Fiber element modeling of circular double-skin concrete-filled stainless-carbon steel tubular columns under axial load and bending

Abstract

Circular concrete-filled double-skin steel tubular (CFDST) columns with external stainless-steel are high-performance composite columns that have potential applications in civil construction including the construction of offshore structures, bridge piers, and transmission towers. Reflecting the limited research performed on investigating their mechanical performance, this study develops a computationally efficient fiber model to simulate the responses of short and slender beam-columns accounting for the influences of material and geometric nonlinearities. Accurate material laws of stainless steel, carbon steel, and confined concrete are implemented in the mathematical modeling scheme developed. A new solution algorithm based on the Regula-Falsi method is developed to maintain the equilibrium condition. The independent test results of short and slender CFDST beam-column are utilized to validate the accuracy of the theoretical solutions. The influences of various column parameters are studied on the load-axial strain $(P - ε)$ curves, load-lateral deflection $(P - u_{m})$ curves, column strength curves, and interaction curves of CFDST columns. Design formulas are suggested for designing short and beam-columns and validated against the numerical results. The computational model is found to be capable of simulating the responses of CFDST short and slender columns reasonably well. Parametric studies show that the consideration of the concrete confinement is important for the accuracy of the prediction of their mechanical responses. Furthermore, high-strength concrete can be utilized to enhance their load-carrying capacity particularly for short and intermediate slender beam-columns. The strengths of CFDST columns computed by the suggested design model are in good agreement with the test and numerical results.

Keywords

circular concrete-filled double-skin steel tubular columns composite columns computational analysis short and slender columns design models

Introduction

A circular concrete-filled double-skin steel tubular (CFDST) column is composed of two circular hollow tubes sitting concentrically and their sandwiched section is filled with concrete as illustrated in Figure 1. Owing to the inner hollow tube, the CFDST columns are much lighter compared to concrete-filled steel tubular (CFST) columns and lead to a saving in foundation costs (Li et al., 2012). Furthermore, the flexural stiffness and capacity of CFDST columns, as well as their cyclic performance, are higher than CFST columns. Applications of such columns include the construction of offshore structures, bridge piers, and transmission towers (Ahmed et al., 2021; Nakanishi et al., 1999; Sasy Chan et al., 2020; Wei et al., 1995; Zhou and Young, 2019). However, the outer tube may be subjected to a harsh environment which may affect their performance remarkably.

Figure 1.

A cross-sectional view of the circular concrete-filled double-skin steel tubular column.

Due to its excellent corrosion resistance and elegance in terms of appearance, stainless steel has gained wide attraction in the construction industry. Some of the applications of stainless steel include the construction of the Chrysler Building in New York, Pompidou Centre in Paris, and Lloyds Building in London (Gardner, 2008). A circular CFDST column with an external stainless steel tube is an innovative composite column that offers improved mechanical performance compared to CFDST columns made of carbon steel. Furthermore, the utilization of the external stainless steel tube can increase their durability while used in offshore structures. Considering the cost of stainless steel which is about 5 times more expensive compared to carbon tube, high-strength concrete or inner steel tube can be used to reduce the thickness of the outer stainless tube; thus, construction cost of such columns can be reduced. However, proper investigation is required to ascertain their actual performance to develop cost-effective design solutions.

Experimental work on CFDST short and slender columns with carbon steel has been reported earlier (Essopjee and Dundu, 2015; Ekmekyapar and Hasan, 2019; Lin and Tsai, 2001; Li et al., 2012; Li and Cai, 2019; Tao et al., 2004; Uenaka et al., 2010; Yan and Zhao, 2020). Preliminary studies showed that the smaller the diameter-to-thickness $(D_{o} / t_{o})$ ratio of the outer tube, the higher the ductility of the column (Tao et al., 2004). Furthermore, the hollow ratio $(κ)$ of the columns was found to influence the performance of the columns considerably (Yan and Zhao, 2020). However, investigations of the performance of circular CFDST columns with stainless-carbon steel have been very rare. Han et al. (2011), Wang et al. (2019), Zhao et al. (2021), and Wen (2017) investigated CFDST columns with stainless-carbon steel combinations through the experimental setup. Wang et al. (2019) utilized the high-strength carbon tube with the maximum steel yield strength of 1029 MPa, as well as different strengths of concrete to construct CFDST columns. Although the compressive strengths of the tested columns improved for the increased strength of concrete, the column ductility was found to be decreased. Recently, Zhao et al. (2021) investigated CFDST beam-columns loaded eccentrically as well as CFDST beams under flexural loads. The tested columns failed in a ductile manner. The column slenderness $(L / r)$ and loading eccentricity $(e / D_{o})$ ratio were found to influence their load-carrying capacities. Recently, Hamoda et al. (2021) and Zhou and Young (2018) reported test results on CFDST columns where outer and inner steel tubes were made of stainless and aluminum, respectively.

Extensive numerical studies were performed to study the inelastic performance of circular traditional CFST columns with outer stainless steel tube (Hassanein, 2010; Patel et al., 2014, 2017; Tokgoz et al., 2021) and CFDST columns with outer carbon tube (Ahmed et al., 2021; Liang, 2017, 2018; Huang et al., 2010; Pagoulatou et al., 2014; Tao et al., 2004; Yan et al., 2021). However, computational models on CFDST columns with outer stainless steel tube are limited and developed by researchers such as Wang et al. (2019), Wen (2017), Yang et al. (2020), Le et al. (2021), and Hassanein and Kharoob (2014) using finite element (FE) tool ABAQUS. Wang et al. (2019) and Hassanein and Kharoob (2014) adopted the material laws of concrete originally proposed for CFST columns. Their research work showed that the confinement in CFDST columns was overestimated. Recently, Ahmed et al. (2021) suggested a new lateral pressure model for CFDST columns made of carbon steel based on extensive test data that can accurately simulate the responses of such columns. Furthermore, the only FE model developed by Wen (2017) for investigating CFDST beam-columns with external stainless steel tube utilized the two-stage constitutive material laws of stainless steel proposed by Rasmussen (2003). However, the material model of Rasmussen (2003) significantly underestimates the strain-hardening characteristics of stainless steel under compression, and thus underestimates the ultimate strengths of CFDST columns (Patel et al., 2014; Tao et al., 2011). However, the three-stage material model proposed by Quach et al. (2008) can provide more accurate estimations compared to Rasmussen (2003) model. In addition, Hamoda et al. (2021) and Patel et al. (2020) developed numerical models of CFDST short columns with both outer and inner steel tubes composed of stainless steel. It is seen that although inclusions of the inner stainless steel tube improve the ductility compared to the CFDST columns with inner carbon steel tube, the increase in the ultimate strength is very insignificant. This can be attributed to the fact that the inner void cannot provide resistance to the inner steel tube from buckling outwardly; thus, replacing stainless-steel with carbon steel cannot result in improvement of significant structural performance. Although the confinement mechanism of CFDST columns with external stainless steel or carbon steel is the same considering the distinguished strain-hardening behavior of stainless-steel, the ductility of the CFDST columns with external stainless steel tube is higher than CFDST columns with external carbon steel, as reported by Hamoda et al. (2021). Considering the cost of stainless steel which is more than 5 times the cost of carbon steel, it is necessary to investigate the performance of CFDST columns with external stainless steel and develop design recommendation accordingly.

