Behaviour of cold-formed concrete-filled dual steel stiffened tubular short columns

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Introduction
Concrete-filled steel tubular (CFST) columns, as shown in Fig. 1(a), are an important structural solution in applications that require high load-carrying capacity.CFST columns combine the favourable properties of the constituent materials, steel and concrete, to be able to withstand extreme loads.Previous research has shown that CFST columns exhibit excellent seismic and compressive resistance behaviour [1][2][3][4][5][6].Owing to the presence of the outer steel tube, CFST columns tend to have higher bending stiffness compared with similarly-sized traditional reinforced concrete columns [7].The confining effect on the concrete provided by the outer steel tube adds to their capacity, and the presence of the concrete core can also prevent or delay local buckling of the steel tube.Additionally, the construction cost and time can be reduced because the steel tube acts as external formwork in the concrete pouring process.For these reasons, CFST columns have become increasingly popular in challenging engineering applications in recent years.
Whilst the advantages of CFST columns are clear, there are some challenges also associated with their use and behaviour.Firstly, in extremely high-loading scenarios such as in large-span structures and high-rise buildings, very large cross-sections may be required.For example, the diameter of the CFST column in the first storey of ShenZhen Saibo Plaza Building in China is 1600 mm which significantly reduces the useful interior space [8,9].In addition, the benefits to the cross-sectional strength through confinement of the concrete are less significant in relatively large sections [10,11].Secondly, the confinement effect is not effective in the elastic stage of CFST columns because the Poisson's ratio of steel is greater than that of concrete.This phenomenon reduces until the development of initial cracks in the concrete and lateral expansion of the concrete becomes larger than that of steel tubes.This phenomenon can be more pronounced for CFSTs with high strength concrete and thin-walled steel tubes [12].Finally, the fire resistance and the load-carrying capacity of CFST columns after the peak load has been reached cannot be guaranteed in some special cases.As a results of these disadvantages, some innovations have been proposed in the formation of composite columns [8,9,[13][14][15][16][17][18][19][20], such as the use of high strength concrete (HSC) or ultra-high strength concrete (UHSC), stiffeners to the steel tubes and the addition of internal steel tubes.
To date, there has been a considerable amount of experimental and numerical research studies into the behaviour of concrete-filled dual steel tubular columns.These are referred to as CFDST herein, as given in other publications, and a typical cross-section is presented in Fig. 1(b); it is noteworthy that CFDSTs may or may not have concrete included in the inner core region, and it is included herein as this is most relevant to the work presented.These are made using two metallic tubes with different dimensions concentrically positioned one inside the other, and concrete filling the entire cross-section.These sections tend to be smaller than CFSTs to carry comparable loads due to the addition of the inner steel tubes, resulting in efficient use of floor space and a lighter overall structure.Additionally, the integrity of these type of composite columns in some special cases is more reliable than CFSTs because the inner tube is protected by the infill concrete.The key properties of CFDST columns include high strength as well as excellent ductility and stiffness [19][20][21][22][23][24][25][26][27].Ekmekyapar and Al-Eliwi [20] conducted tests on the repair and strengthening behaviour of stressed and deformed CFST columns by converting them into CFDST columns.The test results showed that CFDST columns can be effectively used to repair CFST columns to increase their compression resistance, ductility and stiffness.Therefore, CFDST columns can be used as a strengthening solution in critical areas of the buildings.
Previous research has shown that including stiffeners in the crosssection can effectively delay local buckling of the outer steel tubes [28][29][30].In addition, lateral expansion of the steel tube can be reduced by using embedded stiffeners as shown in Fig. 2. In this case, the stiffeners enhance the bond between the steel tube and the concrete in the inelastic stage thus reducing the development of disproportionate deformations in the steel tube and concrete due to incompatibilities of the Poisson's ratio of steel and concrete.Moreover, using stiffeners can enhance the resistance of the section against lateral loads [31].However, the research into concrete-filled dual stiffened steel tubular (CFDSST) columns is limited.A schematic of a CFDSST section is shown in Fig. 1(c).Wang et al. [32] carried out a series of experiments to investigate the behaviour of CFDSST columns with a square stiffened hollow (SHS) outer section and a circular hollow inner section (CHS) under axial loading.The test results showed that the strength and ductility of the columns were excellent and enhanced by the presence of the inner steel tube and the stiffeners.The columns failed by local outward buckling of the outer square steel tube only when the sandwiched concrete was crushed and the stiffeners buckled.Additionally, Wang et al. [33][34][35] studied the behaviour of CFDSST columns under eccentric compression and the flexural and seismic performance of CFDSST columns.Zhang et al. [36] analysed the behaviour of CFDSST columns with inner circular tubes filled with UHSC through FE analysis.
It is clear that despite the promising performance of CFDSST members that there is a lack of experimental or numerical performance data in the literature, and therefore their behaviour is not fully understood.Therefore, the current paper presents an experimental and numerical study into the axial behaviour of CFDSST columns with inner square tubes.A total of 18 tests were conducted comprising 14 CFDSSTs, as shown in Fig. 3(a), and four other specimens made up of two CFSSTs (Fig. 3(b)) and two concrete-filled double-skin steel tubular columns without core concrete (abbreviated as D-CFSST in this paper, as shown in Fig. 3(c)) for comparison.The paper proceeds with a description of the tests and the results are presented and discussed.A finite element (FE) model was developed and is then described.The accuracy and reliability of the model were validated by comparison with the test results.Thereafter, the details of a parametric analysis are presented to study the behaviour of CFDSST columns with different variables.In the final portion of the paper, the design resistances calculated by using international specifications such as Eurocode 4 [37], BS5400 [38] and DBJ1315-2010 [39] are compared with the experimentally obtained resistances and design recommendations are provided.

