm

Figure 7 Figure 8 Figure 9
Figure 7 Effects of arrangement and number of bar stiffeners on ultimate load capacity

Figure 10
Figure 10 Effect of diameter of bar stiffeners on ultimate load capacity

Figure 7 .
Figure 7. Effects of number and spacing of the bar stiffeners on the ductility are demonstrated in Figure 11.

Figure 11
Figure 11 Effects of number and spacing of bar stiffeners on ductility

Figure 12
Figure 12 Effect of thickness of steel wall on ductility 4.7 Effect of Load Eccentricity on Ultimate Load Capacity

Figure 13
Figure 13 Effect of load eccentricity on ultimate load capacity

Figure 14 Figure 15
Figure 14 Effect of concrete compressive strength on ultimate load capacity .

Figure 16 Figure 17
Figure 16 Typical failure modes of the stiffened CFSC stub columns with C1 bar stiffener: (a) 2 bar stiffeners with spacing of 50 mm, (b) 3 bar stiffeners with spacing of 100 mm, (c) 4 bar stiffeners with spacing of 150 mm

Table 1
Effects of Arrangement and Number of Bar Stiffeners on Ultimate Load Capacity [11]e 2 respectively stand for standard deviation and coefficient of variation determined for the ultimate load capacity values in the table.In accordance with the table, a mean ratio (N pl,Rd /N u ) of 0.949 is obtained with a COV of 0.035 which uncovers that EC4[11]gives the ultimate load capacity by 5.1% lower than the results obtained from the nonlinear analyses.

Table 2 continued
Behaviour of stiffened concrete-filled steel composite (CFSC) stub columns subjected to axial loading has been studied in this paper.The finite element software LUSAS was employed to carry out the nonlinear finite element analyses.Accuracy of the proposed 3D finite element modelling was demonstrated by comparison of the modelling result with the corresponding experimental result.It was uncovered that the proposed modelling can predict the behaviour of the columns accurately.The CFSC stub columns were extensively developed utilising different special arrangements, number, spacing, and diameters of bar stiffeners with various steel wall thicknesses, concrete compressive strengths, and steel yield stresses.It was shown that by the use of C1 and C2 bar stiffeners the ultimate load capacity and ductility of the columns are increased.