Axial Load Behavior of Ultrahigh Strength Concrete-Filled Steel Tube Columns of Various Geometric and Reinforcement Conﬁgurations

: This paper presents the behavior of concrete-ﬁlled steel tube (CFST) columns inﬁlled with ﬁber-reinforced self-consolidating ultrahigh strength concrete (UHSC) subjected to axial concentric monotonic loading to failure. UHSC is expected to improve ease of fabrication, strength, and ductility of CFST columns. Seventeen columns having varying geometric properties such as tube wall thickness, cross-sectional shape (circular, rectangular, and square), and slenderness were constructed and tested by applying load through both steel tube and concrete core. Circular columns were further distinguished by the presence or absence of main and hoop steel reinforcing bars in the core concrete. Axial load-displacement response, axial/transverse strain development, and failure modes were recorded during the loading history to analyze the performance. Experimental conﬁned concrete strength and axial strength of UHSC-ﬁlled CFST columns were compared with those obtained from three suggested analytical models and three code-based design procedures including Eurocode 4, Canadian CAN/CSA S16, and American AISC. Analytical models were found to over-predict the conﬁned concrete strength and the axial strength of CFST columns. Canadian and American codes were found to be most applicable for predicting axial strength of UHSC-ﬁlled CFST columns while remaining conservative.


Introduction
Concrete-filled steel tube (CFST) columns provide structural benefits such as increasing strength and ductility compared with normal reinforced concrete columns [1,2], and such characteristics are expected to be applicable to structures in seismic areas [3,4]. Advantages in CFST columns come from confinement of concrete by the steel tube wall [5]. Slenderness often has an effect on column capacity in general, and this has been found to be true in CFST columns as well. Columns with increasing slenderness "length-to-diameter ratio (L/D) for circular section" or "length-to-depth (minimum dimension) ratio (L/d) for rectangular section", typically fail due to global buckling rather than steel yielding or local buckling. In the case of CFST columns, concrete confinement is not able to fully develop in slender columns [6]; thus, greater confinement is expected in shorter columns [7]. In addition, higher axial strength is expected to develop in CFST columns as compressive strength of core concrete increases due to confinement. Infill concrete plays a significant role in the structural behavior of filled tube columns. Circular columns are capable of achieving better confinement, and thus, higher strength compared with square columns [5,8]. The presence of steel bar reinforcements enables even higher strength and ductility in CFST columns [3,9]. Circular CFST columns have been studied by many authors in the past, and various analytical models and code provisions are based on CFST columns of circular cross-section. Global buckling L: length or height; t: tube wall thickness; D: tube outer diameter; b: breadth (larger dimension of rectangular section); d: depth (minimum dimension for rectangular section); b/t: diameter-to-thickness or depth-to-thickness ratio; L/D or L/d: slenderness ratio; P exp : experimental axial load capacity/strength; U: UHSC; c: circular; s: square; r: rectangular; I and II: with and without longitudinal and hoop reinforcement, respectively.
Columns were designated by infill material (U-ultrahigh-strength concrete), column cross-sectional shape (c, s, or r) and Series I or Series II (without or with longitudinal and tie/hoop reinforcements, respectively for circular columns only). For example, UcII-9 represents Series II UHSC circular column with a L/D of 9. All square and rectangular columns are Series I columns and "I" was not used in their designations. For example, Us2-9 represents Series I square columns with a L/d ratio of 9. Circular columns were made of 114 mm diameter steel tubes with a thickness of 4.8 mm (Figure 1a-c), square columns were made of tubes with 51 × 51 × 1.6 mm and 102 × 102 × 3.2 mm cross-sections, and rectangular columns were made of 102 × 51 × 3.2 mm tubes ( Table 1).
The effect of variables such as cross-sectional area, tube shape, tube thickness, and slenderness (as measured by L/D or L/d ratio) on behavior of CFST columns infilled with self-consolidating fiber-reinforced UHSC was investigated. In addition, four longitudinal bars and hoop reinforcements were incorporated in several Series II circular CFST columns. Longitudinal bars were bent at the ends in the configuration as shown in Figure 1a-c, where hoop/tie spacing and reinforcement specifications are given for circular Series II columns of varying height. slenderness (as measured by L/D or L/d ratio) on behavior of CFST columns infilled with self-consolidating fiber-reinforced UHSC was investigated. In addition, four longitudina bars and hoop reinforcements were incorporated in several Series II circular CFST columns. Longitudinal bars were bent at the ends in the configuration as shown in Figure  1a-c, where hoop/tie spacing and reinforcement specifications are given for circular Series II columns of varying height.

