Numerical analysis of circular double-skin concrete-filled stainless steel tubular short columns under axial loading

Structures 24 (2020) 754–765

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Numerical analysis of circular double-skin concrete-filled stainless steel tubular short columns under axial loading

T

Vipulkumar Ishvarbhai Patela, Qing Quan Liangb, , Muhammad N.S. Hadic ⁎

a

School of Engineering and Mathematical Sciences, La Trobe University, Bendigo, VIC 3552, Australia College of Engineering and Science, Victoria University, PO Box 14428, Melbourne, VIC 8001, Australia c School of Civil, Mining and Environmental Engineering, University of Wollongong, Wollongong, NSW 2522, Australia b

ARTICLE INFO

ABSTRACT

Keywords: Concrete-filled stainless steel tubes Computational modeling Double-skin confinement Nonlinear analysis Stainless steel

Circular double-skin concrete-filled stainless-steel tubular (DCFSST) columns have the distinguishing feature of high resistance to corrosion so that they can be constructed by either normal concrete or seawater sea-sand based concrete without corrosion. The numerical study of circular short DCFSST columns is very limited. This paper presents the computational modeling and behavior of short DCFSST columns of circular sections loaded concentrically. A computational model is developed for simulating the structural behavior of concentrically loaded short circular DCFSST columns, taking into account the effects of the concrete confinement induced by the double stainless-steel skins and significant strain hardening of stainless steel. The accuracy of the computational modeling technique proposed herein is assessed by means of comparing computations with available experimental data. The verified computational method is utilized to investigate the significance of geometric configurations as well as material strengths on the structural performance of circular DCFSST columns. The applicability of the current design provisions for steel tubular columns filled with concrete to the design of circular DCFSST columns is evaluated by comparisons against experimental and numerical results on DCFSST columns. The comparative study shows that the present computational model and the design formula proposed by Liang predict well the ultimate strengths of short DCFSST columns composed of circular tubes. The codified design approaches in current design codes generally give conservative estimations of the strengths of circular DCFSST stub columns.

1. Introduction The seawater sea-sand based concrete could be used to fill the carbon steel tubular hollow column to form a composite column. The major concern for using seawater sea-sand based concrete in carbon steel tubular composite columns is the corrosion of carbon-steel tubes caused by the seawater sea-sand made concrete. The use of stainless steel instead of carbon steel in composite columns made of seawaterbased concrete can overcome the corrosion problem. Double-skin concrete-filled stainless steel tubular (DCFSST) columns composed of circular sections as depicted in Fig. 1 not only have an excellent resistance to corrosion but also have high bending stiffness, strength and ductility [1]. Stainless steels display significant strain-hardening behavior without a clear yield point, which should be recognized in the design and nonlinear response simulation of DCFSST columns to achieve economical designs. Both the circular internal and external stainlesssteel tubes produce lateral confinement to the concrete in a circular

⁎

DCFSST column [2,3]. As a result of this, the ductility and compressive strength of the sandwiched concrete improve considerably. Design methods based on carbon steel material models without considering confinement effects significantly underestimate the load-carrying capacities of DCFSST circular columns. The design standards, such as Eurocode 4 [4] and ANSI/AISC 360-16 [5], do not specify design rules for designing DCFSST columns of circular sections because the suitable design methods have not been derived from limited research works on such composite columns. Therefore, further studies on the behavior of DCFSST columns are much needed. There has been an increasing amount of experimental studies on circular double-skin concrete-filled steel tubular (DCFST) composite short columns made of carbon steel tubes loaded axially [6–11]. The DCFST columns are usually constructed by the river water and riversand based concrete. To reduce the usage of river-based constructional materials, an experimental investigation of seawater and sea-sand based DCFSST columns with the circular section under concentric

Corresponding author. E-mail address: [email protected] (Q.Q. Liang).

https://doi.org/10.1016/j.istruc.2020.02.001 Received 28 August 2019; Received in revised form 3 January 2020; Accepted 2 February 2020 2352-0124/ © 2020 Institution of Structural Engineers. