Behaviour of ultra-high strength concrete-filled dual-stiffened steel tubular slender columns

This paper is concerned with the behaviour of square concrete-filled dual-stiffened steel tubular (CFDSST) slender columns with a concentrically-placed inner circular steel tube. Previous studies have illustrated that these columns have greater structural performance in terms of load-carrying capacity compared with conventional concrete-filled stiffened steel tubular (CFSST) columns. However, the behaviour of CFDSST slender columns filled with ultra-high strength concrete (UHSC) has not been investigated and current design codes do not include provisions for UHSC, although it is increasingly popular owing to demands for structures to be lighter and more sustainable. Accordingly, the current paper fills that gap in existing knowledge and explores the behaviour of CFDSST slender columns using finite element (FE) analysis. The available test results from previous studies were collated and are employed to validate the numerical model. The validated FE model is then employed to investigate the axial load versus deflection responses for a wide variety of UHS-CFDSST slender columns. The behaviour of both intermediate-length and long columns is assessed through parametric analyses. The results of these studies show that the strength of the concrete sandwiched between the two steel sections, the yield strength of outer steel tube, and the outer tube slenderness ratio have a significant effect on the axial resistance of UHS-CFDSST intermediate-length columns, while the capacity of long columns is most affected by the sandwiched concrete strength. The ultimate resistances are compared with different available design methods, and AISC 360 – 16 code is recommended for predicting the ultimate resistance of UHS-CFDSST slender columns with modifications proposed to account for the different components forming this innovative cross-section.


Introduction
This paper investigates the behaviour of ultra high-strength concrete-filled, dual-stiffened steel tubular (CFDSST) slender columns, with a stiffened outer tube, a circular inner tube, and ultra high strength concrete for the infill regions.These are a relatively new type of composite cross-section, which can offer enhanced structural, economic and environmental benefits compared with traditional composite columns in appropriate scenarios.Composite columns, comprising steel sections working together with concrete in different arrangements, provide a very attractive structural solution as the two (or more) constituent materials work together to create strong, ductile members with excellent fire resistance properties.The most common forms composite column are concrete filled steel tubular (CFST) sections and concrete-filled double skin steel tubular (CFDST) columns, both of which can be made using variety of material types (e.g.hot-rolled carbon steel, stainless steel, regular concrete, high strength concrete, etc.).Both CFSTs and CFDSTs possess similar excellent strength and stability characteristics, whilst CFDSTs offer the additional benefits of enhanced ductility, energy absorption and fire resistance due to the thermally protected inner tube [1][2][3][4][5][6][7].However, they can be prone to buckling problems for intermediate-length and longer members, owing to the relatively small cross-sectional area.For this reason, it is necessary to carefully study the behaviour of slender composite columns and fully understand their performance.
To date, the most common types of CFDST sections studied in the literature comprise combinations of circular (CHS) and square (SHS) hollow sections, which are typically made from hot-rolled steel [e.g.[8][9][10][11][12][13][14][15][16][17][18].Ci et al. [8] and Huang et al. [9] conducted experiments and a numerical study on circular CFDST slender columns and studied the relative influence of a number of parameters including slenderness ratio, thickness of the inner steel tube and concrete strength.Wan et al. [10] tested two CFDST slender columns with different steel yield strength values for the inner and outer tubes.It was generally concluded that the steel tubes in CFDST columns provide confining effects to the core concrete, resulting in stronger members with greater load capacity and ductility compared with CFST columns.
Hassanein et al. [11] investigated the axial compressive behaviour of CFDST slender columns with a stainless steel outer tube and a carbon steel inner tube by finite element (FE) analysis.Chen et al. [12] tested six square CFDST slender columns and the results showed that the members failed due to overall buckling of the columns together with local buckling of the outer steel tube and crushing of the concrete; it was also shown that existing design codes significantly underestimate the ultimate loads of CFDST slender columns.Wang et al. [13] tested fourteen circular and square slender CFDST columns under both concentric and eccentric axial loading and the results showed that these members had higher load-bearing capacity and ductility than comparable CFST columns owing to the exist of inner steel tube.Ahmed et al. [14] described a mathematical model for the simulation of the interaction between local and global buckling in square CFDST slender beam-columns (i.e.axial compression in combination with uniaxial bending).The members studied had square outer tubes and circular inner tubes made using high strength steel.However, it was shown that the outer square tubes experienced local buckling relatively early in the load-deflection response, especially for members with a relatively large cross-section.
It is clear from these studies that a key failure mode for CFDST slender columns is local buckling of the outer steel tube.In order to overcome this issue, researchers have proposed the addition of stiffeners to the cross-section which has been shown to effectively delay the development of local buckling in the steel tubes of both slender CFDST members [15][16][17] as well as concrete-filled stiffened steel tubular (CFSST) columns [17,18].More recently, the effect of different types of stiffeners (i.e.stud, bilateral tie, diagonal tie, steel plate, diagonal rib and internal diaphragm) on the behaviour of CFST columns has been investigated [19][20][21][22].Although the contribution made by the stiffeners is clear, there is very little information available in the literature on concrete-filled dual-stiffened steel tubular (CFDSST) slender columns.The only tests that have been conducted to date included a programme comprising three CFDSST columns and two CFSST columns [23].The results indicated that the CFDSST slender columns exhibited greater residual load-carrying capacity and ductility compared with the CFSST columns.
In light of these positive results for CFDSST slender members, the current paper conducts a thorough study into their behaviour, and focusses on using ultra-high strength concrete with a cylinder strength of at least 90 MPa (UHSC) for the infill [24].There have been rapid improvements in concrete production technology in recent years, resulting in improved performance with lower manufacturing costs.Although UHSC has not been studied before for CFDSST slender columns, there have been some studies into its use in CFDST members, mostly focused on CFDST slender columns with CHS-CHS cross-sections [2,[25][26][27].In addition, it has been shown that CFDSST short columns with UHSC can achieve very high axial capacities, in the range of 10000 kN, with a total cross-sectional area of 78400 mm 2 and overall length of 840 mm [28].However, the length of the studied members is clearly not practical for real applications, and the study did not consider issues relating to slenderness and global buckling as these are less relevant for short members.Accordingly, the current paper presents the details and analysis of a numerical study conducted to examine the behaviour of CFDSST slender columns with UHSC infill.The model is first developed using the ABAQUS software [29], and then validated against available data, before being employed to understand the key behavioural features.