General
A total of eighteen specimens were designed and fabricated for the experimental programme, including fourteen CFDSST columns, two CFSST columns and two D-CFSST columns.The cross-sections of the      1, where B o is the overall width of steel tube, t o and t i are the thicknesses of the outer and inner steel tubes, respectively, f yo and f yi are the yield strengths of the outer and inner steel tubes, f cu is the concrete compressive strength.The height of the longitudinal stiffeners h s was 25 mm for all tests.The first term in the specimen designations is either "S" or "SS" which refer to the 4 CFSSTs (G1) and D-CFSSTs (G2) included for comparison and the CFDSST columns (G3-G6), respectively.The next terms is either 160 or 180 and represents the width of the outer steel tubes (B o ), in mm.The last number (between 1 and 7) refers to an individual specimen, with individual characteristics (like geometry and material properties).The symbol "#" is used for the D-CFSST columns.
The main experimental parameters examined in this programme were (i) the presence, or not, of an inner steel tube; (ii) the inclusion of core concrete; (iii) the concrete compressive strength; and (iv) the D/B o ratio of the cross-section.The height (L) of the specimens was three  times the width of the outer steel tube (B o ).In addition, the second moment of area of the longitudinal stiffeners (I s ) was defined to meet the requirement proposed by Tao et al. [40] and given in Eq. (1):

Material properties
Based on the availability of materials in the market at the time of specimen preparation, carbon steel grade Q235 was used for the outer steel tubes and Q355 was used for the inner steel tubes and endplates in this experimental investigation.The properties of the carbon steel used for tube specimens were determined by conducting a series of tensile coupon tests.The coupon dimensions conformed to the Australian Standard AS 1391 [41] for the tensile testing of metals using 12.5 mm wide coupons with a gauge length of 50 mm, as detailed in Fig. 4. The actual yield strength of carbon steels can be seen as Table 1, which is taken as the average value of at least three repeat tensile tests.Note that since the width of the inner tubes was around 60-80 mm, the compactness of the concrete inside the inner tube is very important [42].Therefore, during the specimen preparation, the concrete was compacted carefully using a vibrator to increase the interlocking between the steel and concrete components.
Three concrete mixes with target cube compressive strengths of 40 MPa, 50 MPa and 70 MPa were employed in the test programme.The sandwiched concrete and the core concrete were filled with the same concrete mix, and the mix designs are presented in Table 2, together with the concrete cube strengths (f cu ).In the table, the w/c ratio refers to the water to cement ratio.It is also noteworthy that the mix design for C70 contained fly ash and silica fume, which are cement replacement products.They replaced 22% (fly ash) and 8% (silica fume) of the cement, with cement making up the remaining 70% in the mix design.
The CFDSST columns comprised two endplates, four lipped angles to create the outer steel tube, an inner steel section, sandwiched concrete between the two steel tubes and core concrete inside the inner steel section.The manufacturing process of the lipped angles to create the outer steel section is shown in Fig. 5.The specimens were made by first welding the inner steel tubes to the bottom endplate, which had a thickness of 20 mm.The four lipped angles were then welded together and welded to the bottom endplate.The concrete was filled into the steel tubes in the laboratory of the Southwest Petroleum University, China, and compacted by a vibrator.After 14 days of curing, a layer of highstrength mortar was applied to the top of each specimen to ensure uniformity of the top surface.28 days after pouring the concrete, another endplate with a thickness of 20 mm was welded to the upper end of each column.This process and the final specimens are shown in Fig. 6.It is noteworthy that the extended flanges which are in contact between adjacent angles (i.e. the longitudinal stiffeners) were welded together by spot welding for positioning purposes only and their contact was maintained mainly by the pressure of the infilled concrete on their inner surfaces.