Specimen Casting, Curing, Instrumentation, and Testing
UHSC mix developed at Ryerson University made of Type 10 (GU) cement as per Canadian Standard Association (CSA) specifications, silica sand, silica fume, superplasticizer (SP), and 13 mm-long straight steel fibers with diameters of 0.2 mm were used UHSC was mixed in a 150 L capacity shear mixer where water and superplasticizer were added to dry materials excluding steel fiber and mixed. Then steel fibers were added gradually on to the lubricated flowable mixture during further mixing for even distribution After making, UHSC was poured directly into the steel tube without any manual compaction as the concrete was designed to consolidate under its own weight. Casting was done in a vertically upright position as shown in Figure 2a and UHSC was poured from the top of the specimen. During casting, control specimens in the form of 100 mm × 200 mm cylinders and prisms were also made to determine UHSC compressive and flexura strengths, respectively at the age of testing. After casting, column and control specimens were covered for 24 h to prevent moisture loss and then air cured until testing at 28 days

Specimen Casting, Curing, Instrumentation, and Testing
UHSC mix developed at Ryerson University made of Type 10 (GU) cement as per Canadian Standard Association (CSA) specifications, silica sand, silica fume, superplasticizer (SP), and 13 mm-long straight steel fibers with diameters of 0.2 mm were used. UHSC was mixed in a 150 L capacity shear mixer where water and superplasticizer were added to dry materials excluding steel fiber and mixed. Then steel fibers were added gradually on to the lubricated flowable mixture during further mixing for even distribution. After making, UHSC was poured directly into the steel tube without any manual compaction as the concrete was designed to consolidate under its own weight. Casting was done in a vertically upright position as shown in Figure 2a and UHSC was poured from the top of the specimen. During casting, control specimens in the form of 100 mm × 200 mm cylinders and prisms were also made to determine UHSC compressive and flexural strengths, respectively at the age of testing. After casting, column and control specimens were covered for 24 h to prevent moisture loss and then air cured until testing at 28 days. Figure 3 shows typical compressive stress-strain and flexural stress-displacement curves for UHSC. The mean 28-day cylinder compressive strength of UHSC (as derived from 15 specimens) was 130 ± 3 MPa. The yield strength and modulus of elasticity of steel tubes and reinforcing bars were also determined from coupon tests. The yield strengths of longitudinal and hoop reinforcements were 635 and 662 MPa, respectively. The yield strength of circular, rectangular, square (102 × 102 mm) and square (51 × 55 mm) tubes were 333, 372, 351, and 365 MPa, respectively while modulus of elasticity were 176, 236, 205, and 206 GPa, respectively. The test setup is shown in Figure 2b. Before testing at the age of 28 days, two strain gauges (g1 and g2) were installed on the sanded surface of steel tubes of circular and square/rectangular columns according to the configurations shown in Figure 2c in order to record lateral strain and axial strain, respectively, during testing. Linear voltage displacement transducers (LVDTs) were installed to measure lateral displacement of the columns (Figure 2b) while load and axial displacement were directly provided by the loading machine. The top and bottom surfaces of the columns were grinded flat in order to apply load evenly over the cross-section and to avoid undesired load eccentricity. In addition, in most of the columns, two axial strain gauges (g2) were installed on opposite faces of the steel tube. Equal axial strain development during initial stages of loading ensured concentric application of loading. The columns were loaded axially under static monotonic loading at a rate of 0.2 MPa/s under load control until failure. During loading history till failure, strains, load, and axial/lateral displacements were recorded through a computer-aided data acquisition system. In addition, buckling of steel tube and failure mode of column specimens were also observed.    curves for UHSC. The mean 28-day cylinder compressive strength of UHSC (as derived from 15 specimens) was 130 ± 3 MPa. The yield strength and modulus of elasticity of steel tubes and reinforcing bars were also determined from coupon tests. The yield strengths of longitudinal and hoop reinforcements were 635 and 662 MPa, respectively. The yield strength of circular, rectangular, square (102 × 102 mm) and square (51 × 55 mm) tubes were 333, 372, 351, and 365 MPa, respectively while modulus of elasticity were 176, 236, 205, and 206 GPa, respectively.

Load-Displacement Responses and Failure Modes of CFST Columns
Axial load-displacement responses of UHSC-filled CFST columns are shown in Figure 4a,b. All columns displayed similar behavior up to the first peak load. The rising and falling of axial load in the responses are attributed to the formation of multiple cycles of local buckling and their stabilization in formation of successive local buckles as confirmed from previous research studies [3]. The first peak load always governed the maximum capacity of most of the columns, especially with square and rectangular cross-sections. Square and rectangular UHSC-filled columns behaved similarly, as a large decrease in axial load often occurred after the first peak load. However, CFST columns of circular cross-section and lower slenderness gained greater load capacity after the first peak load or had no significant first peak load at all as observed in Series II columns (Figure 2a). Circular columns showed greater ductility (in terms of post first peak deformation) compared with square and rectangular CFST infilled with UHSC (Figure 4a,b). The addition of bar reinforcements in Series II columns improved strength and ductility even more as observed in other studies [3]. The test setup is shown in Figure 2b. Before testing at the age of 28 days, two strain gauges (g1 and g2) were installed on the sanded surface of steel tubes of circular and square/rectangular columns according to the configurations shown in Figure 2c in order to record lateral strain and axial strain, respectively, during testing. Linear voltage displacement transducers (LVDTs) were installed to measure lateral displacement of the columns (Figure 2b) while load and axial displacement were directly provided by the loading machine. The top and bottom surfaces of the columns were grinded flat in order to apply load evenly over the cross-section and to avoid undesired load eccentricity. In addition, in most of the columns, two axial strain gauges (g2) were installed on opposite faces of the steel tube. Equal axial strain development during initial stages of loading ensured concentric application of loading. The columns were loaded axially under static monotonic loading at a rate of 0.2 MPa/s under load control until failure. During loading history till failure, strains, load, and axial/lateral displacements were recorded through a computeraided data acquisition system. In addition, buckling of steel tube and failure mode of column specimens were also observed.