Development of the FE model
Fig. 1 presents a schematic view of the cross-section of CFDSST members which are examined in this study, including the stiffened square outer tube, circular inner section and concrete infill.The stiffened outer section is created by welding four lipped angles together as shown.The finite element model to analyse these sections was developed using the commercially-available ABAQUS software [29], as has been used for other similar analyses [28,30].The software is capable of accurately simulating the nonlinear behaviour of both the constituent materials and the geometry.

Initial model conditions
A schematic of the 3D model is presented in Fig. 2, including the two rigid plates at the member ends, the outer steel tube with stiffeners, the inner steel tube, the sandwiched concrete between the two tubes and the core concrete inside the inner tube.The concrete is modelled using the C3D8R element available in the ABAQUS library, while the rigid steel plates, steel tubular sections and stiffeners are simulated using the S4R element.To ensure computational convergence of the model and also to optimise computational efficiency and accuracy of the results, the mesh size is taken as B/10 in the cross-sectional direction and three times B/ 10 in the axial direction, where B is the width of outer steel tube.
The end conditions of the slender columns are applied at userdefined reference points which are located at the centre of the added endplates.A concentrated axial load is applied at one end of the column, as shown in Fig. 2, through a reference point.In the analysis presented herein, all three translational degrees of freedom at both ends are restrained, except for the axial direction displacement at the loading end (U3 at the "Loading end" in Fig. 2).Similarly, the rotational degrees of freedom about the y-and z-axes (UR2 and UR3, respectively) at both ends are restrained but permit rotation about the x-axis (UR1) to simulate a pinned end condition.With reference to the boundary conditions in Fig. 2, U1, U2, U3, UR1, UR2 and UR3 are the displacements and rotations about the global x-, y-and z-axes, respectively.
The bond between the outer and inner steel tubes and the infilled concrete is modelled using the surface-to-surface contact available in the ABAQUS library.A 'hard contact' is employed in the normal direction and a Coulomb friction model is used in the tangential direction.Simultaneous stresses in the concrete and steel tubes, with no relative movement between the two materials, indicate that the behaviour of CFDSST columns is insensitive to the friction coefficient.Accordingly, the friction coefficient is taken as 0.6 in accordance with the value proposed by Tao et al. [31].Both of the endplates are set as rigid bodies Fig. 1. : Cross-section of UHS-CFDSST slender columns.and are effectively tied to the steel tube, and the surface-to-surface contact described before is used to account for the interaction between the endplates and the concrete.Additionally, the same contact behaviour that was assigned between the tubes and concrete was also applied between the stiffeners and the concrete.The interactions between the four lipped steel angles to create the square outer sections are defined using the 'tie constraint'.