This paper presents a theoretical model that is capable of capturing the behavior of CFDST short and slender columns loaded either concentrically or eccentrically. Accurate material laws of stainless steel, confined concrete, and carbon steel tube are implemented in the mathematical model developed. The validation of the computational model is presented. The fundamental behavior of CFDST columns is investigated in detail. The design equations are also suggested for estimating their compressive strengths and interaction curves.

Fiber model formulation

General

The computational model employs the fiber analysis approach for predicting the load-strain curves, load-lateral deflection curves, and interaction curves of CFDST columns. The formulation of the fiber method includes dividing the cross-section into small fibers as illustrated in Figure 2. The assumptions behind the computational model are that the plane section remains plane after deformation and the contact of the steel and concrete is intact (Ahmed and Liang, 2020a, 2020b, 2021). The plane section assumption results in a linear strain distribution through the cross-sectional depth as seen in Figure 2. For beam-column analysis, strains of the fibers are estimated from the neutral axis depth $(d_{n})$ and curvature $(φ)$ of the column (Ahmed et al., 2019a; Liang, 2009). The bending moment (M) and compressive load $(P)$ are calculated by the stress integration.

Figure 2.

Strain distributions and fiber discretization of the cross-section (Liang, 2018).

Simulation of axial load-strain $(P - ε)$ relationship curves

During the cross-section analysis under axial loading, the stresses of the fibers are determined from the uniaxial material relationships. The axial load $(P)$ is determined as the stress resultant. An iterative computational scheme as illustrated in Figure 3 is employed to simulate the complete $P - ε$ curves. The peak load is taken as the maximum axial load from the $P - ε$ curves.

Figure 3.

Analysis procedure for simulating $P - ε$ analysis. (a) Stainless-steel and (b) structural steel.

Simulation of axial load-lateral deflection $(P - u_{m})$ relationships

During the overall buckling analysis, the slender CFDST beam-column is assumed to be loaded at both ends under the same eccentricity (e) and the deflection of the column will be part of the sine wave. The initial imperfection $(u_{o})$ and second-order effects $(u_{m})$ are included in the mathematical formulation. The nonlinear axial load-lateral deflection $(P - u_{m})$ response analysis of CFDST slender beam-columns considering initial imperfection $(u_{o})$ of the columns and second-order effects due to load eccentricity (e) and lateral displacement (u_m) is performed utilizing a displacement-control method where lateral displacement (u_m) at the mid-length of the column is initialized and the corresponding curvature $(ϕ_{m})$ at the column mid-length is calculated. The external moment at its mid-height is calculated as

M_{m e} = P (e + u_{m} + u_{o})

(1)

For each increment of the curvature, the axis neutral depth is adjusted using the Regula-Falsi method until the external and internal bending moments at the column mid-length become equal to ensure the equilibrium condition is met. The internal axial load (P) is then calculated. The lateral displacement (u_m) is increased incrementally, and an iterative procedure is employed until either the maximum specified displacement limit is reached or the axial load drops to 50% of the maximum axial load $(P < 0.5 P_{\max})$ . The formulation and analysis steps to obtain the $P - u_{m}$ curves of beam-columns are given in detail by Liang (2018) and Ahmed et al. (2020b).

Simulation of strength envelopes

The strength envelopes of the beam-columns are simulated by employing the mathematical model developed. The analysis procedure includes firstly calculating the peak compressive strength (P_o) of concentrically compressed slender columns using the nonlinear analysis process described in the Section Simulation of Axial Load-Lateral Deflection (P−u_m) Relationships. For an increment of axial load $(P_{u})$ which is taken as the one-tenth of the peak load (P_o), the internal bending moment is solved from the load-moment-curvature relationships proposed by Liang (2018) and Ahmed et al. (2020b). The Regula-Falsi method is employed to adjust the curvature at the column end to maintain the mid-length moment equilibrium condition. An incremental-iterative computational analysis is performed to capture the maximum end moment at each curvature increase for load increment from zero to P_o.

The Regula-Falsi method

The Regula-Falsi method is employed to adjust the depth of the neutral axis $(d_{n})$ during the nonlinear analysis in order to maintain the force equilibrium condition (Ahmed et al., 2021a). The Regula-Falsi method requires two initial guesses to initiate the analysis. The depth of the neutral axis is then calculated as

d_{n, j + 3} = d_{n, j + 2} - \frac{(d_{n, j + 2} - d_{n, j + 1}) r_{p, j + 2}}{r_{p, j + 2} - r_{p, j + 1}}

(2)

in which j is the iteration number and

r_{p}

is the residual moment. The values of

d_{n, 1}

and

d_{n, 2}

are taken as

D_{o}

and

D_{o} / 2

, respectively. According to the Regula-Falsi method when

(r_{p, 1}) \times (r_{p, 2}) < 0 then d_{n, 2} = d_{n, 3}; else d_{n, 1} = d_{n, 3}

. The analysis stops when the residual moment obtained the convergence criterion of

| r_{p} | < ε_{k}

, in which

ε_{k} = 10^{- 4}

Similarly, the moment equilibrium condition for the increase of the curvature during the interaction diagram analysis is maintained using the Regula-Falsi equation given in equation (2). The initial values of $ϕ_{n, 1}$ and $ϕ_{n, 2}$ are taken as $10^{- 6}$ and $10^{- 10}$ , respectively.

Material constitutive models

Steel

The material models account for the confinement effects on the steel tubes by applying a reduction factor of 0.9 to reduce their yield stress (Ahmed et al., 2018, 2019b; Liang, 2017; Patel et al., 2014, 2017). The accurate material model suggested by Quach et al. (2008) shown in Figure 3 is adopted for the stainless steel tube. Abdella et al. (2011) proposed the inverse version of the material model proposed by Quach et al. (2008) to calculate the stresses as a function of strains. Figure 4 illustrates the material relationships of structural carbon steel adopted in mathematical modeling. Expressions proposed by Liang (2009) are used to calculate the stress from the reduced yield strain $(ε_{0.9 s y})$ to hardening strain $(ε_{s t})$ taken as 0.005. On the onset of the hardening strain, formulas suggested by Mander (1983) are employed to calculate the stresses up to the ultimate strain $(ε_{s u})$ which is prescribed as 0.2 (Ahmed and Liang, 2020a; Ahmed et al., 2021; Liang, 2017).

