Behavior and design of axially loaded square concrete-filled double steel tubular slender columns

Abstract

A square concrete-filled double steel tubular (CFDST) column composed of a circular core concrete-filled tube offers the advantages of both square and circular concrete-filled steel tubular (CFST) columns. However, limited tests were performed to investigate the axial performance of CFDST slender columns. This paper investigates the behavior and design of square CFDST slender columns subjected to concentric loading. A total of eight columns, including six CFDST slender columns and two CFDST short columns were tested under concentric loading. The test parameter includes the slenderness ratio of the columns and the thickness of the inner tube. The ultimate load, failure modes and axial load-deflection relationships of CFDST slender columns are presented. It was observed that square CFDST slender columns failed due to the overall buckling of the columns together with the localized buckling of the steel tube and concrete crushing. Increasing the slenderness ratio and decreasing the thickness of the inner steel tube reduced the ultimate load of CFDST slender columns. The applicability of the existing design code of CFST columns in designing CFDST slender columns was evaluated. It was found that the existing design codes significantly underestimated the ultimate loads of CFDST columns.

Keywords

concrete-filled double steel tubular columns slender section axial load design model

Introduction

Concrete-filled steel tubular (CFST) columns are often used in constructing tall buildings and bridge piers to carry large axial loads. The steel tube confines the infilled concrete effectively and acts as formwork during the construction. The CFST columns offer better mechanical performance in terms of strength, ductility, seismic and fire performance compared to the traditional reinforced concrete columns (Ahmed and Liang, 2021; Ahmed et al., 2022; Ci et al., 2021a; Ci et al., 2021b). Existing studies showed that confinement was more uniform for the circular cross-section than the square or rectangular cross-sections of CFST columns; therefore, the strength and ductility of square or rectangular CFST columns are lower than their circular counterparts (Sakino et al., 2004). However, the square and rectangular cross-sections of CFST columns offer ease of connection to the beams; thus, are deemed a preferred cross-section for construction (Wang et al., 2017).

The concrete-filled double steel tubular (CFDST) columns, an improved version (cross-section) of CFST columns, can be constructed by placing two steel tubes concentrically and filling the sandwiched and core section with concrete. The inner steel confined core concrete significantly improves the mechanical performance of the CFDST columns in terms of strength, ductility, seismic and fire performance, providing better performance than the conventional CFST columns and concrete-filled double-skin steel tubular (CFDST) columns with inner hollow section (Ahmed et al., 2019c; Ci et al., 2021a; Ci et al., 2021c; Xiong et al., 2017). As illustrated in Figure 1(a), square CFDST column composed of a circular core concrete-filled tube offers the advantages of both square and circular CFST columns. Pei (2005); Qian et al. (2011); Qian et al. (2015); Wang et al. (2017) and Ahmed et al. (2019a) reported test results of CFDST short columns under concentric and eccentric loading. Test results showed that the inner tube improved the strength and ductility of CFDST columns. Numerical models were also developed for short CFDST columns with square cross-sections to investigate their behavior under axial loading (Ahmed et al., 2018; Ci et al., 2020; Wang et al., 2017). However, all the existing studies were focused on short CFDST columns with a maximum length-to-width ratio (L/B₀) of 4. Generally, for investigating short CFDST columns, the length of the tested columns is limited to a maximum of 4 times the width of the square hollow section (SHS) to avoid the influences of the global buckling failure mechanism. A square CFDST column can be considered as a slender column if the L/B₀ ratio is greater than 4. However, until today, experimental investigation on square CFDST slender columns has rarely been performed. The only test found, based on an extensive literature review, was on three square CFDST slender columns performed by Liew et al. (2016), where the concrete strength of the columns was about 180 MPa. Test results showed that for very slender columns, the effective utilization of ultra-high-strength concrete was very minimum as the main failure of the columns was due to global buckling. On the contrary to square cross-section, more tests on circular CFDST slender columns were reported in the literature (Ibañez et al., 2017; Liew et al., 2016; Romero et al., 2017). In the absence of test data, Ahmed et al. (2019b, 2020) developed mathematical models to study the behavior of square CFDST slender columns under eccentric loading, considering preload effects, and developed design models.

Figure 1.