Load-Displacement Responses and Failure Modes of CFST Columns
Axial load-displacement responses of UHSC-filled CFST columns are shown in Figure 4a,b. All columns displayed similar behavior up to the first peak load. The rising and falling of axial load in the responses are attributed to the formation of multiple cycles of local buckling and their stabilization in formation of successive local buckles as confirmed from previous research studies [3]. The first peak load always governed the maximum capacity of most of the columns, especially with square and rectangular cross-sections. Square and rectangular UHSC-filled columns behaved similarly, as a large decrease in axial load often occurred after the first peak load. However, CFST columns of circular cross-section and lower slenderness gained greater load capacity after the first peak load or had no significant first peak load at all as observed in Series II columns ( Figure 2a). Circular columns showed greater ductility (in terms of post first peak deformation) compared with square and rectangular CFST infilled with UHSC ( Figure 4a,b). The addition of bar reinforcements in Series II columns improved strength and ductility even more as observed in other studies [3]. Axial displacement (mm) cI, cII, and r CFST columns UcII-3 UcII-4 UcII-9 Ur-6 Ur-12 Ur-20   Figure 5 shows the failure modes of CFST columns. Table 1 summarizes failure modes and experimental axial capacity (Pu) of columns. Columns with slenderness ratios of 20 and 16 failed by global buckling at mid-height, and those with L/D ratios of 12, 10, 9, 6, and 4 often failed by shear and local buckling ( Figure 5 and Table 1). All columns with a L/D ratio of 3 failed due to concrete radially expanding at mid-height, resulting in tearing of the steel wall. In general, slender columns failed due to global buckling while short columns (low slenderness) exhibited failure due to local buckling and plastic yielding of regions between local buckling showing significant bulging and tearing of steel. Experimental ultimate axial strength capacities were larger for columns with larger crosssectional areas.   Figure 5 shows the failure modes of CFST columns. Table 1 summarizes failure modes and experimental axial capacity (P u ) of columns. Columns with slenderness ratios of 20 and 16 failed by global buckling at mid-height, and those with L/D ratios of 12, 10, 9, 6, and 4 often failed by shear and local buckling ( Figure 5 and Table 1). All columns with a L/D ratio of 3 failed due to concrete radially expanding at mid-height, resulting in tearing of the steel wall. In general, slender columns failed due to global buckling while short columns (low slenderness) exhibited failure due to local buckling and plastic yielding of regions between local buckling showing significant bulging and tearing of steel. Experimental ultimate axial strength capacities were larger for columns with larger cross-sectional areas.
(b)   Table 1 summarizes failure modes and experimental axial capacity (Pu) of columns. Columns with slenderness ratios of 20 and 16 failed by global buckling at mid-height, and those with L/D ratios of 12, 10, 9, 6, and 4 often failed by shear and local buckling ( Figure 5 and Table 1). All columns with a L/D ratio of 3 failed due to concrete radially expanding at mid-height, resulting in tearing of the steel wall. In general, slender columns failed due to global buckling while short columns (low slenderness) exhibited failure due to local buckling and plastic yielding of regions between local buckling showing significant bulging and tearing of steel. Experimental ultimate axial strength capacities were larger for columns with larger crosssectional areas.  Infrastructures 2021, 6, 66 8 of 18 Figure 6 presents the variation of axial load capacity of CFST columns with slenderness (L/D and L/d). Axial load capacity generally decreased with the increase in slenderness. The presence of longitudinal reinforcement with hoop/ties (Series II) increased the axial load capacity of circular columns compared to Series I columns. Circular columns (cI) showed higher axial load capacity compared to their rectangular (r) counterparts. For circular UcI columns, axial strength decreased from 1681 to 1573 kN (6.4% decrease) while the UcII columns' strength decreased from 1853 to 1751 kN (5.6% decrease) when the L/D ratio increased from 3 to 9. Circular CII columns exhibited higher (10 to 15%) strength than CI columns, as expected. Similar strength reduction was also observed for rectangular CI columns (Ur) (from 809 to 754 kN-a 6.8% decrease for L/d varying from 3 to 9) and for square (Us) columns (from 376 to 326 kN-a 13.3% decrease for L/d from 9 to 20).
Infrastructures 2021, 6, x FOR PEER REVIEW 8 of 19 Figure 6 presents the variation of axial load capacity of CFST columns with slenderness (L/D and L/d). Axial load capacity generally decreased with the increase in slenderness. The presence of longitudinal reinforcement with hoop/ties (Series II) increased the axial load capacity of circular columns compared to Series I columns. Circular columns (cI) showed higher axial load capacity compared to their rectangular (r) counterparts. For circular UcI columns, axial strength decreased from 1681 to 1573 kN (6.4% decrease) while the UcII columns' strength decreased from 1853 to 1751 kN (5.6% decrease) when the L/D ratio increased from 3 to 9. Circular CII columns exhibited higher (10 to 15%) strength than CI columns, as expected. Similar strength reduction was also observed for rectangular CI columns (Ur) (from 809 to 754 kN-a 6.8% decrease for L/d varying from 3 to 9) and for square (Us) columns (from 376 to 326 kN-a 13.3% decrease for L/d from 9 to 20). Overall the axial strength of the columns depends on the combined effect of D/t, L/D or L/d, shape of the steel tube, and failure modes as observed in past research studies [5]. The confinement effect provided by the steel tube is demonstrated by the enhanced ultimate load capacity of UHSC infilled CFST columns using UHSC. However, matching of UHSC with a particular steel tube is necessary to effectively improve the ultimate load capacity of CFST columns as confirmed from other research studies [13,16].

Biaxial Stress Development and Confinement in CFST Columns
Under axial compression load, the concrete core of CFST columns begins to crack. After cracking, the concrete dilates creating lateral pressure on the steel tube. The concrete is under triaxial confinement from the presence of the steel tube, while the steel tube is under biaxial stress due to axial load and lateral hoop stresses developed from the concrete core pushing outwards on the tube wall. Therefore, biaxial yielding in steel can be modeled by the von-Mises failure criterion in Equation (1) [9,23].
The von-Mises yield stress (fys) is constant and taken as the steel tube yield strength. Each fys value corresponds to a different failure envelope. Axial stress and hoop stress denoted by σa and σh respectively can be obtained from experimental strain data. The various combinations of axial and transverse stresses contributing to biaxial yield stress forms the von-Mises stress path shown in Figure 7. Overall the axial strength of the columns depends on the combined effect of D/t, L/D or L/d, shape of the steel tube, and failure modes as observed in past research studies [5]. The confinement effect provided by the steel tube is demonstrated by the enhanced ultimate load capacity of UHSC infilled CFST columns using UHSC. However, matching of UHSC with a particular steel tube is necessary to effectively improve the ultimate load capacity of CFST columns as confirmed from other research studies [13,16].

Biaxial Stress Development and Confinement in CFST Columns
Under axial compression load, the concrete core of CFST columns begins to crack. After cracking, the concrete dilates creating lateral pressure on the steel tube. The concrete is under triaxial confinement from the presence of the steel tube, while the steel tube is under biaxial stress due to axial load and lateral hoop stresses developed from the concrete core pushing outwards on the tube wall. Therefore, biaxial yielding in steel can be modeled by the von-Mises failure criterion in Equation (1) [9,23].
where σ a = β f ys , σ h = α f ys . The von-Mises yield stress (f ys ) is constant and taken as the steel tube yield strength. Each f ys value corresponds to a different failure envelope. Axial stress and hoop stress denoted by σ a and σ h respectively can be obtained from experimental strain data. The various combinations of axial and transverse stresses contributing to biaxial yield stress forms the von-Mises stress path shown in Figure 7. Development of biaxial stresses in UHSC CFST columns are compared in Figure  7a,b). The transverse stress factor and axial stress factor, α and β in Equation (1), can be determined at the location where experimental stresses intersect the theoretical von-Mises failure criterion. Axial stress factor (β) is found to be greater than transverse stress factor (α), as axial stresses develop in early stages of loading while transverse stresses develop after concrete begins to dilate and induce transverse stresses in the steel tube [24]. Figure 8a,b shows typical experimental axial and transverse (hoop) strain development in UHSC CFST columns, illustrating significantly greater axial strain development while transverse strain often did not reach theoretical steel yield strain for columns with high slenderness. Experimental stress factors α and β are presented in Table 2 for UHSCfilled CFST columns. Development of biaxial stresses in UHSC CFST columns are compared in Figure 7a,b). The transverse stress factor and axial stress factor, α and β in Equation (1), can be determined at the location where experimental stresses intersect the theoretical von-Mises failure criterion. Axial stress factor (β) is found to be greater than transverse stress factor (α), as axial stresses develop in early stages of loading while transverse stresses develop after concrete begins to dilate and induce transverse stresses in the steel tube [24]. Figure 8a,b shows typical experimental axial and transverse (hoop) strain development in UHSC CFST columns, illustrating significantly greater axial strain development while transverse strain often did not reach theoretical steel yield strain for columns with high slenderness. Experimental stress factors α and β are presented in Table 2 for UHSC-filled CFST columns.  Development of biaxial stresses in UHSC CFST columns are compared in Figure  7a,b). The transverse stress factor and axial stress factor, α and β in Equation (1), can be determined at the location where experimental stresses intersect the theoretical von-Mises failure criterion. Axial stress factor (β) is found to be greater than transverse stress factor (α), as axial stresses develop in early stages of loading while transverse stresses develop after concrete begins to dilate and induce transverse stresses in the steel tube [24]. Figure 8a,b shows typical experimental axial and transverse (hoop) strain development in UHSC CFST columns, illustrating significantly greater axial strain development while transverse strain often did not reach theoretical steel yield strain for columns with high slenderness. Experimental stress factors α and β are presented in Table 2 for UHSCfilled CFST columns.    Table 3 summarizes the ultimate axial load (Pu), axial strain at ultimate axial load (εu), load at biaxial yielding (Pys), and axial strain at biaxial yielding (εys) of tested CFST columns infilled with UHSC. The point of biaxial yielding where Pys and εys are determined is based on von-Mises failure criterion described previously in Equation (1). εys/εu ratios are found to be always greater than 1 as biaxial steel yielding always occurred before the axial capacity of the columns (Table 3). Pys/Pu ratios indicate that the axial strength of CFST columns occurred between 1.99 and 6.85 times the load at biaxial yielding indicating that steel yielding was not the final cause of failure of CFST columns (Table 3). In all columns, steel yielded both uniaxially and biaxially before the failure. Shorter columns (with lower slenderness) had generally higher Pu/Pys ratios compared to longer columns. Higher Pu/Pys ratios (>1.0) show that the shorter columns had the ability to take relatively larger amount of additional load (even after the biaxial steel yielding) before failure which can be attributed to the higher ductility behavior of such columns.  Table 3 summarizes the ultimate axial load (P u ), axial strain at ultimate axial load (ε u ), load at biaxial yielding (P ys ), and axial strain at biaxial yielding (ε ys ) of tested CFST columns infilled with UHSC. The point of biaxial yielding where P ys and ε ys are determined is based on von-Mises failure criterion described previously in Equation (1). ε ys /ε u ratios are found to be always greater than 1 as biaxial steel yielding always occurred before the axial capacity of the columns (Table 3). P ys /P u ratios indicate that the axial strength of CFST columns occurred between 1.99 and 6.85 times the load at biaxial yielding indicating that steel yielding was not the final cause of failure of CFST columns (Table 3). In all columns, steel yielded both uniaxially and biaxially before the failure. Shorter columns (with lower slenderness) had generally higher P u /P ys ratios compared to longer columns. Higher P u /P ys ratios (>1.0) show that the shorter columns had the ability to take relatively larger amount of additional load (even after the biaxial steel yielding) before failure which can be attributed to the higher ductility behavior of such columns.