Initial imperfections and residual stresses
Whilst initial imperfections can generally be ignored in short columns [32], they can be more significant for longer members [33] and therefore should be included in the numerical analysis.The value of initial global geometrical imperfection assumed in the current work is equal to L/1000, where L is the overall length of the column [34].Fig. 3 presents the buckling shape for a typical CFDSST slender column based on this value.
The outer steel section is fabricated by welding four lipped coldformed angles together.Residual stresses are generated during the cold-forming process for the angles, and are also likely to be introduced during the welding process.Previous studies have shown that the tensile residual stresses (σ rt ) close to the centre of the welds are the most significant and are often similar in value to the material yield stress (f y ).The residual compressive stresses (σ rc ) are generally taken as 0.2f y in the current work [35,36].The idealized residual stress distribution adopted in the FE model is shown in Fig. 4. The strengthening effect caused by cold-forming developed in the corner regions of the outer steel tube corner are determined in accordance with Eqs.(1-3), as proposed by Han [36].
In these equations, f y and f y1 are the yield strengths of the steel generally and in the corner region, respectively, f u is the tensile strength of the steel, B c and m are coefficients related to the ratio of fu fy determined in accordance with Eqs.(2-3), and r is the outer radius of the corners of    the lipped angles used in fabricating the outer steel tubes and is taken as 2.5t o in the current work, where t o is the thickness of the outer steel tube.Wang et al. [23] studied the effect of residual stresses and the cold-forming strengthening effect at the corners on the performance of CFDSST slender columns.It was shown that the ultimate resistance was reduced by approximately 1.4 % due to the residual stresses and, on the other hand, increased by approximately 1.2 % due to the higher strength in the corner regions.These effects are considered to be relatively low in the current work and therefore, the effects of both residual stresses due to welding and corner strengthening due to cold-forming are neglected in the FE model.

Material modelling
The UHSC, employed for both the sandwiched and the core concrete, is modelled using the constitutive model proposed by Tao et al. [31] as shown in Fig. 5(a).This constitutive model, including the elasticity modulus of conventional concrete as described later, has previously been shown to provide an accurate representation of the behaviour in CFDSST columns [28].From Fig. 5(a), it can be seen that the curve can be defined in three distinct stages, i.e., the initial stage (from point O to point A), the plateau stage (from point A to point B), and the descending stage (beyond point B).Eq. ( 4) is used to describe the initial stage: where 0, E c is the elasticity modulus and is taken as 4700 , and f ′ c denotes the cylinder concrete strength.The strain at the ultimate stress (ε c0 ) is calculated using Eq. ( 5): The plateau stage (from point A to point B) reflects the influence of confinement on the concrete response.The strength increase of the concrete owing to confinement is captured in the simulation through the interaction between the steel tube and the concrete infill.The strain at point B (ε cc ) and the value of f B are determined by Eq. ( 6) and (7), respectively: In the descending branch of the stress-strain relationship (beyond B point), there is a softening behaviour with increased ductility resulting from confinement and this is expressed as: where f r and α are determined using Eqs.( 9) and (10), respectively: 3.49  (circularCFST) ξ c represents the confinement factor [37], and is defined as: In these expressions, A s and A c denote the cross-sectional areas of the inner steel tube and the concrete, respectively, f ck is the characteristic strength of the concrete, and β is a factor which is taken as 0.92 and 1.2 for the rectangular and circular columns [31], respectively.
It was shown that square steel tubes are more susceptible to local buckling compared with circular steel tubes, and also experience less benefit and strength enhancement due to confinement provided to the infill concrete [31].There is also very limited strain-hardening behaviour exhibited in the steel section for square CFST columns.Therefore, for the cold-formed steel employed for the outer tube, the elastic-perfectly plastic material model shown in Fig. 5(b) is employed, in accordance with the recommendations of Zhang et al. [28] and Wang et al. [30].For the inner hot-rolled steel tube, the multi-stage stress-strain relationship proposed by Tao et al. [38] and shown in Fig. 5(c) is employed, which is expressed in Eq. ( 12): Fig. 5. Constitutive models for the materials employed in the FE model.
J.-H.Zhang et al.In this expression, the subscript of "i" represents the inner steel tube, E s is the Youngs modulus for the steel is taken as 210 GPa, f ui is the ultimate strength of the steel, ε yi is the strain corresponding to the yield strength f yi (calculated as f yi /E s ), p is the strain-hardening exponent and expressed in Eq. (13), and E p is the initial modulus of elasticity at the onset of strain-hardening and is taken as 0.02E s .
With reference to Fig. 5(c), the values for f ui , ε pi and ε ui are determined in accordance with Eqs.(14)(15), respectively: In order to accurately describe the deformation of steel, the normal stress and normal strain are converted in to true stress and true strain, as expressed in Eqs.(17)(18):

Validation of the numerical model
There are no test results in the public domain on the behaviour of CFDSST slender columns with UHSC infill.Therefore, in order to ensure that the model developed in the current paper provides accurate and reliable results, a number of different validations were conducted, with a view to confirming that the model can capture all of the key performance criteria.The different types of cross-sections examined in the validation exercise are presented in Fig. 6, and also described in Table 1.These include tests on cold-formed CFDSST slender columns [23] and also experiments on CFST, CFSST and CFDST slender columns [12,13,18,23,39].The geometrical and material properties of the specimens are listed in Table 1.The ultimate loads predicted by the FE model (N ul,FE ) are compared with the corresponding experimental values (N ul,Exp ) in the table.It is shown that the numerical model provides a good reflection of the ultimate capacity with a mean and COV value of 0.98 and 0.065, respectively, for N ul,FE /N ul,Exp .Fig. 7 presents a selection of typical comparisons for the axial load versus deflection from both the model and the corresponding test.It is clear that the behaviour is well represented by the numerical model, with the key features such as overall shape, peak load and softening behaviour clearly well reflected.On the other hand, Fig. 8 presents deformed shape images to compare failure modes.Again, it is observed that the FE predicted failure modes compare favourably with those that developed in the experiments and reported in the associated publications [13,23].

Parametric studies on UHSC-CFDSST slender columns
A thorough parametric study was undertaken on CFDSST slender columns with UHSC infill to fully understand their behaviour and evaluate their ultimate resistance with different properties.The variables examined include the slenderness ratio, typical failure modes, the sandwiched concrete strength (f cs ), yield strength of the outer steel tube (f yo ), core concrete strength (f ci ), yield strength of the inner steel tube (f yi ), diameter-to-thickness ratio of the inner circular steel tube (D/t i ), diameter-to-width ratio (D/B) and width-to-thickness ratio of the outer square steel tube (B/t o ).A total of 108 models were simulated, and these are categorised into eight different groups (G1-G8 in Table 2) for ease of comparison, depending on their geometric and material properties.The terms λ and λ as presented in Table 2 represent the slenderness ratio and the non-dimensional slenderness, respectively.These are defined in accordance with Eq. ( 19) [11] and (20) [40], respectively: where, for CFDSST columns, L e is the effective buckling length, I DS is the second moment of area of the CFDSST section, A DS is the gross crosssectional area, N pl,Rk is the characteristic plastic resistance of the composite section under compressive axial force, as given by Eq. ( 21), and N cr is the elastic critical normal force, calculated using Eq.(22).
where A yo , A ss , A yi , A cs and A cc correspond to the cross-sectional areas of the outer steel tube, stiffeners, inner steel tube, sandwiched concrete and core concrete, respectively.(EI) eff is the effective flexural stiffness for calculation of the elative slenderness and is expressed as: where I so , I ss , I si , I cs and I ci are the second moments of area of the outer steel section, stiffeners, inner steel section, uncracked sandwiched concrete section and uncracked core concrete section for the bending plane being considered, respectively.E so , E ss , E si and E cs and E ci are the moduli of elasticity of the outer steel section, stiffeners, inner steel section, sandwiched concrete and core concrete, respectively.

Results and discussion
This section presents the key findings from the parametric study, with each influential parameter discussed in the following sub-sections.Fig. 6.Cross-section types of slender columns.

Column slenderness
The column slenderness ratio (λ) is a key factor that significantly affects the behaviour of UHS-CFDSST slender columns.Fig. 9 presents the relationship between the ultimate axial strength (N ul,FE ) and λ from the parametric study.From Fig. 9(a), it is observed that as the slenderness of the UHS-CFDSST slender column increases, the resistance declines for different cross-section sizes.Fig. 10 shows the typical load versus mid-height deflection (i.e.lateral displacement, given as u m ) for UHS-CFDSST slender columns.As can be seen, the resistance of UHS-CFDSST slender columns of shorter lengths reduces rapidly after the ultimate load compared to longer columns.Long columns have a more stable load versus u m relationship throughout the loading process than intermediate-length columns.In addition, as the increase of the length of the columns, the influence of second order effects is more prominent and the relationship between the applied load and the mid-length moment is no longer linear.The lateral displacements have a negative influence on the load-bearing capacity of the columns because of the generation of mid-length secondary moments.Since the secondary bending moments increase with length [41], it can be seen that the lateral displacements at the mid-length for long columns is significantly greater than for intermediate-length columns.
Fig. 11 shows the typical axial strength (N) versus slenderness ratio relationship for axially-loaded columns, based on the behaviour observed numerically in Fig. 9, from which it is observed that the buckling mode of slender columns may occur elastically or inelastically.To distinguish between intermediate-length and long UHS-CFDSST columns, the relationships between the resistance and the longitudinal strain and stress at ultimate load are examined, as shown in Fig. 12.The negative and positive values on x-axis indicate the compressive and tensile strains, respectively.Two different columns are presented for illustration, namely S14 and S19 which have lengths of 3.6 m and 8.1 m, respectively.The stress distributions in the concrete (at the mid-height sections of the columns) and the outer steel tubes at the ultimate load also can be seen in Fig. 12.The longitudinal strains are obtained from the FE results at the mid-height of the outer and inner steel tubes on both the compression and tension sides.The stress distributions presented show the stresses in the infill as obtained from the ABAQUS model.Note that the figure shows the limits of the yield strain of the steel material used; this value was calculated as the yield stress divided by the modulus of elasticity.
From Fig. 12(a), it can be seen that both outer and inner tubes of column S14 (L=3.6 m) are fully under compression until the ultimate load was reached.The yield strain (1690 με l ) of the outer tube is higher than the longitudinal compressive and tensile strains.Hence, it is concluded that inelastic buckling has taken place in S14.From the stress distribution of the steel tube in Fig. 12(a), it is shown that the external edge of the steel tube has yielded to a significant degree.On the other hand, from the load versus longitudinal strain relationship in Fig. 12(b), the outer tube of column S19 (L=8.1 m) is under tensile stress before reaching the ultimate resistance.However, the longitudinal compressive and tensile strains are less than the yield strain of the outer tube.Additionally, the inner tube of S19 was totally compressed at the ultimate load, but with a strain value which was also less than the yield strain.Accordingly, it is deduced that elastic buckling has taken place in S19.
With reference to the stress distribution in the concrete infill at the mid-height, it is shown that both compressive and tensile stresses are evident for S19.As the length of the column is further increased, the secondary bending moments increase significantly owing to second order effects, which may be as a result of elastic buckling.Therefore, on the basis of this analysis, S19 is defined as a long column and S14 is an intermediate-length column.
By checking the longitudinal strains of the outer tubes for the specimens in groups G1, G2 and G3, the different failure modes were identified and then listed in Table 3.In the table, EB and INB represent the elastic and inelastic buckling failure modes, respectively.It is clearly shown that failure mode of the columns was effected by slenderness ratio.According to DBJ/T13-51-2010 [42], the slenderness limit (λ r in Fig. 11) differentiating between intermediate-length and long columns for rectangular CFST columns is calculated as 118  ̅̅̅̅̅̅̅̅̅̅ fy/235 √ , and it was found to have a value of 96.12 for the current UHS-CFDSST slender columns where the yield stress of the outer tubes was 355 MPa; see Fig. 9(b).However, from these slenderness limits in a reliable manner.

Concrete strength
As the concrete component of composite columns carries most of the compressive load under normal structural conditions, it is important to investigate the influence of the concrete strength on the behaviour of UHS-CFDSST slender columns.In the current study, three ultra highstrength concretes with compressive strengths of 110, 130 and 150 MPa are examined, and the results are presented in Fig. 13.From the data presented, it is clear that the influence of the sandwiched concrete between the two steel tubes is quite significant, with an increase in strength resulting in a corresponding increase in ultimate capacity of the column, whereas the strength of the core concrete inside the inner steel tube has a negligible effect.This is because the role of the concrete infill in long columns is generally restricted to increasing their flexural stiffness and preventing inward local buckling of the steel tubes, which is different in intermediate length columns for which the concrete bears additional load.Similar results have been found by Romero et al. [2] and Zeghiche and Chaoui [43].Additionally, it is possible to determine the influence of concrete strength on the efficiency of UHS-CFDSST slender columns, through the calculation of IE (for "increase in efficiency") using the expression given in Eq. ( 24), and the results are presented in Table 4: where N ul,FE and N ul,110 represent the ultimate resistance of UHS-CFDSST slender columns and the columns with the concrete strength 110 MPa, respectively.From  14.78 %, respectively.This trend is independent of the B/t o ratio and member length.From the data presented, it is noted that the efficiency gains by increasing the strength of the concrete is greater for intermediate-length UHS-CFDSST columns compared with long columns.

Steel strength
The study examines the influence of steel yield strength on the behaviour by assessing the response for slender columns made using tubes with a yield strength of 355, 550 and 690 MPa, and the results are presented in Fig. 14.It is observed that increasing the outer steel tube yield strength results in a corresponding increase in the ultimate strength of UHS-CFDSST intermediate-length columns, while it has a  negligible influence for long columns as they fail elastically.Additionally, increasing the inner steel tube yield strength has a negligible influence on the ultimate strength of intermediate-length or long UHS-CFDSST slender columns.For long columns, the yield strength of the steel has very little influence of the capacity because of the slenderness of the columns and the likelihood that failure is dominated by buckling.These members generally do not develop their full load-carrying capacity based on material strength.The influence of the yield strength of the outer steel tube on the efficiency of UHS-CFDSST intermediatelength columns is given in Table 5.For example, compared with column S49 which has a steel yield strength of 355 MPa, the ultimate axial resistance of columns S50 (yield strength of 550 MPa) and S51 (yield strength of 690 MPa) increase by 14.60 % and 23.57%, respectively.This trend is independent of the B/t o ratio.

B/t o
In order to illustrate the influence of the width-to-thickness ratio of the outer steel tube (i.e.B/t o ) on the resistance of UHS-CFDSST slender columns, the relationship between B/t o with members with different concrete strengths and steel yield strengths on the axial compressive resistance of UHS-CFDSST slender columns is presented in Fig. 15.Note that all columns were made using fully-effective cross-sections to focus on the flexural buckling response.The primary observation is that the ultimate resistance of both intermediate-length and long UHS-CFDSST columns reduces as the B/t o ratios increases.This is because of the reduction of the confining stress on the concrete and also the increased likelihood of local buckling in the steel tubes.Additionally, it is noted that for intermediate-length columns, employing steel tubes with a  relatively high yield strength together with higher strength sandwiched concrete and a stockier outer tube is the most efficient way of increasing the overall.On the other hand, for long columns, using a lower tube yield strength together with higher strength sandwiched concrete and a stockier outer tube provides the most efficient solution.The influence of B/t o on the axial load versus deflection at mid-height responses are given in Fig. 16.It is observed that employing steel tubes with a relatively large B/t o ratio results in a significant reduction in the columns initial stiffness, especially for long columns.Also, in comparison with intermediate-length columns, long columns have better post-peak residual capacity.

D/t i
Fig. 17 presents the effect of diameter-to-thickness ratio of the inner circular tube (D/t i ) for UHS-CFDSST columns with different core concrete strengths and inner steel tube yield strengths.The data shows that the resistance of UHS-CFDSST slender columns is relatively unaffected for different D/t i values, especially for long columns.Additionally, for the intermediate-length columns, using a relatively stocky inner steel tube with a higher yield strength together with relatively high core concrete in the infill, is the most efficient way to improve the columns overall resistance.On the other hand, for long columns, owing to the likelihood for buckling to occur before the full axial load capacity can be reached by yielding, using higher strength steel and concrete is inefficient as the full strength values are not attained.Fig. 18 presents the influence of D/t i on the axial load versus deflection responses where it is observed that D/t i does not have a notable influence on the behaviour.

D/B
Although the influence of the B/t o and D/t i ratios on the overall behaviour have been discussed in detail in earlier sub-sections, the current sub-section assessed the influence of D/B.Altering this ratio has an effect on the ratio of the volume of sandwiched concrete to inner core concrete also, which were earlier shown to have different influences on the overall capacity.The results are presented in Fig. 19 and it is shown that the resistance of the intermediate-length and long columns increases for members with a relatively higher D/B ratio.This is because increasing the D/B ratio, by increasing the diameter of inner steel tube, increases the second moment of area of the steel overall in the columns.The influence of D/B on the axial load versus deflection responses are given in Fig. 20 and it is observed that the effect is negligible for the range of values examined.J.-H.Zhang et al.

Design resistance
There are currently no design specifications available for UHS-CFDSST slender columns.The applicability of the design expressions given in Eurocode 4 Part 1-1 [40] and AISC 360-16 [44] for concrete filled steel sections are examined herein, as are the design models proposed by Ahmed et al. [14] and Wang et al. [23] for concrete filled double skin tubular (CFDST) sections.Although none of these exactly represent the members assessed in the current work, rational amendments are made as described in the following sub-sections, to allow for the differences.

EN 1994 part 1-1 [40]
Eurocode 4 Part 1-1 [40], hereafter referred to as EC4, includes design guidance for composite columns and composite compression members with concrete encased sections, partially encased sections and concrete filled rectangular and circular tubes.So, there is no inner steel tube in this case, although there is typically inner reinforcement, and the sandwiched concrete and core concrete are a single entity.The code suggests that a slenderness reduction factor χ can be used to determine the ultimate axial resistance (N ul,EC4 ) of a composite slender section as: where N ul is the ultimate strength of the member.
χ is determined in accordance with guidance given in EN 1993-1-1 [45] as: In these expressions, α is the imperfection factor corresponding to the relevant buckling curve, which is taken as 0.49 for buckling curve "c" in the current analysis, for UHS-CFDSST columns.N ul is determined as: where A sy,eff is the effective cross-sectional area of outer steel tube, A ss is the cross-sectional area of steel stiffeners and f ys is the yield strength of the steel stiffeners.