Test methodology
The columns were tested in the structures laboratory at the Southwest University of Science and Technology, China using a 10,000 kN capacity hydraulic testing machine.The columns were instrumented with a series of strain gauges and dial (displacement) gauges at locations as shown in Fig. 7 and Fig. 8, respectively.There were two strain gauges on each side (labelled A-D) of the columns, with one in the longitudinal (L) and another in the transverse (T) direction.Fig. 8 shows a schematic view of the test set-up.The strains at the contact between the steel section inner surface and the concrete infill were not measured during the experiments, as they have been shown previously to be identical [43].All columns were positioned in the testing machine to ensure perfect alignment and verticality.Previous research [44] found that premature local crushing phenomena was observed at the end of short columns and researchers suggested using clamping devices on at ends of the columns to prevent localized crushing in this region.Accordingly, similar clamping devices were used in this programme as shown in Fig. 8. Additionally, the ultimate axial resistances (N ul,Exp ) of the test specimens were predicted numerically, using the finite element model described in this paper, before testing.Before the axial load reached a value equal to 0.5N ul,Exp , load control was adopted with a load interval of 0.25N ul,Exp and a loading rate of 5 N/s initially, and at each level the load was held for about 2 min.After that, displacement control was employed with a displacement rate of 0.5 mm/min until the axial force in the column in the descending branch of the response reached approximately 60% of the ultimate load capacity.This testing protocol was adopted following observations from other research programmes.Tao et al. [45][46] showed that the response in the ascending branch of the load-displacement curve can be controlled appropriately by loadcontrol, while this is more challenging during the softening phase, post-peak load.It was found that to achieve the most accurate response in the softening phase, displacement-control should be employed with a slow rate of displacement applied.Accordingly, in the current tests, load control was employed up to 50% of the peak load and then the controller was switched to displacement control to measure the ultimate load and the post-peak behaviour.This approach was also adopted by many other researchers (e.g.[47][48][49]).

Test results and discussion
The test results are presented in tabulated form in Table 1, and are discussed in the following sub-sections.The table presents the ultimate load in each test N ul,Exp , as well as the ductility index DI and the strength index SI.The ductility index DI is determined as given in Eq. ( 2), which was proposed by Tao et al. [40]: where ε 85% is the axial strain corresponding to 0.85N ul,Exp in the descending response of the load-axial strain response, and ε 75% is the axial strain corresponding to 0.75N ul,Exp in the ascending response of the load-axial strain curve.On the other hand, the strength index SI is calculated as given in Eq. ( 3): where N ul represents the maximum axial load (either in the experiments, in which case it is equal to N ul,Exp , or through other means such as finite element analysis, as discussed later in this paper) and N ul,s is determined as: In this expression, A ss , A si , A cs and A ci are the cross-sectional areas of the stiffeners, the inner steel tube, the sandwiched concrete and the core  concrete, respectively; f yo , f ys and f yi are the yield strengths of the outer steel section, the stiffeners and the inner steel tube, respectively; and f cs and f ci are the compressive strengths of the sandwiched concrete and the core concrete, respectively.The relationship between the concrete compressive strength (f cs and f ci ) and the concrete cube compressive strength (f cu ) is determined as given in Eq. ( 5): A sy,eff is the effective cross-sectional area of the outer steel tube as given in Eurocode 3 Part 1-1 [50] which accounts for local buckling which may take place in thin-walled steel tubes, and is given as: where ρ is the reduction factor for plate buckling, as defined in Eq. ( 7): and ψ is the stress ratio which it is taken as unity for symmetrical crosssections, while λ p is given by Eq. ( 8): In this expression, ε is taken as and k σ is taken as 4 when ψ = 1.

Ultimate loads and failure modes
The maximum loads carried by each specimen N ul,Exp is presented in Table 1.It is clear that the CFDSSTs generally reached greater loads compared with the CFSST and D-CFSST members.The strongest member of those examined was SS-180-3 which had the largest cross-section of those examined (B o = 180 mm), was filled with concrete with a compressive strength of 70.30MPa.Interestingly, this member did not necessarily contain steel sections with the highest yield strengths or thicknesses of those examined in this programme, and the concrete strength was clearly the most important material parameter in terms of the overall load-carrying capacity.This is explored in more detail later in this paper, together with an analysis of other important parameters to the overall load-displacement response.
The failure modes of all columns are shown in Fig. 9 and Fig. 10.It can be seen that all CFDSST columns failed due to local outward buckling of the outer steel tubes.However, although local buckling occurred at a number of locations along the columns length, as shown in the images, these did not occur in the same cross-section, which prevented the whole cross-section from failing with a sudden loss in load capacity.This may be a reason that the CFDSST columns had a greater post-failure bearing capacity compared with the CFSSTs or D-CFSST members.Additionally, no steel fracture was observed in the corner regions or welds of the test specimens.The prevention of corner fracture in particular, which may occur if the welds were in the corner regions, ensured good deformation capacity of the composite columns.
Additionally, it can be seen in Fig. 9 that local failure of the outer steel tube was more obvious with an increase in the concrete strength.This is because the higher strength concrete had less ductility and stiffness compared with lower strength concrete.Fig. 10 shows the failure modes of CFDSST columns with variation of t o or B i , and it can be seen that local failure of the outer steel tube was more obvious for members with a relatively thin outer tube and small width of the inner tube B i .This phenomenon highlights that specimens that employed a relatively thick outer tube and large inner tube width had greater performance owing to the confinement provided to the sandwiched concrete.After testing, the outer steel tube was removed from the columns where possible to observe the failure modes in the sandwiched concrete; the images from a typical specimen are presented in Fig. 11(a).The crushing in the sandwiched concrete occurred largely at the buckling location of the outer steel tube.This is because there was no confinement after buckling of the outer steel tube.Additionally, the deformation of the inner square steel tube is shown in Fig. 11(b) and it is observed that there was no obvious deformation owing to the effective restraint provided by the outer and inner concrete.This ensured that the CFDSST columns had higher post-failure bearing capacity and energy absorption capacity compared with the CFSST and D-CFSST columns.