Cross-section of a square CFDST column composed of a circular core concrete-filled tube.

This study presents an experimental work performed on square CFDST slender columns under concentric loading. The test parameters included the slenderness ratio of the columns and the wall thickness of the inner tube. The accuracy of the existing design formulae of CFST columns specified by various design codes was also evaluated for the design of CFDST slender columns.

Test program

Preparation of test columns

A total of eight CFDST columns were tested in this study under concentric loading. The cross-section of the outer square tube was 200 × 200 mm and the diameter of the circular tube was 114 mm. While the thickness of the square tube was kept constant as 4.5 mm, two different wall thicknesses for the circular tubes, namely: 2.5 and 3.5 mm, were investigated. The tested columns were divided into two different groups (G1 and G2) according to the wall thickness of the circular tubes. The length of the columns (L) was changed to vary the slenderness ratio of the columns. Group G1 consisted of five columns, with the length-to-width ratio (L/ $B_{o}$ ) varying as 4, 6, 8, 10 and 12, whereas Group G2 consisted of three columns with L/ $B_{o}$ ratio varying as 4, 8 and 12. In the naming of the tested columns, the two numbers followed by the alphabet ‘S’ represent the Group number and L/ $B_{o}$ ratio. For example, in ‘S-1-6’, ‘S’ indicates the test specimen as square, ‘1’ indicates that the column belongs to Group G1, ‘6’ indicates that L/ $B_{o}$ ratio is 6.

Readily available square and circular hollow sections with a nominal yield strength of 235 MPa were used to fabricate the tested columns. To ensure that the steel tubes were placed concentrically, the outer and inner steel tubes were connected using two thin steel bars at both ends of the columns. All the tested columns were cast using the same concrete strength. The details of the tested columns are given in Table 1, where

f^{'} c u

is the concrete cube strength, L is the physical length of the columns,

B_{o}

and

t_{o}

are the width and thickness of the square tube, respectively and

D_{i}

and

t_{i}

are the diameter and thickness of the circular steel tube, respectively.

Table 1.

Details of square CFDST tested slender columns.

Group	No.	Specimen	Outer tube		Inner tube		$\frac{B_{o}}{t_{o}}$	$\frac{D_{i}}{t_{i}}$	L (mm)	L/ $B_{o}$	$f_{c u}^{'}$ (MPa)	$N_{\exp}$ (kN)
Group	No.	Specimen	$B_{o}$ (mm)	$t_{o}$ (mm)	$D_{i}$ (mm)	$t_{i}$ (mm)	$\frac{B_{o}}{t_{o}}$	$\frac{D_{i}}{t_{i}}$	L (mm)	L/ $B_{o}$	$f_{c u}^{'}$ (MPa)	$N_{\exp}$ (kN)
G1	1	S-1-4	200	4.5	114	3.5	44.44	32.57	800	4	47	3265
	2	S-1-6	200	4.5	114	3.5	44.44	32.57	1200	6	47	3211
	3	S-1-8	200	4.5	114	3.5	44.44	32.57	1600	8	47	3186
	4	S-1-10	200	4.5	114	3.5	44.44	32.57	2000	10	47	3172
	5	S-1-12	200	4.5	114	3.5	44.44	32.57	2400	12	47	2978
G2	6	S-2-4	200	4.5	114	2.5	44.44	45.60	800	4	47	3102
	7	S-2-8	200	4.5	114	2.5	44.44	45.60	1600	8	47	2957
	8	S-2-12	200	4.5	114	2.5	44.44	45.60	2400	12	47	2876

Note: $B_{o}$ and $t_{o}$ are the width and thickness of the outer square tube, respectively; $D_{i}$ and $t_{i}$ are the diameter and thickness of the inner circular steel tube, respectively; $f'_{c u}$ is the concrete cube strength and L is the length of the columns; N_exp is the experimental ultimate load.

Properties of steel and concrete

Three different steel tubes including outer tube and inner tubes with different thicknesses were used to construct the CFDST columns. Standard tensile test coupons were performed according to GB/T 228.1-2010 (2010) to measure the steel properties. The stress-strain curves obtained from the tensile coupons test, presented in Figure 2, show an obvious yield plateau. Table 2 summarizes the steel properties obtained from the coupon tests. The yield strength $(f_{s y})$ , tensile strength $(f_{s u})$ , elastic modulus $(E_{s})$ and the strain at peak stress $(ε)$ of the steel tubes are calculated from the average values of the three coupons results.