Quantification of Lateral Stresses and Concrete Confinement
Lateral stress/pressure (f 2 ) developed in the steel tube as shown in Figure 9 can be calculated by Equation (2) [9,23]. As concrete crushes in order for lateral stresses to initialize on the steel tube, lateral pressure is expected to be at a maximum when steel yields. Hoop stress, σ h , can be substituted from Equation (1) to (2), where α is obtained from experimental results.

Quantification of Lateral Stresses and Concrete Confinement
Lateral stress/pressure (f2) developed in the steel tube as shown in Figure 9 can be calculated by Equation (2) [9,23]. As concrete crushes in order for lateral stresses to initialize on the steel tube, lateral pressure is expected to be at a maximum when steel yields. Hoop stress, σh, can be substituted from Equation (1) to (2), where α is obtained from experimental results.
Lateral pressure (f2) is related to the tube wall thickness (t) and equivalent outer diameter (D) of the cross-section (as the equation is designed for circular cross-sections, square or rectangular sections are converted to circular sections with equivalent area). The maximum lateral pressure (f2max) in CFST columns with additional confinement due to tie or hoop reinforcement can be calculated by Equation (3).
where Asr and fyr are area and yield strength of hoop/tie reinforcing bars and Dc is the diameter of concrete confined by hoops, and s is the hoop spacing. Biaxial yielding of steel always occurred before the ultimate capacity of the column. Therefore, it can be assumed that CFST column ultimate capacity is associated with the maximum confined concrete strength. Total axial load (P) can be separated by the portion Lateral pressure (f 2 ) is related to the tube wall thickness (t) and equivalent outer diameter (D) of the cross-section (as the equation is designed for circular cross-sections, square or rectangular sections are converted to circular sections with equivalent area).
The maximum lateral pressure (f 2max ) in CFST columns with additional confinement due to tie or hoop reinforcement can be calculated by Equation (3).
where A sr and f yr are area and yield strength of hoop/tie reinforcing bars and D c is the diameter of concrete confined by hoops, and s is the hoop spacing. Biaxial yielding of steel always occurred before the ultimate capacity of the column. Therefore, it can be assumed that CFST column ultimate capacity is associated with the maximum confined concrete strength. Total axial load (P) can be separated by the portion carried by concrete (P c ) and that carried by steel (P s ) as in Equation (4). Axial concrete stress (f c ) can be obtained from Equation (5) and P s from Equation (6). A s and A c are the steel tube cross-sectional area and concrete core area respectively.
where A s and A c are the steel tube cross-sectional area and concrete core area respectively, σ a is the axial stress in steel tube, E t and ε t are the elastic modulus and axial strain in steel tube, respectively. Load carried by the steel tube (P s ) can be calculated from the experimental axial steel tube strain (ε t ). Variation of concrete stress (f c ), which can be considered as experimental concrete confined strength during loading history can be calculated based on Equation (5).
Typical concrete stress (f c ) vs. axial steel tube strain (ε t ) development during loading history for a CFST column is shown in Figure 10a,b. It can be observed that axial concrete stress decreased soon after a peak is reached in square and rectangular columns (Figure 10b) compared with circular ones (Figure 10a). Such a decrease in concrete axial stress after the peak is especially evident in columns with higher slenderness. This can be attributed to the difference in tube shape and thickness.
concrete confined strength during loading history can be calculated based on Equation (5). Typical concrete stress (fc) vs. axial steel tube strain (εt) development during loading history for a CFST column is shown in Figure 10a,b. It can be observed that axial concrete stress decreased soon after a peak is reached in square and rectangular columns ( Figure  10b) compared with circular ones (Figure 10a). Such a decrease in concrete axial stress after the peak is especially evident in columns with higher slenderness. This can be attributed to the difference in tube shape and thickness. Total lateral stress on the steel (f2max or f2) calculated as per Equations (2) and (3) are presented in Table 4. From graphs such as shown in Figure 10, the fc value at ultimate load can be extracted as experimental confined concrete strength (f'cc) and are also presented in Table 4 for columns (of each group) having a minimum and maximum slenderness ratio. Confined concrete strength is then compared with concrete control cylinder compressive strength (f'c) by f'cc/f'c ratios. The confined strength of UHSC-filled columns increased with the increase of steel tube thickness and also tended to decrease for UHSC-filled columns with higher slenderness. Series II columns allowed for greater confined concrete strength (f'cc/f'c values ranging between 1.17 and 1.27) and particularly high values of f2max due to contributions from bar reinforcements (Table 4) Total lateral stress on the steel (f 2max or f 2 ) calculated as per Equations (2) and (3) are presented in Table 4. From graphs such as shown in Figure 10, the f c value at ultimate load can be extracted as experimental confined concrete strength (f cc ) and are also presented in Table 4 for columns (of each group) having a minimum and maximum slenderness ratio. Confined concrete strength is then compared with concrete control cylinder compressive strength (f c ) by f cc /f c ratios. The confined strength of UHSC-filled columns increased with the increase of steel tube thickness and also tended to decrease for UHSC-filled columns with higher slenderness. Series II columns allowed for greater confined concrete strength (f cc /f c values ranging between 1.17 and 1.27) and particularly high values of f 2max due to contributions from bar reinforcements (Table 4). On the other hand, square and circular columns showed lower confinement effects compared to circular ones as evident from the f cc /f c values ranging between 0.78 and 0.98. Overall f cc / f c ratios for UHSC-filled steel tube columns ranged from 0.78 to 1.27. This has been observed by other researchers studying high-strength CFST columns [8]. It is expected that the use of high-strength steel will improve the effect of UHSC confinement [25].