AISC 360-16 [44]
The design resistance proposed in AISC 360-16 [44] suitable for composite members and encased composite members.The concrete encasement of the steel core shall be reinforced with continuous longitudinal bars and lateral ties or spirals.So, there is used inner tube replace the longitudinal bars and lateral ties or spirals.The effect of Fig. 13.Influence of concrete strength on the resistance of UHS-CFDSST slender columns.

Table 4
Relationship between concrete strength and column efficiency (IE).

Specimens
f cs (MPa) Increase in concrete strength (%) concrete confinement on the capacity does not include provisions in AISC 360-16 [44].The ultimate axial load capacity of UHS-CFDSST slender columns (N ul,AISC ) is given as: Where ) where 0.85 and 0.95 in Eq. ( 30) are reduction factors for rectangular (representing the outer tubes) and circular (representing the inner tubes) sections, respectively, according to Section I2.2b of AISC 360-16 [44].C 4 in Eq. ( 32) represents the coefficient for calculation of effective rigidity of composite compression member.C 4 can be calculated as Eq.(33) as suggesting by Chen et al. [12].A s and A c are the area of steel and concrete, respectively.It should be noticed that the area of stiffeners is included in A s for outer steel tube.

Ahmed et al. [14]
Ahmed et al. [14] proposed a design formula to calculate the  ultimate resistance of square high strength concrete-filled double steel tubular slender beam-columns (with columns also considered).The CFDST slender members considered have a square outer section and a circular inner section, with sandwiched concrete between the two steel tubes and core concrete filled in the inner steel tube.For the UHS-CFDSST slender columns in this paper, the proposed capacity (N ul, Ahmed ) is slightly modified to account for the core concrete as: where γ c is the strength reduction factor for the compressive strength accounting for the column size effect, as proposed by Liang et al. [46].This is expressed as 1.85D c − 0.135 and D c is calculated as (B-2t o ) for square cross-sections and (D-2t i ) for circular cross-sections.f cci is the confined compressive strength of the core concrete calculated as: where f rp is the lateral pressure and is calculated as: (0.006241) − 0.0000357 In these expressions, ν e and ν s represent the Poisson's ratios of the CFST columns and the hollow steel tube, respectively.These are determined in accordance with Tang et al. [47] and so ν s is taken as 0.5 once the steel has yielded and ν e is calculated using Eqs.(37)(38): ν e = 0.2312 + 0.3582ν e ′ − 0.1524 ν e ′ = 0.881 × 10 − 6 In Eq. ( 34), χ is calculated as Eq. ( 26), while Ahmed et al. [14] suggested a formula to calculate Φ using Eq. ( 39), which is adopted in 6.4.Wang et al. [23] Wang et al. [23] proposed a design formula to calculate the ultimate resistance of composite concrete-filled square thin-walled steel tubular slender columns under axial compression.The proposed expression for the capacity of these columns (N ul,Wang ), is given as: where φ is a slenderness reduction factor obtained by linear-regression analysis, and it can be calculated by Eq. ( 41): N us is the superposition resistance of UHS-CFDSST columns which is can be expressed by Eq. ( 42):

Evaluation of the design predictions
A comparison of the ultimate load-carrying capacities predicted by the international design standards and proposed design models from the literature, with the FE data presented herein, for UHS-CFDSST slender columns are summarised in Table 6.From the data presented, it is observed that the capacities predicted by EC4 [40] and Ahmed et al. [14] tend to underestimate the resistance of UHS-CFDSST slender columns by approximately 20-28 % on average.Earlier analysis in the current paper showed that the material strength of the various components, and the D/t i and D/B ratios, have a negligible effect on the ultimate resistance of UHS-CFDSST long columns.In contrast, the design model proposed by Wang et al. [23] provides different accuracies with regard to the length of the column.As can be seen, it provides unsafe predictions for intermediate-length UHS-CFDSST columns with a mean of 1.13, while it is suitable predictions for long columns with a mean of 0.94.Therefore, the design model of Wang et al. [23] can be used for predicting the resistance of UHS-CFDSST long columns.With regard to the predictions of AISC 360-16 [44], it is seen that predictions are mostly falling on the safe side.However, AISC 360-16 [44] gives suitable prediction for the resistances of intermediate-length UHS-CFDSST slender columns with a mean value of 0.97 and a COV of 0.077, while it underestimates the resistance of long UHS-CFDSST columns with a mean value of 0.82 and a COV of 0.029.Accordingly, it is recommended to use the design specification AISC 360-160 [44] to predict and design the resistance of UHS-CFDSST slender columns in practical engineering, despite the method of Wang et al. [23] is better for long columns.