Figure 4.

Stress–strain relationships of: (a) stainless-steel and (b) structural steel.

Concrete

The two-stage idealized material relationships of concrete are given in Figure 5 where the longitudinal stress $(σ_{c})$ of the concrete at the ascending branch is calculated based on the formulations of Mander et al. (1988) written as

σ_{c} = \frac{f_{c c}^{'} (ε_{c} / ε_{c c}^{'}) λ}{{(ε_{c} / ε_{c c}^{'})}^{λ} + λ - 1} for 0 \leq ε_{c} \leq ε_{cc}^{'}

(3)

λ = \frac{E_{c} ε_{c c}^{'}}{E_{c} ε_{c c}^{'} - f_{c c}^{'}}

(4)

where

ε_{c}

is the longitudinal strain of concrete fiber;

f_{c c}^{'}

and

ε_{c c}^{'}

are the compressive strength of confined concrete and the compressive strain;

E_{c}

is the elastic modulus of concrete given by Lim and Ozbakkaloglu (2014)

E_{c} = 4400 \sqrt{γ_{c} f_{c}^{'}} (MPa)

(5)

where

γ_{c}

is the reduction factor of concrete strength in CFDST columns suggested by Liang (2017) as

γ_{c} = 1.85 D_{c}^{- 0.135}

, where

D_{c} = D_{o} / 2 - t_{o} - D_{i} / 2

Figure 5.

Material constitutive laws of confined and unconfined concrete.

Mander et al. (1988) suggested expressions to estimate the confined concrete strength $(f_{c c}^{'})$ and the corresponding strain $(ε_{c c}^{'})$ written as

f_{c c}^{'} = (1 + \frac{4.1 f_{r p}}{γ_{c} f_{c}^{'}}) γ_{c} f_{c}^{'}

(6)

ε_{c c}^{'} = ε_{c}^{'} + \frac{20.5 f_{r p} ε_{c}^{'}}{γ_{c} f_{c}^{'}}

(7)

ε_{c}^{'} = 0.00076 + \sqrt{(0.626 γ_{c} f_{c}^{'} - 4.33) \times 10^{- 7}}

(8)

in which

f_{r p}

is the lateral pressure inserted by the steel tubes to confined concrete. Ahmed et al. (2021) proposed expressions to calculate

f_{r p}

for CFDST columns made of carbon steel based on extensive test results defined as

f_{r p} = 23.471 \times (\frac{t_{o}}{D_{o}}) \times (\frac{σ_{0.2}}{γ_{c} f_{c}^{'}}) - 0.096 ξ^{2} - 0.067 κ^{2} + 0.411

(9)

where

ξ

is the confinement factor defined as

ξ = \frac{A_{s o} σ_{0.2} + A_{s i} f_{s y i}}{A_{c} γ_{c} f_{c}^{'}}

(10)

where

A_{s o}

A_{s i}

, and

A_{c}

are the cross-sectional area of stainless steel tube, carbon tube, and concrete, respectively. The hollow ratio

(κ)

is calculated as

κ = \frac{D_{i}}{D_{o} - 2 t_{o}}

(11)

Lim and Ozbakkaloglu (2014) provided formulas to calculate the stresses at the descending branch of the stress–strain curve defined as

σ_{c} = f_{c c}^{'} - \frac{f_{c c}^{'} - f_{c r}}{1 + {(ε_{c} - ε_{c c}^{'} / ε_{c i} - ε_{c c}^{'})}^{- 2}} for ε_{c} > ε_{cc}^{'}

(12)

where

f_{c r}

and

ε_{c i}

are the residual concrete strength and the strain at the inflection point that controlled the shape of the curve used as 0.02 in this study.

The residual strength of confine concrete $(f_{c r})$ can be calculated as $f_{c r} = β_{c} f_{c c}^{'}$ in which $β_{c}$ is the factor for the strength degradation which is ranged between 0 and 1. By interpreting the test results, expressions to determine $β_{c}$ are suggested herein as

β_{c} = 3.705 \times (\frac{t_{o}}{D_{o}}) \times (\frac{σ_{0.2}}{γ_{c} f_{c}^{'}}) + 0.023 ξ^{2} - 0.321 κ^{2} + 0.002 \times (\frac{t_{i}}{D_{i}}) \times f_{s y i} + 0.108

(13)

The tensile behavior of concrete under tension is simulated using the stress–strain model depicted in Figure 5 in which stress decreases linearly from the onset of the cracking strain $(ε_{t c})$ to the maximum tensile strain where $ε_{t u} = 10 ε_{t c}$ . The maximum tensile strength is calculated as $0.6 \sqrt{γ_{c} f_{c}^{'}}$ (Ahmed et al., 2020b).

Model validation

CFDST short columns under axial loading

The fiber model was used to analyze the load-axial strain responses of test specimens reported by Wang et al. (2019), Han et al. (2011), and Wen (2017). The measured peak compressive strengths of the tested columns are compared with the numerical prediction in Table 1. The peak compressive strength is taken as the first peak load if the measured

P - ε

curve has a strain-softening branch, whereas the ultimate load is defined as the axial load at the onset of the strain at 0.01 if the

P - ε

curve has no obvious strain-softening branch (Katwal et al., 2017; Tao et al., 2013; Wang et al., 2019). As can be observed, the fiber model can predict the peak test compressive strengths of the columns reasonably well. The average prediction-to-measured ultimate strength is estimated as 0.96 with a corresponding SD value of 0.06. The accuracy of the model is further validated by comparing the predicted

P - ε

curves of CFDST columns with the test results. For comparison purposes, when the ultimate strain of the column under simulation reached the maximum strain of the tested column, the analysis was stopped. From the comparisons given in Figure 6, it is observed that the computer model can as well reasonably predict the

P - ε

curves of such columns observed experimentally.

Table 1.

Peak compressive strengths of circular concrete-filled double-skin steel tubular short columns.