Analytical Models for Confined Concrete Strength
Richart et al. [26], Mander et al. [27], and O'Shea and Bridge's [28] models are modified for calculating confined strength of concrete in CFST columns. The total concrete confined strength (f cct ) as presented in Equation (7) is considered as the summation of contributions derived from confining steel tube (f cc ) and reinforcing hoops (f cch ) where A cc and A cch are area confined by the steel tube and area confined by hoops respectively. The total global buckling failures. The Mander et al.-based model generally made slightly higher estimations compared with other models.

Code-Based Design Procedures for CFST Columns
Several design codes have incorporated procedures for CFST column strength calculations. Canadian, American, and European codes are studied herein and are briefly described as follows.
Reduction factors φ s and φ c are equal to unity in order to compare with experimental results. The effects of slenderness and the diameter-to-thickness ratio are incorporated into τ and τ' strength modification factors. An equivalent elastic modulus and moment of inertia for the composite section, EI e , is calculated in order to obtain elastic critical load in determining relative slenderness, λ. α 1 = 0.85-0.0015f c , and n factor is taken with a value of 1.80.
The load capacity of CFST columns (P n ) as defined by the AISC [22] code is as follows in Equation (12).
The cross-sectional shape is considered by a factor in P o , where P o is the sum of axial loads carried by the concrete core, steel tube, and bar reinforcements. The term, P e , is the elastic critical load which incorporates an equivalent elastic modulus and moment of inertia for the composite section, and column boundary conditions, similar to the Canadian code.
Eurocode 4 [20] takes the sum of concrete, steel, and bar reinforcement cross-section contributions in Equation (13) to obtain the ultimate load capacity of CFST columns (N pl,Rd ). Reinforcement area and bar strength are denoted by A sz and f yr , respectively. The effect of confinement is considered by η a and η b modification factors.