Axial load versus axial strain responses
Fig. 12 presents the outer steel strain distribution of typical specimens, where the symbols L and T are used to denote longitudinal strain and transverse strain, respectively, and negative and positive values of the strain readings denote compression and tension, respectively.From the Fig. 12, it is observed that the outer steel tube was fully under compression due to the negative longitudinal strains measured during the tests.Additionally, the strain developed slowly until the ultimate resistance was reached, and relatively low levels of deformation occurred in the outer steel tube until the ultimate resistance was achieved.On the descending branch of the response, after the peak values were reached, the deformation of the outer steel tubes developed much more rapidly, especially in the transverse direction.This illustrates that the lateral confinement provided to the sandwiched concrete maximises after reaching the ultimate resistance.

Effect of the inner steel tube and core concrete
In order to comprehensively understand the behaviour of the CFDSST columns and their advantages, the effects of the inner steel tube and concrete are analysed in this section.Fig. 13 (1) In general, the axial load bearing capacity of CFDSST columns was higher than that of comparable CFSST and D-CFSST members.This is because the cross-section of the steel tube and concrete was higher than for CFSSTs and D-CFSSTs, respectively.This is further verified by examining Fig. 13(b) and (d) which present the normalised axial load versus axial shortening responses, whereby the loads on the y-axis are normalised against N ul,s , as given in of Eq. ( 4). ( 2) The residual bearing capacity of CFDSST columns was much higher than that of CFSST columns.Additionally, CFDSST columns showed better ductility than CFSST columns.This is also demonstrated in the normalised load graphs given in Fig. 13(b) and (d).
(3) The initial stiffness of CFDSST columns was greater than that of CFSST and D-CFSST columns.

Effect of concrete strength
The axial compressive behaviour of CFDSST columns with different concrete strengths is analysed in the current section.As observed in the axial load versus axial shortening results given in Fig. 14(a) and (c), the axial compressive bearing capacity of CFDSST columns tended to be greater for columns containing relatively higher strength concrete.Fig. 14(a) presents the data from group G3 as given in Table 1 and Fig. 14(c) presents the corresponding results for group G5.In these specimens the − 1, − 2 and − 3 terms of the designations represent members with f cu values of 49.18 MPa, 53.58 MPa and 70.30MPa, respectively.It is clear that the bearing capacity of the CFDSST columns increased by 32.5% for identical specimens with f cu values which increased from 49.18 MPa (SS-160-1 and SS-180-1) to 70.30 MPa (SS-160-3 and SS-180-3).On the other hand however, the ductility of the same members was greatly reduced.This is evidenced by the ductility index (DI) as presented in Table 1, which reduced from 1.94 to 1.40 for SS-160-1 to SS-160-3, and from 2.02 to 1.29 for SS-180-1 to SS-180-3.With reference to Fig. 14(b) and (d), which present the normalised axial load versus axial shortening responses, similar conclusion can be drawn.

Ductility
In order to determine the effect of the inner steel tube on the ductility of the section, the ductility coefficient DI is used to evaluate the ductility of the columns, as presented in Table 1 and graphically presented in Fig. 15.It is observed by comparison of the DI for S-160 and SS-160-1, SS-160-4 and SS-160-6 that the ductility of the CFSST column S-160 was significantly improved by adding the inner steel tube to create the CFDSST sections.The same result was also observed for the columns with B o = 180 mm.Additionally, the DI value decreased when the strength of the concrete increased, as previously discussed.

Compressive strength
The axial compressive strength of CFDSSTs is made up of the sum of the five individual components which form part of the cross-section (i.e. the outer steel tube, inner steel tube, stiffeners, sandwiched concrete and core concrete) as well as any contribution made through composite action (e.g.additional strength in the concrete due to confinement).With reference to the data presented in Table 1, it is clear that the concrete strength f cu was a very influential property in terms of the overall load-carrying capacity, as well as the overall geometry.As stated before, all of the CFDSSTs resisted greater axial loads compared with the comparable CFSSTs and D-CFSST columns examined.
To evaluate the influence of the stiffeners and the inner steel tube on ultimate strength, as well as the effect of composite action on the overall load-carrying capacity, the strength index (SI) as given in Eq. ( 3) was determined for each test specimen and the results are presented in Fig. 12. Strain versus axial load responses for typical specimens.Table 1.For the fourteen CFDSST columns, the SI values range from 0.925 to 1.182 and the average SI value is 1.032.SI values which are greater than unity indicate that the composite action, largely through confinement of the sandwiched concrete, is playing a role in the load capacity.On the other hand, the average SI value for the two CFSST columns is 1.083 with a corresponding value of 1.001 for the two D-CFSST columns examined.From Table 1, it is observed that the SI value for specimens with a side width of 160 mm is generally greater than for those with a width of 180 mm.This indicates that there was greater confinement provided to the sandwiched concrete by the outer steel tube for the smaller specimens.

Finite element (FE) analysis
The experimental study was designed to understand the influence of some key parameters on the behaviour of CFDSSTs.This study is supplemented in the current section by the development of a finite element analysis model, which is validated against the test data and then employed to conduct a more detailed parametric study than was possible with the physical tests.The model was developed using the ABAQUS software [51] as described hereafter.