Column	$D_{o} \times t_{o} (mm)$	$σ_{0.2} (MPa)$	$D_{i} \times t_{i} (mm)$	$f_{s y i} (MPa)$	$f_{c}^{'} (MPa)$	$P_{u, \exp} (kN)$	$P_{u, n u m} (kN)$	$P_{u, n u m} / P_{u, \exp}$	Ref
C1-1	220 × 3.6	320	159 × 3.7	380.6	55.8	2537	2537	1.00	Han et al. (2011)
C1-2	220 × 3.6	320	159 × 3.7	380.6	55.8	2566	2537	0.99
C2-1	220 × 3.6	320	106 × 3.7	380.6	55.8	3436	3048	0.89
C2-2	220 × 3.6	320	106 × 3.7	380.6	55.8	3506	3048	0.87
AC140 × 3-HC22 × 4-C40	140.2 × 2.9	300	22.1 × 4.1	794	40.5	1410	1394	0.99	Wang et al. (2019)
AC140 × 3-HC22 × 4-C80	140.2 × 2.9	300	22.1 × 4.1	794	79.9	1845	1806	0.98
AC140 × 3-HC22 × 4-C120	140.2 × 2.9	300	22.1 × 4.1	794	115.6	2321	2263	0.98
AC140 × 3-HC32 × 6-C40	140.2 × 2.9	300	32 × 5.5	619	40.5	1423	1453	1.02
AC140 × 3-HC32 × 6-C80	140.2 × 2.9	300	32 × 5.5	619	79.9	2012	1866	0.93
AC140 × 3-HC32 × 6-C120	140.2 × 2.9	300	32 × 5.5	619	115.6	2537	2311	0.91
AC140 × 3-HC38 × 8-C40	140.2 × 2.9	300	38.1 × 7.6	433	40.5	1626	1466	0.90
AC140 × 3-HC38 × 8-C80	140.2 × 2.9	300	38.1 × 7.6	433	79.9	2083	1868	0.90
AC140 × 3-HC38 × 8-C120	140.2 × 2.9	300	38.1 × 7.6	433	115.6	2500	2302	0.92
AC140 × 3-HC55 × 11-C40	140.2 × 2.9	300	55.1 × 10.6	739	40.5	2543	2177	0.86
AC140 × 3-HC55 × 11-C80	140.2 × 2.9	300	55.1 × 10.6	739	79.9	2775	2527	0.91
AC140 × 3-HC89 × 4-C40	140.2 × 2.9	300	89 × 3.9	1029	40.5	2025	1903	0.94
AC140 × 3-HC89 × 4-C80	140.2 × 2.9	300	89 × 3.9	1029	79.9	2107	2154	1.02
AC140 × 3-HC89 × 4-C120	140.2 × 2.9	300	89 × 3.9	1029	115.6	2195	2424	1.10
AC165 × 3-HC22 × 4-C40	165.3 × 2.94	276	22.1 × 4.1	794	40.5	1750	1683	0.96
AC165 × 3-HC22 × 4-C80	165.3 × 2.94	276	22.1 × 4.1	794	79.9	2413	2326	0.96
AC165 × 3-HC22 × 4-C120	165.3 × 2.94	276	22.1 × 4.1	794	115.6	2911	2988	1.03
AC165 × 3-HC32 × 6-C40	165.3 × 2.94	276	31.9 × 5.4	619	40.5	1943	1753	0.90
AC165 × 3-HC32 × 6-C40R	165.3 × 2.94	276	31.9 × 5.4	619	40.5	1891	1753	0.93
AC165 × 3-HC32 × 6-C80	165.3 × 2.94	276	31.9 × 5.4	619	79.9	2550	2383	0.93
AC165 × 3-HC89 × 4-C40	165.3 × 2.94	276	89 × 3.9	1029	40.5	2375	2216	0.93
AC165 × 3-HC89 × 4-C80	165.3 × 2.94	276	89 × 3.9	1029	79.9	2580	2686	1.04
Z48-a	114 × 2.0	279	48 × 1.6	235	40.8	698	683	0.98	Wen (2017)
Z48-b	114 × 2.0	279	48 × 1.6	235	40.8	660	683	1.03
Z76-a	114 × 2.0	279	76 × 1.6	235	40.8	618	570	0.92
Z76-b	114 × 2.0	279	76 × 1.6	235	40.8	578	570	0.99
Z89-a	114 × 2.0	279	89 × 1.6	235	40.8	493	498	1.01
Z89-b	114 × 2.0	279	89 × 1.6	235	40.8	520	498	0.96
Mean								0.96
Standard Deviation (SD)								0.06
Coefficients of Variance (CoV)								0.06

Figure 6.

Validations of the computational results by comparing the test $P - ε$ curves of short columns against the numerical predictions: (a) AC140 × 3-HC22 × 4-C40, (b) AC140 × 3-HC22 × 4-C80, (c) AC165 × 3-HC22 × 4-C80, and (d) AC165 × 3-HC22 × 4-C120.

Eccentrically loaded circular concrete-filled double-skin steel tubular slender columns

The validation of the fiber model in simulating the responses of the eccentrically loaded CFDST beam-columns is verified by comparing the numerical results against the experimental observations reported by Zhao et al. (2021) and Wen (2017). The details of the test columns are summarized in Table 2. The initial imperfection of the tested columns was not measured during the tests; therefore, a value of L/1000 was considered based on the previous studies of authors (Ahmed et al., 2020a, 2020b). The fiber analysis was stopped when the mid-height deflection of the column reached the maximum mid-height deflection of the tested columns. From the comparisons of the peak compressive strengths of the slender columns given in Table 2, it is seen that there is a reasonable agreement between the test and the mathematical solutions. The average value of

P_{u, n u m} / P_{u, \exp}

is calculated as 0.96. The corresponding standard deviation value is attained as 0.07 from the statistical analysis. The

P - u_{m}

curves given in Figure 7 show that the mathematical model is capable of simulating the responses of such columns under combined actions reasonably well.

Table 2.

Peak compressive strengths of CFDST slender beam-columns loaded eccentrically.