Suggested Analytical Models for the Strength of CFST Columns
Three analytical models for axial strength (N a ) of CFST columns (denoted by subscripts N a(R) , N a(M) , and N a( O) based on Equation (14) are derived by substituting f cc and f cch values from Richart et al. [26], Mander et al. [27], and O'Shea and Bridge [28], presented in Equations (8)-(10), respectively: where steel tube-sectional area, tube confined area, hoop confined area, area of longitudinal reinforcements, and axial stress factor (taken from experimental results) are denoted by A s , A cc , A cch , A ra , and β, respectively. Equation (14) can be applied to Series I and Series II CFST columns, as terms corresponding to bar and hoop confined strength can be eliminated for columns without such reinforcements. Table 6 compares experimental axial load capacities (P expt ) of CFST columns with those predicted (P p ) from three theoretical models (Equation (14)) and three code-based models (CSA, AISC, and Eurocode 4). All the three models were found to overpredict the axial load capacities UHSC-filled CFST as the ratio of experimental to predicted values (P exp /P p ) are found to be less than 1.0. This may be attributed to the overestimation of confined concrete strength especially for CFST columns with higher slenderness (L/D or L/d) ratios. Possible reasons for lower experimental concrete confined strength than theoretical might be due to high strength/stiffness of UHSC which prevented effective concrete dilation resulting in lower steel confinement. CFST columns compared with that of the CSA design code, as the AISC model especially accounted for the effect of cross-sectional shape. CSA (with a mean P exp /P p value of 1.17) and AISC (with a mean P exp /P p value of 1.19) models performed well and can be used in predicting axial load capacity of UHSC-filled CFST columns within the range of geometric configurations used in this study.

Conclusions
This paper analyzed concrete-filled steel tube (CFST) columns with self-consolidating fiber-reinforced ultrahigh-strength concrete (UHSC) core material. Columns were tested under concentric axial compression loading to failure. Axial load-displacement behavior, stress-strain response, concrete confined strength, and axial load capacity/strength of CFST columns were studied and compared with analytical models and code-based design equations. The effects of cross-sectional shape and area, length-to-diameter (L/D) or lengthto-depth (L/d) ratios, tube wall thickness (t), and longitudinal steel reinforcing bars with hoops were investigated for their effects on behavior of UHSC-filled tube columns. The following conclusions are drawn from this study.
• UHSC-filled CFST columns failed to exhibit different types of failure based on slenderness (L/D or L/d ratios). Failure modes included global buckling for slenderness ranging between 16 and 20, shear yielding associated with successive formation of local buckling for slenderness varying from 4 to 12, and radial expansion with tube tearing for slenderness of 3.

•
Axial load-displacement responses of circular CFST columns generally showed multiple peaks and drops showing increase in load after each drop producing large post-peak deformation (ductility) before failure but the first peak always governed the load capacity. Square and rectangular columns displayed similar load-displacement responses exhibiting decrease in load after the first peak and lower ductility. • Axial load capacity/strength generally decreased with the increase of slenderness and increased with the presence of longitudinal and hoop reinforcement. Circular columns showed higher axial load strength and ductility compared to their rectangular/square counterparts. The combined effect of D/t, L/D or L/d, steel tube geometry and failure modes governed the axial strength of CFST columns. • Experimental UHSC confined strength increased with the increase of tube thickness, decreased for columns of higher slenderness and increased (by 11 to 27%) with the presence of longitudinal and hoop reinforcements. Existing analytical models overestimated the confined concrete strength resulting from tube and hoop confinement in CFST columns compared to those of experiments. This is attributed to overestimating the ability of UHSC to soften and dilate with progressive loading. • Predicted axial strength from the three suggested analytical models were often greater than those obtained from experiments. This overestimation is attributed to the overprediction of confined UHSC strength and reduction factors are suggested for incorporation in analytical models for strength prediction. • Eurocode 4 overpredicted the strength of CFST columns. Canadian CAN/CSA S16-09 and American AISC code provisions performed well, especially in estimating the strength of circular columns with or without bar/hoop reinforcements. The AISC code was especially good for square and rectangular UHSC-filled tube columns as it took into account cross-sectional shape.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.