Initial model conditions
The numerical models were initially developed based on the material and geometrical properties of the test programme as described in Table 1.Fig. 16 presents schematic views of the FE columns and mesh.Both the sandwiched concrete and the concrete core were modelled using solid elements, known as C3D8R in the ABAQUS library, and the endplates were also simulated using C3D8R elements.On the other hand, shell elements (S4R) were employed to simulate the outer and inner steel tubes; these were selected because they can capture local buckling modes in the steel tubes due to lateral expansion of the infilled concrete [52].To ensure computational convergence of the model and to reduce the computational time without compromising the accuracy of the results, the overall element size was taken as B o /10 following a mesh sensitivity study.The end conditions of the columns are as shown in Fig. 16, where reference points were located at the centre of both endplates.Except for the axial direction displacement at the loading end (U z ), all other translational degrees of freedom (U x and U y at the top end and U x , U y and U z at the bottom end) were restrained.Additionally, all rotational degrees of freedom (UR x , UR y and UR z ) at both ends of the column were restrained against movement.The columns were loaded in displacement control at the top of each member through the defined reference point.
The four lipped angles were restrained using a "tie" constraint between the contact faces of the stiffeners.Both endplates were set as rigid bodies and were effectively tied to the steel tube.A 'surface to surface contact' was defined at the interfaces between the concrete and steel elements and a 'hard contact' and 'penalty constraint algorithm' were selected to simulate the normal and tangential behaviour of the interactions between the interface of the steel tube and concrete as well as the interface of the concrete and the endplates.The bond and friction are important factors which influence the composite response.Liu et al. [43] studied the effect of the friction on axially loaded concrete filled steel tubular stub columns.It was shown that at the interface between the concrete and the steel tube, there was essentially no sliding between the two materials, indicating that the behaviour of CFST short columns is insensitive to the friction coefficient.In accordance with this study, the friction coefficient (μ) employed in the FE model developed herein for CFDSSTs was varied between 0.0 and 1.0 to explore its influence on the  axial capacity.The results for two of the specimens selected for illustration are presented in Table 3, where N ul,FE is the ultimate resistance obtained using the FE model.It is clear that μ has a negligible effect on the results and therefore, the value of the friction coefficient was taken as 0.6 in this study as recommended by Liu et al. [43] and Han et al. [53].

Initial imperfections and residual stresses
Residual stresses develop in steel sections during the fabrication process, and may play a role in the performance of CFDSST columns.
Previous studies show that tensile residual stresses σ rt are typically near or equal to the material yield stress f y [54] and the residual compressive stresses σ rc are generally taken as 0.2f y [55].The idealized residual stress distribution adopted in the current study is shown in Fig. 17.The effect of residual stress on the axial load-deformation curve for specimen SS-160-1 (selected for illustration) is shown in Fig. 18.Although it is believed that residual stresses are influential to the behaviour of thinwalled hollow tubes, this effect is not significant for thin-walled concrete-filled composite columns, as most the column's strength is due to the concrete core [45].
The effects of initial imperfections on the axial resistance of thinwalled stiffened composite columns were analysed by Tao et al. [45].Since short columns are not affected by global instability failure during loading, only local imperfections were considered in this study.The results demonstrate that although initial imperfections slightly reduce the overall capacity of composite columns, the influence is relatively small.Hence, the effect of initial imperfections and residual stresses on the ultimate resistance of CFDSST columns was neglected in the current study.It is noteworthy that similar conclusions were also determined elsewhere [56], when only axial compression behaviour was considered as in the current paper.

Material modelling
In this sub-section, the simulation of both the steel components and the concrete infill is described.All of the steel in the CFDSSTs is modelled using an identical material model, and this is also true for the concrete.For the steel sections, it is widely accepted that local buckling is more likely in square hollow sections compared with circular hollow sections, and also the benefits of concrete confinement can be less effective.Therefore, square CFST columns seldom demonstrate significant levels of strain hardening as they typically remain within the elastic region of the response [46].Hence, in the current analysis of CFDSSTs, an elastic-perfectly plastic material model was employed to simulate the steel material in both the inner and outer steel tubes.Additionally, to accurately describe the change in cross-sectional area, the true stress (σ true ) and logarithmic plastic true strain (ε true ) values were employed.These were calculated in accordance with Eqs. ( 9) and ( 10), respectively: where σ and ε are the engineering stress and strain, respectively.
For the sandwiched and core concrete, the commonly-used concrete damage plasticity (CDP) model in the ABAQUS library was employed.The stress-strain response for concrete proposed by Tao et al. [46] which accounts for confinement due to the steel tubes, was adopted, and this is presented in Fig. 19.It is observed that for confined concrete, the plateau stage from point A to point B reflects an increase in peak strain which occurs due to confinement.The strength increase due to confinement was captured in the simulation through the interaction between the steel sections and the concrete.The concrete constitutive relationship proposed by Tao et al. [46] and adopted in the FE model is expressed in Eq. ( 11):

√
, and these terms are defined as given in Fig. 19.The residual stress f r is taken as 0.1f c .The parameter α is determined in  accordance with Eq. ( 12) and β is taken as 0.92.The strain values at point A (ε c0 ) and at point B (ε cc ) were determined by Eqs. ( 13) and ( 14), respectively.
where f B was proposed by Tao et al. [46] based on a regression analysis, and as expressed as: The confinement factor ξ c is a crucial parameter for composite columns, and is expressed as:   where A s and A c are the cross-sectional areas of the steel tube and infill concrete, respectively, and f y and f ck are the characteristic design strengths of the two component materials, respectively, and f ck was taken as 0.67 f cu .To simplify the calculation, the stiffeners were not considered when determining A s and A c as suggested by Wang et al. [32] .

Validation of the FE model
The accuracy of the FE model for predicting the response of CFDSST columns was assessed by comparing the results with the experimental values described earlier in this paper.The ultimate resistances predicted by the model N ul,FE are listed in Table 1, together with the corresponding experimental values N ul,Exp , and the N ul,FE /N ul,Exp ratios.With a mean N ul,FE /N ul,Exp value of 1.008 and a coefficient of variation (COV) value of 0.064, it is observed that the proposed FE model provides an accurate prediction of the ultimate resistance of CFDSST short columns.
For further validation, a comparison of the experimental and predicted axial load versus displacement responses is presented in Fig. 20.Overall, it is shown that the FE model is able to provide a good depiction of the response.There are some discrepancies, which are attributed to the idealisation of the material properties and boundary conditions in  the FE model.The model is not able to capture an unknown or random material defects, slip at the supports and loading, or voltage interferences in the strain gauge measurements, for example.Nevertheless, the comparisons are reasonable and it is clear that the FE model captures the main behavioural trends including stiffening behaviour, peak loads and displacements and also the softening responses.

Parametric analysis
The validated FE model was employed to conduct a detailed parametric study, so that the key influential properties could be carefully examined.The variables examined included the yield strength of the outer and inner steel tubes, the strength of the sandwiched concrete and the core concrete, the depth of the stiffeners, the diameter-to-width ratio of the outer and inner steel tubes, and the hollow ratio χ.A total of 75 models were simulated, and these are divided herein into three different groups according to different B o values.The details and ultimate resistances obtained by the FE models of CFDSST columns are given in Table 4. Unless otherwise stated, the benchmark properties for the specimens examined are as follows: the yield strength and thickness of the outer section are taken as f yo = 235 MPa and t o = 2 mm, respectively; the concrete in both the sandwiched and core regions (f cs and f ci ) has a compressive strength of 40 MPa; the width, thickness and yield strength of the inner steel section are B i = 80 mm, t i = 3 mm and f yi = 355 MPa; and the height of the stiffeners h s is 30 mm.

Steel strength
The influence of steel yield strength of the outer and inner steel tubes on the behaviour of CFDSST columns was investigated by varying the grade of steel in the FE model.Four different yield strengths were examined, including 235, 355, 420 and 550 MPa.Note that despite the steel and concrete material strengths of columns S4, S11, S29, S36, S54, S61 are not compatible according to Liew et al. [57], they have been checked.The results are presented in Figs.21 and 22.It is observed that increasing the yield strength of the outer tube leads to a corresponding increase in the ultimate strength of CFDSST columns and an improvement in the ductility and stiffness of CFDSST columns.On the other hand, the behaviour and ultimate resistance of CFDSST columns were not greatly affected by increasing of the yield strength of the inner tube.Additionally, from Fig. 23, it can be seen that as the outer tube width increases, the ductility and post-failure bearing capacity decrease quite clearly.This is because the lateral confinement of the filled concrete reduces as the width of the outer tube increases, which is in agreement with previous research findings [10,11].With reference to Fig. 22(b) and (d), which present the normalised load versus axial shortening responses, it is observed that the behaviour of all the specimens is quite similar.The initial stiffness tends to increase with a reduction of B o , irrespective of the steel strength.Additionally, as in all cases, the normalised ultimate load is greater than unity, it is demonstrated that confirms the composite action in CFDSST columns is effective for strengthening the columns.It is also observed that the initial stiffness does not change for members made using hollow sections with different steel strengths.

Concrete strength
A range of different concrete values were examined, from normal strength concrete (NSC) with a compressive strength of 40 MPa, to ultrahigh strength concrete (UHSC) with a maximum compressive strength of 130 MPa.The concrete classification is based on the guidance given in Eurocode 2 Part 1-1 [58].The results are presented in Figs.23 and 24.It is clear that the influence of the sandwiched concrete between the two steel tubes is significant, with increased strength resulting in a corresponding improvement to the ultimate resistance of the column.On the other hand, the strength of the core concrete within the inner steel tube is significantly less influential to both the peak capacity as well as the overall behaviour.Additionally, as the width of the outer steel tube increases, the relative benefit of employing higher strength concrete in the sandwich region is even greater.This is because the concrete component of composite columns bears most of the compressive load under normal structural conditions, and the cross-sectional area of sandwiched concrete is larger as the width of the outer steel tube increases.With reference to the normalised axial load versus axial shortening graphs presented in Fig. 24(b), it is observed that the initial stiffness increases with a reduction in the cross-sectional width and the sandwiched concrete strength.Additionally, the normalised ultimate load is greater than unity in all cases, confirming the positive contribution made by composite action for these columns.Furthermore, as shown in Fig. 24(d), the effect of the core concrete strength on the normalised load versus axial shortening behaviour is negligible.

Stiffener depth h s
The depth of the stiffeners employed in the outer steel tubes was varied in the FE model.The minimum values examined were calculated  in accordance with the guidance proposed by Tao et al. [40], and reasonable maximum values were adopted based on engineering judgement.Accordingly, the range of values of stiffener depth examined for specimens with B o = 200 mm was between 22.3 and 50 mm, for those with B o = 280 mm, was 33 to 70 mm, and when B o = 400 mm, h s was varied between 50 and 90 mm.Fig. 25 illustrates the relationships between N ul,FE and h s .It is observed that the capacity was only slightly affected by changing the stiffeners depth and it is concluded that the increasing depth of stiffeners has little effect on the resistance of CFDSST columns.

B o /t o and B i /t i ratios
Figs. 26 and 27 present the influence that the width-to-thickness ratio of the outer steel tube (B o /t o ) and the inner steel tube (B i /t i ) has on the behaviour and resistance of CFDSST columns.From Fig. 26(a) and Fig. 27(a), it is observed that the ultimate resistance, ductility and post-failure bearing resistance of CFDSST columns reduces as the B o /t o ratio increases.This is due to the reduction in the confining stress of the concrete and the increased possibility of local buckling in the steel tubes.From Fig. 26(b) and Fig. 27(c), it is shown that the ultimate resistance of the columns only slightly reduces with an increase of the B i /t i ratio and this is generally a quite uninfluential parameter to the behaviour.This is because of the constraint effect of the concrete to the inner circular tube from both sides that prevent it from buckling locally.With reference to Fig. 26(b) and (d), it is observed that the initial stiffness tends to increase with a reduction in the cross-sectional width irrespective of B o /t o and B i / t i .

Hollow ratio χ
The hollow ratio χ in the current study is defined as the ratio of the width of the inner steel tube to that of the outer steel tube (i.e.B i /B o ).28 presents the effect of χ on the resistance of CFDSST columns whilst Fig. 29 presents the influence of χ on the axial load versus displacement response.It is observed that the ultimate resistance increases marginally for CFDSSTs with higher B i /B o ratios.As before, the total cross-sectional area of concrete is the most influential parameter to the load-carrying capacity, and therefore it is not surprising that the B i / B o ratio has little influence, since the total concrete volume remains unchanged.With reference to Fig. 29, it is shown that the ductility and post-failure load capacity generally increases for CFDSSTs with higher χ values.From Fig. 29(b), it is observed that the initial stiffness increases with a reduction in the cross-sectional width irrespective of the value of the hollow ratio χ.Moreover, increasing the hollow ratio χ of the columns results in relatively higher post-peak load behaviour, which may be attributed to the increase in the strength of the inner tubes.

Design resistance
Currently, there are no design specifications available for CFDSST columns in the international design standards.The applicability of the design expressions given in Eurocode 4 [37], BS 5400 [38] and DBJ 1315-2010 [39], which were developed for CFST composite columns, was examined in the current study for CFDSST columns.The results are presented in Table 5, where N ul,EC4 , N ul,BS5400 and N ul,DBJ represent the capacity values determined using Eurocode 4 [37], BS 5400 [38] and DBJ 1315-2010 [39], respectively.The following points are relevant to the calculations are results presented: (i) the effective area specified by Eurocode 3 [50] was employed to determine the cross-sectional area of the outer steel tube in these calculations, and (ii) the expressions given in Eurocode 4 [37] and BS 5400 [38] neglect the confinement effect of concrete for square cross-sections, while DBJ 1315-2010 [39] does take it into account.

Eurocode 4 [37]
The concrete compressive strength employed in the design expressions in Eurocode 4 [37] is equal to 0.85f c .The ultimate axial compressive resistance N pl,Rd is determined in accordance with Eq. ( 17), which has been adapted for CFDSST columns and is given here as N pl,EC4 in Eq. (18).
6.2.BS 5400 [38] According to BS 5400 [38], the compressive resistance of CFDSST columns N ul,BS5400 can be calculated in accordance with Eq. (19).It should be noted that the concrete cube strength (f cu ) is used in this equation and f cu,s and f cu,i represent the cube strength of the sandwiched concrete and the core concrete, respectively.
6.3.DBJ 1315 [39] The confinement effect of concrete is taken into account in this design method through a confinement factor ξ. The standard compressive strength of concrete (f ck ) is used and is taken as 0.67f cu .For CFDSST columns, the design resistance N ul,DBJ is given in Eq. ( 20) where f ck,s and f ck,i represent the standard compressive strength of the sandwiched concrete and core concrete, respectively.