Column	Length, L (mm)	Outer tube		Inner tube		e (mm)	$Concrete f_{c}^{'} (MPa)$	Ultimate strength			Ref
Column	Length, L (mm)	$D_{o} \times t_{o} (mm)$	$σ_{0.2} (MPa)$	$D_{i} \times t_{i} (mm)$	$f_{s y i} (MPa)$	e (mm)	$Concrete f_{c}^{'} (MPa)$	$P_{u, \exp} (kN)$	$P_{u, n u m} (kN)$	$P_{u, n u m} / P_{u, \exp}$	Ref
C1-0.44-4-a	800	114 × 1.88	322	48 × 2.5	276	4	47.0	638	633	0.99	Zhao et al. (2021)
C1-0.44-4-b	800	114 × 1.89	322	48 × 2.5	276	4	47.0	590	633	1.07
C1-0.69-14-a	800	114 × 1.90	322	76 × 2.0	275	14	47.0	425	424	1.00
C1-0.69-14-b	800	114 × 1.91	322	76 × 2.0	275	14	47.0	429	424	0.99
C2-0.44-4- a	1300	114 × 1.92	322	48 × 2.5	276	4	47.0	533	546	1.02
C2-0.44-4- b	1300	114 × 1.93	322	48 × 2.5	276	4	47.0	560	546	0.98
C2-0.69-14-a	1300	114 × 1.94	322	76 × 2.0	275	14	47.0	356	365	1.03
C2-0.69-14-b	1300	114 × 1.95	322	76 × 2.0	275	14	47.0	378	365	0.97
C3-0.44-4- a	1800	114 × 1.96	322	48 × 2.5	276	4	47.0	411	456	1.11
C3-0.44-4- b	1800	114 × 1.97	322	48 × 2.5	276	4	47.0	487	456	0.94
C3-0.69-14-a	1800	114 × 1.98	322	76 × 2.0	275	14	47.0	307	307	1.00
C3-0.69-14-b	1800	114 × 1.99	322	76 × 2.0	275	14	47.0	276	307	1.11
P800-50-4-a	800	114 × 2	279	50 × 1.2	235	4	49.3	605	579	0.96	Wen (2017)
P800-50-4-b	800	114 × 2	279	50 × 1.2	235	4	49.3	695	579	0.83
P800-76-14-a	800	114 × 2	279	76 × 1.6	235	14	49.3	439	397	0.90
P800-76-14-b	800	114 × 2	279	76 × 1.6	235	14	49.3	433	397	0.92
P800-89-45-a	800	114 × 2	279	89 × 1.6	235	45	49.3	203	180	0.89
P800-89-45-b	800	114 × 2	279	89 × 1.6	235	45	49.3	197	180	0.91
P1300-50-4-a	1300	114 × 2	279	50 × 1.2	235	4	49.3	547	505	0.92
P1300-50-4-b	1300	114 × 2	279	50 × 1.2	235	4	49.3	564	505	0.90
P1300-76-14-a	1300	114 × 2	279	76 × 1.6	235	14	49.3	375	344	0.92
P1300-76-14-b	1300	114 × 2	279	76 × 1.6	235	14	49.3	384	344	0.90
P1800-50-4-a	1800	114 × 2	279	89 × 1.6	235	4	49.3	487	427	0.88
P1800-50-4-b	1800	114 × 2	279	89 × 1.6	235	4	49.3	494	427	0.86
P1800-76-14-a	1800	114 × 2	279	50 × 1.2	235	14	49.3	308	292	0.95
P1800-76-14-b	1800	114 × 2	279	50 × 1.2	235	14	49.3	290	292	1.01
Mean										0.96
Standard Deviation (SD)										0.07
Coefficients of Variance (CoV)										0.08

Figure 7.

Validations of the computational results by comparing the test $P - u_{m}$ curves of beam-columns against the numerical predictions: (a) C1-0.44–4-b, (b) C2-0.44-4- a, (c) C1-0.69–14-a, and (d) P800-50-4-a.

Behavior of circular concrete-filled double-skin steel tubular short and slender columns

The verified computer program was utilized to perform a detailed investigation of the influences of important column parameters. Columns in Groups G1, G2, G3, G4, G5, G6, G7, G8, and G9 in Table 3 were analyzed to investigate the column slenderness

L / r

ratio, eccentricity

(e / D_{o})

ratio, hollow

(κ)

ratio,

D_{o} / t_{o}

ratio,

D_{i} / t_{i}

ratio, the strength of concrete, proof stress of the outer tube, yield stress of the inner steel tube, and effects of concrete confinement, respectively, on the

P - ε

curves,

P - u_{m}

curves, column strength curves, and interaction diagrams of CFDST columns. It should be noted that while studying any specific parameter, the other column parameters in that specific Group remained the same. For example, while investigating the influences of column slenderness

(L / r)

ratio, the other column parameters in Group G1 remained the same except for the

L / r

ratio of the columns. Similarly, for Group G2, only the eccentricity

(e / D_{o})

ratio of the columns was changed.

Table 3.

Details of the columns for the parameter study.

Group	Column	Outer tube		Inner tube		$σ_{0 .2} (MPa)$	$f_{s y i} (MPa)$	$f_{c o}^{'} (MPa)$	$κ$	$L / r$	$e / D_{o}$
Group	Column	$D_{o} \times t_{o} (mm)$	$D_{o} / t_{o}$	$D_{i} \times t_{i} (mm)$	$D_{i} / t_{i}$	$σ_{0 .2} (MPa)$	$f_{s y i} (MPa)$	$f_{c o}^{'} (MPa)$	$κ$	$L / r$	$e / D_{o}$
G1	C1	500 × 10	50	250 × 4	62.5	275	350	50	0.52	22	0.2
	C2	500 × 10	50	250 × 4	62.5	275	350	50	0.52	40	0.2
	C3	500 × 10	50	250 × 4	62.5	275	350	50	0.52	60	0.2
	C4	500 × 10	50	250 × 4	62.5	275	350	50	0.52	80	0.2
G2	C5	600 × 7.5	80	300 × 5	60	275	350	60	0.51	50	0.1
	C6	600 × 7.5	80	300 × 5	60	275	350	60	0.51	50	0.2
	C7	600 × 7.5	80	300 × 5	60	275	350	60	0.51	50	0.3
	C8	600 × 7.5	80	300 × 5	60	275	350	60	0.51	50	0.4
G3	C9	500 × 8	62.5	145 × 4.83	30	275	350	40	0.30	40	0.1
	C10	500 × 8	62.5	195 × 3.54	55	275	350	40	0.40	40	0.1
	C11	500 × 8	62.5	240 × 3.86	62.2	275	350	40	0.50	40	0.1
	C12	500 × 8	62.5	290 × 2.35	123.4	275	350	40	0.60	40	0.1
G4	C13	600 × 15	40	350 × 6	58.3	275	350	50	0.61	30	0.3
	C14	600 × 10	60	350 × 6	58.3	275	350	50	0.61	30	0.3
	C15	600 × 7.5	80	350 × 6	58.3	275	350	50	0.61	30	0.3
	C16	600 × 6	100	350 × 6	58.3	275	350	50	0.61	30	0.3
G5	C17	700 × 14	80	350 × 8.75	40	275	350	50	0.52	45	0.3
	C18	700 × 14	80	350 × 5.83	60	275	350	50	0.52	45	0.3
	C19	700 × 14	80	350 × 4.38	80	275	350	50	0.52	45	0.3
	C20	700 × 14	80	350 × 3.5	100	275	350	50	0.52	45	0.3
G6	C21	800 × 13.3	60	400 × 6.67	60	275	350	40	0.52	35	0.3
	C22	800 × 13.3	60	400 × 6.67	60	275	350	60	0.52	35	0.3
	C23	800 × 13.3	60	400 × 6.67	60	275	350	80	0.52	35	0.3
	C24	800 × 13.3	60	400 × 6.67	60	275	350	100	0.52	35	0.3
G7	C25	600 × 8	75	300 × 5	60	205	350	60	0.51	40	0.2
	C26	600 × 8	75	300 × 5	60	275	350	60	0.51	40	0.2
	C27	600 × 8	75	300 × 5	60	350	350	60	0.51	40	0.2
	C28	600 × 8	75	300 × 5	60	430	350	60	0.51	40	0.2
G8	C29	600 × 8	75	300 × 5	60	275	250	60	0.51	40	0.2
	C30	600 × 8	75	300 × 5	60	275	350	60	0.51	40	0.2
	C31	600 × 8	75	300 × 5	60	275	450	60	0.51	40	0.2
	C32	600 × 8	75	300 × 5	60	275	690	60	0.51	40	0.2
G9	C33	400 × 12	33.3	200 × 4	50	275	350	40	0.53	35	0.1