Influence of UHSC
To evaluate the effect of using UHSC instead of conventional normalstrength concrete in CFDSST slender columns, this section remodels the six columns given in    presented in Fig. 21 which shows the comparison of the axial load versus axial shortening responses for CFDSST columns with concrete strengths of 50 MPa and 110 MPa.The increase in load capacity as a percentage by using UHSC is also shown in Table 7. Generally, the positive effect of using UHSC becomes greater for relatively shorter members.It is also shown that when the cross-section is relatively larger, the benefit of using UHSC also increases.Hence, using UHSC with intermediate-length columns is beneficial, while this is not the case for slender columns.This is because for slender columns the main role of the concrete is to increase the flexural stiffness [2,43], as discussed previously in Section 5.2.Accordingly, using UHSC is not recommended for use with CFDSST long columns based on their insignificant effect.

Advantages of UHS-CFDSST slender columns compared to CFSST slender columns
To evaluate the influence of the inner steel tube on the ultimate resistance and axial behaviour of UHS-CFDSST slender columns, specimens of S3 and S8, which were intermediate-length and long columns, respectively, were remodelled without the inner steel tube to form the UHS-CFSST comparison columns.Table 8 shows the geometric and material properties of these columns.It is observed that the ultimate resistance of the columns is improved by the inclusion of inner tubes in UHS-CFSST slender columns.This is because the inner steel tubes bear part of the load and also increases the flexural stiffness of the crosssection.Fig. 22 shows the comparison between the FE axial load versus axial shortening responses of the UHS-CFDSST slender columns with those of the UHS-CFSST slender columns, where an increase in initial stiffness and post-peak strength is observed.However, the relative increase in strength for the intermediate-length columns was clearly greater than for the long columns, as can be seen in the data presented in the table.This again is related to the role of the inner steel tube in bearing additional load and increasing the flexural stiffness in intermediate-length columns, while the later is only increased in case of long columns.

Fig. 2 .
Fig. 2. Schematic of the FE model with meshing scheme, load and boundary conditions.

Fig. 4 .
Fig. 4. Distribution of residual stresses in the outer section.

Fig. 7 .
Fig. 7. Comparison of the axial load versus deflection/shortening responses obtained numerically from the FE model and from the experiments.

Fig. 14 .
Fig. 14.Influence of outer steel tube yield strength on the resistance of UHS-CFDSST slender columns.

Fig. 15 .
Fig. 15.Influence of B/t o on the resistance of UHS-CFDSST slender columns.

Fig. 16 .
Fig. 16.Influence of B/t o on the axial load versus deflection responses of UHS-CFDSST slender columns.

Fig. 17 .
Fig. 17.Influence of D/t i on the resistance of UHS-CFDSST slender columns.

Fig. 18 .
Fig. 18.Influence of D/t i on the axial load versus deflection responses of UHS-CFDSST slender columns.

Fig. 19 .
Fig. 19.Influence of D/B on the resistance of UHS-CFDSST slender columns.

Fig. 20 .
Fig. 20.Influence of D/B ratio on the axial load versus deflection of UHS-CFDSST slender columns.

Fig. 21 .
Fig. 21.: Comparison of the axial load versus axial shortening responses of CFDSST columns with concrete of compressive strength equal to 50 MPa and 110 MPa.

Table 3
, it is observed that the λ limit which delineates between intermediate-length and long UHS-CFDSST columns was around 110 and the normalized value was 89.5, determined according to λ ̅̅̅̅̅̅̅̅̅̅ fy/235 √ .Generally, additional research is recommended to establish

Table 1
Details and resistances of slender columns.

Table 4
, it is observed that by increasing the sandwiched concrete strength from 110 MPa to 130 MPa and 150 MPa, the axial capacity of the columns increases by 8.05 % and

Table 2
Details of the parametric study on UHS-CFDSST slender columns.
(continued on next page) J.-H.Zhang et al.

Table 3
Failure modes for the UHS-CFDSST slender columns.

Table 5
Relationship between outer steel tube yield strength and column efficiency (IE).

Table 2 ,
including intermediate-length columns and long columns with different values of B and concrete compressive strength of either 50 MPa or 110 MPa.Table7shows the most important geometric and material properties for these columns.The results are

Table 6
Comparison of various design resistances with the capacities predicted by the FE model.

Table 7
Details and resistances of CFDSST slender columns with concrete of 50 and 110 MPa.

Table 8
Details and resistances of UHS-CFDSST slender columns and UHS-CFSST slender columns.