Figure 2.

Experimental stress-strain curves of steel tubes.

Table 2.

Summary of the tensile coupon tests results.

Tube type	No.	Dimension of tube (mm)	$f_{s y}$ (MPa)	$E_{s}$ (GPa)	$f_{s u}$ (MPa)	$ε$
Outer tube B_o × B_o × t_o (mm)	1	200 × 200 × 4.5	356.6 ± 7.2	202.6 ± 6.1	481.5 ± 0.6	0.15 ± 0.01
Inner tube D_i × t_i (mm)	2	114 × 2.5	314.4 ± 5.2	205.4 ± 5.3	375.3 ± 2.5	0.19 ± 0.01
Inner tube D_i × t_i (mm)	3	114 × 3.5	328.8 ± 10.0	198.2 ± 2.4	415.5 ± 6.5	0.15 ± 0.01

Note: ± represents the standard deviation of three coupon test results.

All columns were filled with ready mixed concrete having the same compressive strength. Three concrete cubes of 150 mm × 150 mm × 150 mm were cast and tested after 28 days to measure the compressive strength. The average compressive strength of the concrete cube was 47 MPa.

Instrumentation

All columns were tested using a 4000 kN hydraulic testing machine at the Beijing University of Technology, China. Considering the safety of the test and the height of the longest test specimen exceeding the height of the reaction frame, all test columns were loaded horizontally, as shown in Figure 3. In order to eliminate elephant foot buckling failure mode, both ends of all columns were restrained by steel clamps. The details of the steel clamps used in the tests are shown in Figure 4. The load was applied through two sets of loading devices, as shown in Figure 5, specially designed comprising loading and adapter plates. Similar loading devices were also used by Hadi and Widiarsa (2012) for testing composite columns. The loading plate had a unidirectional spherical hinge, as illustrated in Figure 6. The thickness of each adapter plate was 50 mm. Therefore, the distance from the hinge support to the other hinge support should be calculated as the sum of the length of the test specimens 100 mm. The end faces of the tested columns were coated with superhard gypsum and flattened to ensure evenness and to eliminate the gap between the columns and the loading adaptor plate.

Figure 3.

Test setup of a CFDST slender column under axial loading.

Figure 4.

Photo and schematic diagram of the fixed clamp: (a) steel clamps and (b) dimensions.

Figure 5.

Details of loading end of the test specimen.

Figure 6.

Photo and schematic diagram of the plate used for loading purposes: (a) loading plate and (b) dimensions of the loading plate.

The strain distributions of the tested columns were measured at the midheight of the columns using bi-directional strain gauges attached to the outer tube. Each bi-directional strain gauge included a pair of strain gauges to measure both the axial and hoop strains. Two pairs of bi-directional strain gauges were pasted on the tensile (H1-Z1) and compression (H3-Z3) sides of the midheight of the columns. The position of the bi-directional strain gauges is shown in Figure 7. The lateral and axial displacements of the tested columns were measured using displacement sensors. Except for Columns S-1-12 and S-2-12, lateral displacements of all tested columns were measured using three displacement sensors, whereas, for Columns S-1-12 and S-2-12, lateral displacements were measured using five sensors. The axial displacements of all tested columns were also measured during the tests using two displacement sensors. The arrangement of the test setup, including the placement of sensors and strain gauges, is shown in Figure 3. Before formal loading, each test column was preloaded to 100 kN. This was to remove any gap between the test columns and the loading devices. The columns were tested under displacement control at the rate of 1 mm/min. The end of the test was called when the axial deformation of the tested columns reached 30 mm. The DH18 acquisition system was used to record the data of applied load, strain gauges and displacement sensors.

Figure 7.

Position of the strain gauges on the square tube.

Test results

Failure modes

Figure 8 illustrates the typical failure modes of tested columns under concentric loading. The failure of Columns S-1-4 and S-2-4 was due to the localized buckling of the outer steel tubes, as illustrated in Figure 9. The local buckling was found to occur at the outer tube away from the center of the columns. Similar failure modes of CFDST short columns were observed by Ahmed et al. (2019a). The concrete in the tested columns was crushed at the region where the steel tube buckled. A similar failure mode of concrete was reported by Ahmed et al. (2019a). For Columns S-1-6, S-1-8, S1-10 and S-1-12, which had a larger slenderness ratio than Columns S-1-4 and S-2-4, global buckling of the columns was observed together with the buckling of the outer tubes. For Column S-1-12, buckling of the outer tube occurred at the center of the column. No elephant foot buckling failure was observed for the tested columns. The test results also showed that the utilization of steel clamps prevented the occurrence of elephant foot buckling at the column ends. The failure mode of Columns S-2-8 and S-2-12 were identical to Columns S-1-8 and S-1-12.

Figure 8.

Failure modes of test specimens.

Figure 9.

Local buckling of the outer tube of test specimens: (a) short columns and (b) slender columns.

The ultimate compressive loads of CFDST columns

Table 1 summarizes the ultimate loads of the tested columns recorded during the test. It was found that the inner tube provided confinement to the filled concrete that increased the ultimate load of the tested columns. The compressive load of the specimens S-1-4 and S-2-4 was 7% and 6% higher than their nominal load, calculated as $A_{s o} f_{s y o} + A_{c o} f^{'} c o + A_{s i} f_{s y i} + A_{c i} f^{'} c i$ , where, $A_{s o}$ and $A_{s i}$ are the cross-sectional area of outer and inner steel tube, respectively; $A_{c o}$ and $A_{c i}$ are the cross-sectional area of sandwiched and core concrete, respectively; $f_{s y o}$ and $f_{s y i}$ are the yield strength of outer and inner steel tube, respectively; $f^{'} c o$ and $f^{'} c i$ are the concrete compressive strength of sandwiched and core concrete, respectively. It should be noted that in calculating nominal strength, concrete cylindrical strength was used. The concrete cube strength measured in this study was converted to the compressive cylinder strength using equation (1), developed by L’Hermite (1955) as:

f^{'} c = (0.76 + 0.2 l o g_{10} (\frac{f^{'} c u}{19.6})) f^{'} c u

(1)

Furthermore, the test compressive strength of confined concrete to concrete cylindrical strength $(\frac{f^{'} c c}{f^{'} c})$ was calculated by subtracting the steel capacity (steel area × steel yield strength) to investigate the confinement effect. From Figure 10, it is seen that $\frac{f^{'} c c}{f^{'} c}$ decreased as the L/B₀ ratio increased. The $\frac{f^{'} c c}{f^{'} c}$ was higher than 1 for all columns in Group G1 except for the specimen S-1-12. However, for the columns in Group G2, $\frac{f^{'} c c}{f^{'} c}$ were lower than the columns in Group G1 which showed that the thicker inner tube provided more confinement to the core concrete. Test results showed that with the increase in the slenderness ratio (L/ $B_{o}$ ), the compressive loads of the CFDST columns were reduced considerably. When the slenderness ratio increased from 4 to 12, the ultimate loads of the columns in Group G1 decreased by 8.8%. Similarly, the ultimate loads of the columns in Group G2 decreased by 7.3% when the slenderness ratio increased from 4 to 12. Zhu et al. (2020) also found that for square CFDST slender columns with an inner square steel tube, increasing L/ $B_{o}$ ratio from 6 to 10 decreased the ultimate strength of CFDST slender columns by 10.8%. Moreover, decreasing the thickness of the inner steel tube decreased the ultimate loads of the columns. The ultimate load of Column S-2-4 was 5.0% lower than the ultimate load of Column S-1-4. Similarly, for Column S-2-8, the ultimate load was 7.2% lower than the ultimate load of Column S-1-8. However, for Column S-2-12, the reduction of the ultimate strength due to the reduction of the thickness of the inner steel tube was found to be lower compared to Columns S-2-4 and S-2-8. The ultimate load of Column S-2-12 was 3.4% lower than the ultimate load of Column S-1-12. This might be due to the fact that the buckling mode was more dominant than the concrete confinement when reaching the failure load.

Figure 10.

Influences of L/B₀ ratio on the confined compressive strength of concrete. (a) short columns (b) slender columns.