Load-strain $(P - ε)$ curves

The simulated $P - ε$ curves of the columns with varying $κ$ ratio (0.3–0.6), $D_{o} / t_{o}$ ratio (40–100), $D_{i} / t_{i}$ ratio (40–100), the strength of concrete (40–100 MPa), the proof stress of the outer tube (205–430 MPa), and the yield stress of steel (250–550 MPa) are presented in Figure 8. In the parametric analysis, CFDST columns were analyzed for $κ$ ratio ranging from 0.3 to 0.6 for the same steel area. It is seen that the peak compressive strengths of CFDST columns decrease significantly for the increase in the $κ$ ratio. The peak load with a $κ$ ratio of 0.6 is 17.9% less than that of the column which has a $κ$ ratio of 0.3. While investigating the sensitivities of the column diameter-to-thickness ratio, it is seen that the peak load decreases with increasing the $D_{o} / t_{o}$ and $D_{i} / t_{i}$ ratio as seen in Figure 8(b) and (c). However, the influence of the $D_{o} / t_{o}$ ratio is more significant than the $D_{i} / t_{i}$ ratio of the column. The reduction of the peak load for the increase in the $D_{o} / t_{o}$ and $D_{i} / t_{i}$ ratios from 40 to 100 is calculated as 26.8% and 7.2%, respectively.

Figure 8.

Influences of various column parameters on the $P - ε$ curves: (a) hollow ratio $(κ)$ , (b) $D_{o} / t_{o}$ ratio, (c) $D_{i} / t_{i}$ ratio, (d) concrete strength $(f_{c}^{'})$ , (e) proof stress of outer tube ( $σ_{0.2}$ ), (f) yield stress of inner tube ( $f_{s y i}$ ), and (g) concrete confinement.

From Figure 8(d), the peak load of the column is found to be remarkably increased for the increase in the strength of concrete; however, the post-peak ductility of the column with higher strength of concrete is much lower due to the brittleness of the high-strength of concrete. The sensitivities of the yield stress of concrete on the $P - ε$ curves are shown in Figure 8(e) and (f). For the analysis, the outer proof stress changes from 205 MPa to 430 MPa to cover all three grades of stainless steel prescribed in AS/NZS 4673:2001 (2001), namely, duplex, austenitic, and ferritic stainless steel. The initial stiffness and the ultimate load increase remarkably when the proof stress of the outer tube increases. Figure 8(g) shows the influences of the concrete confinement where column RC8 was analyzed with and without considering the concrete confinement effects. It is seen that when the influences of confinement are ignored, the stiffness and peak load are significantly underestimated. The peak strength is underestimated by 17.57%.

Load-deflection $(P - u_{m})$ curves

The $P - u_{m}$ curves of slender beam-columns with varying slenderness $(L / r)$ ratio (22–80), eccentricity $(e / D_{o})$ ratio (0.1–0.4), hollow ( $κ$ ) ratio (0.3–0.6), $D_{o} / t_{o}$ and $D_{i} / t_{i}$ ratio (40–100), the strength of concrete (40–100 MPa), the proof stress of the outer tube (205–430 MPa), and the yield stress of steel (250–550 MPa) are presented in Figure 9. Increasing $L / r$ ratio or $e / D_{o}$ ratio reduces the peak strength of slender columns considerably. The reduction of the peak load is estimated as 54.5% and 74%, respectively, for the increase in $L / r$ ratio from 22 to 80, and $e / D_{o}$ ratio increases from 0.1 to 0.4, respectively. From Figure 9(c), it is seen that $κ$ ratio has an insignificant effect up to the range 0.5; however, the peak load decreases significantly for the increase in the $κ$ ratio greater than 0.5. When $κ$ ratio increases from 0.3 to 0.5, the peak load decreases by only 3.31%; however, with the increasing $κ$ ratio from 0.3 to 0.6, the reduction in the peak load is estimated as 10.36%. Figure 9(d) and (e) show that $D_{o} / t_{o}$ and $D_{i} / t_{i}$ ratio has considerable effects on the $P - u_{m}$ curves. The increase in the $D_{o} / t_{o}$ and $D_{i} / t_{i}$ ratio from 40 to 100 decreases the peak load by 23.53% and 15.18%, respectively.

Figure 9.

Influences of various column parameters on the $P - u_{m}$ curves: (a) slenderness ratio ( $L / r$ ), (b) $e / D_{o}$ ratio, (c) hollow ratio ( $κ$ ), (d) $D_{o} / t_{o}$ ratio, (e) $D_{i} / t_{i}$ ratio, (f) concrete strength $(f_{c}^{'})$ , (g) proof stress of outer tube ( $σ_{0.2}$ ), (h) yield stress of inner tube ( $f_{s y i}$ ), and (i) concrete confinement.

Figure 9(f)-(h) presents the sensitivity analysis of the strength of concrete and yield stress of steel. It is found that the increase in the strength of concrete or the steel proof stress of the outer tube improves the peak loads markedly; however, the yield stress of steel has insignificant effects on the column stiffness and the peak loads of the columns. The peak load increases by 39.4% and 20.5% when the concrete strength and the outer proof stress increase from 40 to 100 MPa and 205 MPa to 430 MPa, respectively. On the contrary, for the inner tube, increasing the yield stress from 250 MPa to 550 MPa increases the peak load by only 2.1%. From Figure 9(i), it can be seen that ignoring the concrete confinement effects remarkably underestimates the peak load by about 10%.