Results and discussion
The predictions of the ultimate resistance from each of the design codes is presented in Table 5.It is observed that Eurocode 4 and BS 5400 tend to provide rather conservative predictions, and underestimate the ultimate resistances of CFDSST columns by 17% on average.On the other hand, DBJ 1315 [39] provides quite accurate predictions with a mean N ul,DBJ /N ul,FE ratio of 0.94 and a coefficient of variation (COV) of 0.036.The accuracy of this method compared with the others is attributed to the consideration given to the concrete confinement effect.In general, DBJ 1315 [39] provides the most suitable prediction for the ultimate resistance of CFDSST columns.In the above analysis, the buckling factor k σ employed with Eq. ( 8) was taken as 4, assuming that ψ = 1.It was proposed by Uy and Bradford [59] that in the current scenario as the steel plates are in contact with a rigid medium, i.e. the concrete infill, a more suitable value for k σ may be taken as 10.3.This  was employed elsewhere also [60], and more accurate and appropriate results were obtained.This value has been applied to the current analysis and the results are presented in Table 6.It is shown that employing k σ =10.3 provides better resistance values and DBJ 1315 [39] still provides the most accurate predictions.

Conclusions
This paper presents a detailed description of a series of tests on coldformed concrete-filled dual steel stiffened tubular (CFDSST) short columns under axial compressive load.These are very efficient members, which offer several advantages over existing typologies of composite column in terms of load-bearing capacity and resistance to local buckling.The tests results are analysed, and it is shown that the strength of the concrete is the most important factor to the overall capacity, and this is fully exploitable through the presence of the stiffened outer tube which provides confinement.The stiffeners also delay or prevent outward buckling of the steel section under compressive load.In addition to the experimental campaign, a detailed numerical investigation was also conducted and discussed here, and both the experimental and numerical findings were employed to examine the validity of existing design expressions.The following important conclusions are observed from the results presented: (1) The experimental test results indicate that CFDSST columns exhibit higher strength and superior ductility than concrete-filled stiffened steel tubular (CFSST) columns due to the presence of the inner square CFST component.All of the test specimens failed by local outward buckling of the outer steel tube, and no steel fracture was found in the corners and welds of the test specimens.
(2) The parametric study showed that increasing the sandwiched concrete strength (f cs ) effectively increase the axial resistance of CFDSST columns.Additionally, it was found that decreasing the B o /t o ratio and increasing the B i /B o ratio and yield strength of the outer tube (f yo ) can increase the ductility and post-failure load capacity of the CFDSST columns.(3) Based on the resistance comparisons of the experimental and numerical resistance values with the predictions from international design codes, it was shown that Eurocode 4 [37] and BS 5400 [38] provide overly conservative predictions.On the other hand, DBJ 1315-2010 [39] provides the most accurate ultimate resistance values for the CFDSST short columns, using a buckling factor of k σ =10.3 which is appropriate for steel plates in contact with a rigid medium.The better performance of this code, compared to the approaches in Eurocode 4 and BS 5400 is attributed to the inclusion of a parameter to account for confinement of the concrete, which is provided by the steel tubes.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Fig. 5 .
Fig. 5. Process of making the outer steel tube from steel plate to final tubular section.

Fig. 6 .
Fig. 6.Images of the CFDSST columns including (a) schematic of the layout (all units in mm) and (b) final specimens after preparation.

Fig. 7 .
Fig. 7. Locations of the strain gauges on the specimens including a (a) plan and (b) elevation view.
(a) and (c) present a comparison of the CFDSST axial load-shortening responses with those from the CFSST and D-CFSST columns.The following observations are drawn from this comparison:

Fig. 9 .
Fig. 9. Failure modes of test CFDSST columns with varying concrete strengths f c .

Fig. 10 .
Fig. 10.Failure modes of test CFDSST columns with varying values of t o or B.

Fig. 11 .
Fig. 11.Examination of the failure modes for a typical specimen including (a) concrete crushing and local buckling of the outer steel tube and (b) image of the inner steel tube with no obvious deformations.

Fig. 16 .
Fig. 16.Schematic of the FE model including (a) overall view with applied load-displacement, (b) the steel elements and (c) the concrete elements.

)Fig. 20 .
Fig. 20.Comparison between FE and experimental axial load-displacement responses of test specimens.

Fig. 21 .
Fig. 21.Influence of different yield strengths for (a) the outer tube and (b) the inner tube, on the ultimate resistance of CFDSST columns.

Fig. 22 .
Fig. 22. Influence of different yield strengths for (a and b) the outer tube and (c and d) the inner tube, on the axial load versus displacement responses of CFDSST columns.

Fig. 23 .
Fig. 23.Influence of different concrete strengths for (a) the sandwiched concrete and (b) the core concrete, on the ultimate resistance of CFDSST columns.

Fig. 24 .
Fig. 24.Influence of different concrete strengths for (a and b) the sandwiched concrete and (c and d) the core concrete.

Fig. 25 .
Fig. 25.Influence of stiffener depth on the resistance of CFDSST columns.

Fig.
Fig.28presents the effect of χ on the resistance of CFDSST columns whilst Fig.29presents the influence of χ on the axial load versus

Fig. 26 .
Fig. 26.Influence of (a) B o /t o and (b) B i /t i on the resistance of CFDSST columns.

Fig. 27 .
Fig. 27.Influence of (a and b) B o /t o and (c and d) B i /t i .

Table 1
Parameters and test results of CFDSST columns under axial loading.

Table 2
Concrete mix designs.

Table 3
Effect of friction coefficient on the axial resistance of CFDSST columns.
Fig. 17.Distribution of residual stresses in the outer section.

Table 4
Details of the parametric study on UHS-CFDDST slender columns.

Table 5
Design resistances from various international design codes.