Load-deflection curves of the columns

Figure 11 presents the load-end shortening curves of the tested columns. The residual strength, which was taken as the axial strength at the end of the test (at 30 mm axial shortening) of short Columns S-1-4 and S-2-4 was calculated as 70% and 68% of their ultimate strengths, respectively. The residual strengths of Columns S-1-6, S-1-8, S1-10 and S-1-12 were calculated as 64, 57, 62 and 51%, respectively. Similarly, the residual strengths of Columns S-2-8 and S-2-12 were calculated as 67% and 66%, respectively. This proves that with the increase of the slenderness ratio, the residual strength of the columns decreased.

Figure 11.

Axial load-end shortening curves of CFDST columns: (a) short columns; (b) slender columns. (a) S-1-6 (b) S-1-8 (c) S-1-10 (d) S-1-12, (e) S-2-8 (f) S-2-12.

The lateral displacements of CFDST slender columns along various heights of the columns at different loading stages were recorded during the tests. From the lateral displacement curves given in Figure 12, it can be seen that with the increase of the axial load, the lateral displacement of the columns increased. However, the increase in the lateral displacement of the columns was significantly higher once the axial load exceeded 75% of the column’s ultimate load.

Figure 12.

Lateral displacement curves of CFDST slender columns along the column height: (a) S-1-6, (b) S-1-8, (c) S-1-10, (d) S-1-12, (e) S-2-8 and (f) S-2-12.

The axial load-midheight lateral displacement curves (N-δ_m) of the tested columns are shown in Figure 13. A small drop of the axial load in Column S-1-10 was observed in Figure 13(c), which might be attributed to local buckling in the outer steel skin close to the failure load. Moreover, for Columns S-1-6 and S-2-8, a rapid decrease of the column axial load with the increase of the midspan lateral displacement was observed. This might be because of the excessive local buckling of the outer tube. However, for other tested columns, the N-δ_m curves can be seen as more flat upon reaching the ultimate load of the columns.

Figure 13.

Axial load versus mid-height lateral displacement curves of CFDST slender columns: (a) S-1-6, (b) S-1-8, (c) S-1-10, (d) S-1-12, (e) S-2-8 and (f) S-2-12.

Design models of square CFDST slender columns

There are no design specifications available for designing CFDST columns. The applicability of existing design models of CFST columns specified by AISC 360-16 (2016) and Eurocode 4 (2004) for designing square CFDST slender columns is evaluated in this section. The test results obtained from this study are used to validate the design predictions.

Eurocode 4 (2004)

Eurocode 4 (2004) considers the confinement of circular CFST columns and the higher resistance of concrete is accounted for using the concrete coefficient of 1.0 in contrast to other design codes such as AISC 360-16 (2016) and ACI 318-19 (2019), where concrete compressive strength is reduced using a factor, which is usually 0.85. According to Eurocode 4 (2004), the formulae to calculate the ultimate strengths $(N_{u})$ of circular and rectangular CFST columns are:

Circular CFST columns

N_{u} = η_{a} A_{s} f_{s y} + A_{c} f^{'} c (1 + η_{c} \frac{t}{D} \frac{f_{s y}}{f^{'} c})

(2)

\begin{matrix} η_{a} = 0.25 (3 + 2 \bar{λ}) & (η_{a} \leq 1 .0) \end{matrix}

(3)

\begin{matrix} η_{c} = 4.9 - 18.5 \bar{λ} + 17 {\bar{λ}}^{2} & (η_{c} > 0) \end{matrix}

(4)

where,

A_{s}

and

A_{c}

are the cross-sectional area of steel and concrete, respectively;

f_{s y}

is the steel yield strength and

f^{'} c

is the concrete compressive strength;

\bar{λ}

is the relative slenderness ratio expressed as:

\bar{λ} = \sqrt{\frac{N_{u}}{N_{c r}}}

(5)

where

N_{c r}

is the Euler buckling load, calculated as:

N_{c r} = \frac{π^{2} {(E I)}_{e f f}}{L^{2}}

(6)

where

{(E I)}_{e f f}

is the effective flexural stiffness, calculated as:

{(E I)}_{e f f} = E_{s} I_{s} + 0.6 E_{c m} I_{c}

(7)

where

E_{s}

and

E_{c m}

are the elastic modulus of steel and concrete, respectively;

I_{s}

and

I_{c}

are the second moment of area of steel and concrete, respectively. In equation (7),

E_{c m}

is calculated as:

E_{c m} = 22000 {(\frac{f^{'} c + 8}{10})}^{\frac{1}{3}}

(8)

Rectangular CFST columns

N_{u} = A_{s} f_{s y} + A_{c} f^{'} c

(9)

Eurocode 4 (2004) specified a slenderness limit

\frac{B_{o}}{t_{o}} \leq 52 \sqrt{\frac{235}{f_{s y o}}}

, beyond which local buckling should be considered. Accordingly, the tested columns in this study were deemed to exceed this limit and therefore, the effective width of the outer tube was calculated using the formula suggested by Eurocode 4 (2004) and Gardner and Theofanous (2008) as:

ρ = \frac{0.772}{{\bar{λ}}_{p}} - \frac{0.079}{{\bar{λ}}_{p}^{2}}

(10)

λ_{p} = \sqrt{\frac{12 (1 - v_{s}^{2}) f_{s y o}}{k π E_{s o}}} \frac{B_{o}}{t_{o}}

(11)

where

ρ

is the local buckling reduction factor;

{\bar{λ}}_{p}

is the plate slenderness;

E_{s o}

is the elastic modulus of outer steel tube;

k

is the buckling coefficient, taken as 4 and

v_{s}

is Poisson’s ratio of steel tube, taken as 0.3.

Therefore, the ultimate strength of square CFDST columns can be calculated as:

N_{u} = A_{s o e} f_{s y o} + A_{c o} f^{'} c o + η_{a} A_{s i} f_{s y i} + A_{c i} f^{'} c i (1 + η_{c} \frac{t_{i}}{D_{i}} \frac{f_{s y i}}{f^{'} c i})

(12)

where,

A_{s o e}

and

A_{s i}

are the effective cross-sectional area of outer and inner steel tube, respectively;

A_{c o}

and

A_{c i}

are the cross-sectional area of sandwiched and core concrete, respectively;

f_{s y o}

and

f_{s y i}

are the yield strength of outer and inner steel tube, respectively;

f^{'} c o

and

f^{'} c i

are the concrete compressive strength of sandwiched and core concrete, respectively.

According to Eurocode 4 (2004), a slenderness reduction factor $χ$ can be used to consider the slenderness ratio in calculating the ultimate loads of slender section as:

N_{u, E C 4} = χ N_{u}

(13)

where,

χ

is suggested in Eurocode 3 (2005) as:

χ = \frac{1}{φ + \sqrt{φ^{2} - {\bar{λ}}^{2}}} \leq 1.0

(14)

φ = \frac{1 + α (\bar{λ} - 0.2) + {\bar{λ}}^{2}}{2}

(15)

where

α

is the imperfection factor corresponding to the relevant buckling curve, which was taken as 0.49 based on buckling curve ‘c’ for CFDST columns.

In calculating the relative slenderness ratio of CFDST columns $(\bar{λ})$ , the effective flexural stiffness ${(E I)}_{e f f}$ was calculated as:

{(E I)}_{e f f} = E_{s, s o} I_{s, s o} + 0.6 E_{c m, c o} I_{c, c o} + E_{s, s i} I_{s, s i} + 0.6 E_{c m, c i} I_{c, c i}

(16)

where

E_{s}

and

E_{c m}

are the elastic modulus of steel and concrete, respectively;

I_{s}

and

I_{c}

are the second moment of area of steel and concrete, respectively; subscripts so, si, co and ci refer to the outer tube, inner tube, sandwiched concrete and core concrete, respectively.

AISC 360-16 (2016)

According to AISC 360-16 (2016), the composite column should be designed based on the category of compact, noncompact or slender sections. A compact section can reach the yield strength, whereas a non-compact section can not reach the yield strength of the steel tube. The normalized slenderness limit according to AISC 360-16 (2016) can be calculated as $\frac{B_{o}}{t_{o}} \sqrt{\frac{f_{s y o}}{E_{s, s o}}} \leq 2.26$ . It was found that the tested columns in this study were less than the slenderness limit specified by AISC 360-16 (2016); therefore, the columns should be considered as the compact section. Thus, the ultimate strength of CFDST columns with the compact section can be calculated as:

N_{u, A I S C} = {\begin{matrix} N_{o} [{0.658}^{(\frac{N_{o}}{N_{e}})}] & for N_{e} \geq 0.44 N_{o} \\ 0.877 N_{e} & for N_{e} < 0.44 N_{o} \end{matrix}

(17)

N_{o} = A_{s o} f_{s y o} + C_{2} A_{c o} f^{'} c o + A_{s i} f_{s y i} + C_{2} A_{c i} f^{'} c i

(18)

N_{e} = \frac{π^{2}}{{(K L)}^{2}} {(E I)}_{e f f}

(19)

{(E I)}_{e f f} = E_{s, s o} I_{s, s o} + E_{s, s i} I_{s, s i} + C_{4} E_{c m, c o} I_{c, c o} + C_{4} E_{c m, c i} I_{c, c i}

(20)

C_{4} = 0.6 + 2 (\frac{A_{s}}{A_{s} + A_{c}}) \leq 0.9

(21)

C₂ in equation (18) was taken as 0.85 for sandwiched concrete and 0.95 for core concrete.

Design model developed by Ahmed et al. (2019b)

Ahmed et al. (2019b) developed design formulae to calculate the ultimate strength of square CFDST slender columns similar to the design guidelines of Eurocode 4 (2004) which applies to a large range of slenderness ratio of the column; however, the accuracy of the model was only validated against the numerical results. The formula to calculate the ultimate strength of the CFDST slender column was suggested as:

N_{u, A h m e d} = χ N_{u}

(22)

where

N_{u}

was suggested as:

N_{u} = f_{s y o} A_{s o e} + f_{s y i} A_{s i} + γ_{c o} {f^{'}}_{c o} A_{c o} + γ_{c i} {f^{'}}_{c c i} A_{c i}

(23)

where

γ_{c}

is the strength reduction factor for the compressive strength of concrete to consider column size effect proposed by Liang (2009) as

1.85 D_{c}^{- 0.135}

where

D_{c}

was calculated as was calculated as;

(B_{o} - 2 t_{o})

the effective area of the outer tube was calculated based on AS/NZS 2327 (2017);

f^{'} c o

is the unconfined compressive strength of sandwiched concrete and

f^{'} c c i

is the compressive confined concrete strength of core concrete calculated as:

{f^{'}}_{c c i} = 5.2 {(γ_{c} f^{'} c i)}^{0 . 91} {(\frac{f_{r p i}}{γ_{c} f^{'} c i})}^{a} + γ_{c} f^{'} c i

(24)

where

a = {(γ_{c} f^{'} c i)}^{- 0.06}

and

f_{r p i}

is the lateral pressure to the core concrete, calculated as (Liang and Fragomeni, 2009)

f_{r p i} = {\begin{matrix} 0.7 (v_{e} - v_{s}) (\frac{2 t_{i}}{D_{i} - 2 t_{i}}) f_{s y i} & for \frac{D_{i}}{t_{i}} \leq 47 \\ (0.006241 - 0.0000357 \frac{D_{i}}{t_{i}}) f_{s y i} & for 47 < \frac{D_{i}}{t_{i}} \leq 150 \end{matrix}

(25)

where

v_{e}

and

v_{s}

are the Poisson’s ratios of the CFST column and the steel hollow tube, respectively proposed by Tang et al. (1996).

In equation (22), $χ$ is calculated as equation (14); however, Ahmed et al. (2019b) suggested a formula to calculate $φ$ as:

φ = \frac{1.03 + 0.21 (\bar{λ} - 0.2) + {\bar{λ}}^{2}}{2}

(26)

Evaluation of design predictions

The ultimate loads of the tested columns reported in this study were predicted using the codified design models and compared with the ultimate loads of the tested columns. From the comparisons given in Table 3, it is seen that Eurocode 4 (2004) and AISC 360-16 (2016) underestimated the ultimate loads of the tested columns. The