Column strength curves

The influences of various column parameters including $L / r$ ratio, $e / D_{o}$ ratio, $κ$ ratio, $D_{o} / t_{o}$ and $D_{i} / t_{i}$ ratio, the strength of concrete, and yield stress of steel on the column strength curves were investigated and presented in Figure 10. The effects of $κ$ ratio on the column strength curves are distinguishable at the cross-sectional level particularly for the column with $κ$ ratio of 0.6. However, as the $L / r$ ratio increases, the effects of $κ$ ratio become less significant. The effect of $κ$ ratio on the column strength diminishes at the $L / r$ ratio of 80. Furthermore, it is seen that at $L / r$ = 140, the ultimate load is only about 20% of the cross-sectional capacity of the column. From Figure 10(b), it is obvious that on the column strength curve, the $e / D_{o}$ ratio has the most significant influence. The $D_{o} / t_{o}$ and $D_{i} / t_{i}$ ratio has moderate effects on the columns strength curves; however, the effects of $D_{i} / t_{i}$ ratio diminish at the $L / r$ ratio of 110. While increasing the strength of concrete and steel yield stress improves the load-carrying capacities of the CFDST column under different $L / r$ ratios, the increase in the yield stress of the inner steel tube on the improvement of the load-carrying capacities becomes insignificant at the $L / r$ ratio of 55. Furthermore, neglecting the concrete confinement effects during the numerical analysis is found to be significant for the column with a slenderness ratio of less than 60.

Figure 10.

Influences of various column parameters on the column strength curves: (a) hollow ratio ( $κ$ ), (b) $e / D_{o}$ ratio, (c) $D_{o} / t_{o}$ ratio, (d) $D_{i} / t_{i}$ ratio, (e) concrete strength $(f_{c}^{'})$ , (f) proof stress of outer tube ( $σ_{0.2}$ ), (g) yield stress of inner tube ( $f_{s y i}$ ), and (h) concrete confinement.

Effects of eccentricity ratio on column ultimate strengths

The influences of $L / r$ ratio, $κ$ ratio, $D_{o} / t_{o}$ and $D_{i} / t_{i}$ ratio, the strength of concrete, steel yield, and concrete confinement on the peak loads for varying $e / D_{o}$ ratio of the columns were investigated and presented in Figure 11, in which $P_{o a}$ represents the peak compressive load of the slender column. The peak load is reduced on average by 97% for varying different column parameters when the $e / D_{o}$ ratio increases from 0.0 to 2.5. The proof stress of the outer tube, $D_{o} / t_{o}$ ratio, and concrete confinement have insignificant effects on the strength reduction of the column when $e / D_{o}$ ratio changes from 0 to 2.5. However, when the value of the $e / D_{o}$ ratio is greater than 0.6, $L / r$ ratio has a moderate effect on the peak load reduction of the column. For columns with varying $D_{i} / t_{i}$ ratio, the reduction of the peak load beyond the $e / D_{o}$ ratio of 0.3 increases as the $D_{i} / t_{i}$ ratio becomes larger. However, using higher steel yield stress for the inner tube decreases the ratio of the strength reduction as seen from Figure 11(g). Therefore, for CFDST columns with a large $D_{i} / t_{i}$ ratio, high strength steel is recommended.

Figure 11.

Influences of various column parameters on the peak loads for varying $e / D_{o}$ ratio of the column: (a) slenderness ratio ( $L / r$ ), (b) hollow ratio ( $κ$ ), (c) $D_{o} / t_{o}$ ratio, (d) $D_{i} / t_{i}$ ratio, (e) concrete strength $(f_{c}^{'})$ , (f) proof stress of outer tube ( $σ_{0.2}$ ), (g) yield stress of inner tube ( $f_{s y i}$ ), and (h) concrete confinement.

Column interaction curves

The interaction curves of slender CFDST beam-columns with varying column parameters are presented in Figure 12. In Figure 12(a), $P_{o}$ and $M_{o}$ are the pure ultimate compressive load and flexural capacity of beam-column with $L / r$ ratio 22, respectively. In Figure 12(b), the benchmark values of $P_{o}$ and $M_{o}$ are taken for beam-column with $κ$ ratio of 0.3. The benchmark $P_{o}$ and $M_{o}$ values for Figure 12(c) and (d) are taken for beam-column with $D_{o} / t_{o}$ and $D_{i} / t_{i}$ ratio of 40. Similarly, in Figure 12(e)-(g), the values of $P_{o}$ and $M_{o}$ for beam-columns with the strength of concrete of 40 MPa, proof stress of 250 MPa, and yield stress of 250 MPa are taken as the benchmark values, respectively.

Figure 12.

Influences of various column parameters on the column interaction curves: (a) slenderness ratio ( $L / r$ ), (b) hollow ratio ( $κ$ ), (c) $D_{o} / t_{o}$ ratio, (d) $D_{i} / t_{i}$ ratio, (e) concrete strength $(f_{c}^{'})$ , (f) proof stress of outer tube ( $σ_{0.2}$ ), (g) yield stress of inner tube ( $f_{s y i}$ ), and (h) concrete confinement.

The $L / r$ and $κ$ ratios have insignificant effects on the bending capacities of beam-columns. However, increasing the strength of concrete and the yield stress of steel tubes increase the bending capacities while the increase in the $D_{o} / t_{o}$ and $D_{i} / t_{i}$ ratio of the column reduces their bending capacities. Moreover, the axial capacities of the beam-column significantly decrease with the increase in the $L / r$ ratio and $D_{o} / t_{o}$ and $D_{i} / t_{i}$ ratio. In the contrast, an increase in the strength of concrete, proof, and yield stress of steel tube increases the axial capacities of the beam-columns. Furthermore, neglecting concrete confinement remarkably underestimates the sectional capacity of the beam-columns as illustrated in Figure 12(h); however, the bending capacity of the beam-column is found to be insignificantly affected.

Differences of performance of circular concrete-filled double-skin steel tubular columns with external stainless steel and carbon steel

To investigate the differences of mechanical behavior of CFDST columns with external stainless-steel and carbon tube, Column C33 in Table 3 was analyzed using the theoretical model developed. Figure 13 presents the comparisons of their $P - ε$ curves, $P - u_{m}$ curves, and column strength curves. It can be seen that due to the distinguished strain-hardening behavior of stainless steel, the ductility of CFDST short columns with external stainless-steel is higher than that of the ones with carbon steel tube, as illustrated in Figure 13(a). Furthermore, the $P - u_{m}$ curves and column strength curves of CFDST columns with external stainless-steel and carbon tube are slightly different due to the differences in the stress–strain relationships of stainless and carbon steel.

Figure 13.

Comparison of the behavior of circular concrete-filled double-skin steel tubular columns with external stainless-steel and carbon tube: (a) the $P - ε$ curves, (b) the $P - u_{m}$ curves, and (c) column strength curves.

Proposed design approach

Axially loaded short columns

The design formula for predicting the peak compressive loads of CFDST columns with an external stainless steel tube that are loaded concentrically is proposed herein as

P_{u, d e s} = γ_{s o} A_{s o} σ_{0.2} + γ_{s i} A_{s i} f_{s y i} + (γ_{c} f_{c}^{'} + 4.1 f_{r p}) A_{c}

(14)

γ_{s o} = 3.5245 {(\frac{D_{o}}{t_{o}})}^{- 0.299}

(15)

γ_{s i} = 1.458 {(\frac{D_{i}}{t_{i}})}^{- 0.1}

(16)

where

γ_{s o}

and

γ_{s i}

are the strain parameters of the stainless and carbon steel tube proposed by Patel et al. (2020) and Liang and Fragomeni (2009), respectively, and given in equations (15) and (16). Figure 14 presents the validations of the proposed design models where it can be seen that the design model can reasonably estimate the ultimate strengths of the short columns. The average predicted-to-test peak load is calculated as 0.98 with an SD value of 0.06.

Figure 14.

Validations of the design formulas for the short columns.

Axially loaded slender columns

Similar to Eurocode 4 (2004), the peak compressive load of slender CFDST columns loaded concentrically can be calculated as

P_{u, d e s} = χ P_{u o}

(17)

where

P_{u o}

denotes the peak compressive strength of the short CFDST column calculated using equation (14);

χ

is the slenderness reduction factor given by Eurocode 3 (2005) as

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

(18)

Based on the numerical analysis, $φ$ is proposed herein as

φ = \frac{1.03 + 0.4 (\bar{λ} - 0.2) + {\bar{λ}}^{2}}{2}

(19)

where

\bar{λ}

is the relative slenderness ratio determined as

\sqrt{P_{u o} / P_{c r}}

, in which the Euler buckling load

(P_{c r})

can be determined as

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

(20)

The effective flexural stiffness ${(E I)}_{e f f}$ is estimated as

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

(21)

where

I_{s, s o}

I_{s, s i}

, and

I_{c}

are the second moment of area of the outer tube, inner tube, and sandwiched concrete, respectively;

E_{c m}

represents the secant modulus of concrete.

A reference column with the outer and inner tube diameters of 600 and 200 mm with the corresponding $D_{o} / t_{o}$ and $D_{i} / t_{i}$ ratio of 60 and 20 was analyzed to validate the design equation proposed. The yield stresses of the outer and inner tubes are taken as 275 and 350 MPa, and the concrete strength was taken as 50 MPa. From the comparison given in Figure 15, it is seen that there is an excellent match between the design and numerical predictions.

Figure 15.

Validation of the design formula proposed for slenderness reduction factor ( $χ$ ).

Eccentrically loaded slender beam-columns

Based on the numerical results, the design formulas to calculate the interaction diagrams of slender beam-columns are suggested herein as

M_{u} = 1.1 M_{o} [1 - {(\frac{P_{u}}{P_{o}})}^{α_{m}}] for P_{u} \geq 0.2 P_{o}

(22)

M_{u} = M_{o} [1 - \frac{1}{10} {(\frac{P_{u}}{P_{o}})}^{α_{n}}] for P_{u} < 0.2 P_{o}

(23)

in which

P_{u}

denotes the eccentric load,

P_{o}

is the peak compressive load of the slender columns,

M_{u}

represents the uniaxial bending moment,

M_{o}

is the flexural load of CFDST columns, and

α_{m}

and

α_{n}

are the shape factors and proposed in this study as.5

α_{m} = 2.25 - 0.0163 (\frac{L}{r}) (α_{m} > 0)

(24)

α_{n} = 1.52 α_{m} - 1.461 (α_{n} \geq 0.1)

(25)

The validation of the design formulas for the interaction curves is performed by comparing with the numerical results given in Figure 16. A reasonable agreement can be seen between the numerical and design prediction. However, it should be mentioned that the design model proposed is limited to beam-columns up to $L / r$ ratio of less than 90.

Figure 16.

Validation of the proposed design model for the interaction curves.

Conclusions

The nonlinear behavior of circular CFDST columns with an external stainless steel tube has been investigated. A fiber-based computational model has been proposed for simulating the load-strain curves, load-deflection curves, and column strength curves of such columns loaded either concentrically or eccentrically. The Regula-Falsi method has been employed to adjust the neutral axis depth during the numerical analysis. For the validation of the accuracy of the numerical prediction, independent test results reported in the literature have been utilized. An extensive parameter study has been performed to study the influences of important column parameters. Design formulas have been suggested to design such columns under various loading conditions and validated against the test and numerical data. The important conclusions can be summarized from this study as follows:

1. The mathematical model can accurately simulate the fundamental behavior of CFDST short and slender columns with external stainless steel tube.

2. Increasing either the strength of concrete or the outer proof stress improves the peak compressive loads, whereas the peak compressive strengths decrease with an increase in the hollow ratio and $D_{o} / t_{o}$ and $D_{i} / t_{i}$ ratio. The yield stress of the inner tube has insignificant influences on the improvement of the peak compressive strength of such columns.

3. The concrete confinement has a remarkable effect on the peak compressive load of CFDST columns; however, this effect diminishes for $L / r$ ratio greater than 60.

4. The $L / r$ and $χ$ ratios do not have a significant effect on the bending capacities of CFDST columns.

5. The design models proposed can reasonably predict the peak compressive strengths and interaction diagrams of beam-columns.

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

Mizan Ahmed

Qing Quan Liang

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Fiber element modeling of circular double-skin concrete-filled stainless-carbon steel tubular columns under axial load and bending

Abstract

Keywords

Introduction

Fiber model formulation

General

Simulation of axial load-strain ( P − ε ) relationship curves

Simulation of axial load-lateral deflection ( P − u m ) relationships

Simulation of strength envelopes

The Regula-Falsi method

Material constitutive models

Steel

Concrete

Model validation

CFDST short columns under axial loading

Eccentrically loaded circular concrete-filled double-skin steel tubular slender columns

Behavior of circular concrete-filled double-skin steel tubular short and slender columns

Load-strain ( P − ε ) curves

Load-deflection ( P − u m ) curves

Column strength curves

Effects of eccentricity ratio on column ultimate strengths

Column interaction curves

Differences of performance of circular concrete-filled double-skin steel tubular columns with external stainless steel and carbon steel

Proposed design approach

Axially loaded short columns

Axially loaded slender columns

Eccentrically loaded slender beam-columns

Conclusions

Footnotes

Declaration of conflicting interests

Funding

ORCID iDs

References

Simulation of axial load-strain $(P - ε)$ relationship curves

Simulation of axial load-lateral deflection $(P - u_{m})$ relationships

Load-strain $(P - ε)$ curves

Load-deflection $(P - u_{m})$ curves