\frac{N_{u, E C 4}}{N_{\exp}}

and

\frac{N_{u, A I S C}}{N_{\exp}}

were calculated as 0.79 and 0.87, respectively. Although Eurocode 4 (2004) utilized the concrete coefficient of 1, it provided a significant underestimation which was due to the reduction of the effective area of the outer tube. On the contrary, the plate slenderness limit used for AISC 360-16 (2016) and Ahmed et al. (2019b) was lower than the noncompact/slender section thus the effective area of the outer tube was taken as the full area of the steel tube. The formulae proposed by Ahmed et al. (2019b) provided the best prediction compared to Eurocode 4 (2004) and AISC 360-16 (2016). The average

\frac{N_{u, A h m e d}}{N_{\exp}}

was calculated as 0.96 based on Ahmed et al. (2019b) equation. The comparisons between the test results and the design buckling curves of Eurocode 3 (2005), AISC 360-16 (2016) and Ahmed et al. (2019b) are presented in Figure 14. It can be seen that AISC 360-16 (2016) and Ahmed et al. (2019b) yield a better prediction compared to Eurocode 3 (2005). However, considering the limited data used for the validation, further test results on CFDST columns with a higher slenderness ratio should be used to evaluate the accuracy of the design model, developed by Ahmed et al. (2019b).

Table 3.

Experimental ultimate strengths of square CFDST columns against design predictions.

Specimen	$N_{\exp}$ (kN)	$N_{u, E C 4}$ (kN)	$N_{u, A I S C}$ (kN)	$N_{u, A h m e d}$ (kN)	$\frac{N_{u, E C 4}}{N_{\exp}}$	$\frac{N_{u, A I S C}}{N_{\exp}}$	$\frac{N_{u, A h m e d}}{N_{\exp}}$
S-1-4	3265	2690	2841	3194	0.82	0.87	0.98
S-1-6	3211	2620	2805	3061	0.82	0.87	0.95
S-1-8	3186	2505	2756	2998	0.79	0.87	0.94
S-1-10	3172	2387	2695	2929	0.75	0.85	0.92
S-1-12	2978	2264	2621	2850	0.76	0.88	0.96
S-2-4	3102	2535	2730	3044	0.82	0.88	0.98
S-2-8	2957	2366	2651	2861	0.80	0.90	0.97
S-2-12	2876	2142	2524	2722	0.74	0.88	0.95
Mean					0.79	0.87	0.96
Standard deviation (SD)					0.03	0.01	0.02
Coefficient of variance (CoV)					0.04	0.02	0.02

Figure 14.

Comparisons of the design buckling curves with the test results.

Conclusions

This paper presents the test results of square CFDST slender columns subjected to concentric loading. A total of 8 columns were tested, where the test parameters were the column slenderness ratio and the wall thickness of the inner tube. The accuracy of the design guidelines of existing CFST columns specified by various design codes was evaluated in predicting the ultimate strengths of the tested columns by comparing the ultimate strengths. The findings from this study are listed below:

(1) The common modes of failure of CFDST columns with a slenderness ratio of less than 8 were the localized buckling of the steel tubes together with the crushing of concrete in the same region. For columns with a higher slenderness ratio, global buckling failure was observed.

(2) With the increase of the slenderness ratio, the column ultimate loads were reduced significantly. In addition, decreasing the inner steel wall tube thickness decreased the column ultimate loads.

(3) The residual strength of CFDST columns, which was taken as the axial strength at the end of the test (at 30 mm axial shortening), ranged between 51% and 70% of the column’s ultimate strength. The residual strength of the column decreased with the increase in the column slenderness.

(4) From the comparisons with the design code predictions, it was found that Eurocode 4 (2004) and AISC 360-16 (2016) significantly underestimated the column ultimate loads. However, the formulae suggested by Ahmed et al. (2019b) provided a better estimation of the column ultimate loads.

This study carried out tests on CFDST slender columns under axial loading. However, tests on CFDST slender columns under axial loading combined with uniaxial bending are also very limited and the accuracy of the N-M interaction curves specified by existing design codes for conventional CFST columns in designing for such a column has not been evaluated yet. Therefore, further tests on such a column under axial loading combined with uniaxial bending can be undertaken in the future to compare the N-M interaction curves.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iDs

Shicai Chen

Mizan Ahmed

Junchang Ci

Appendix

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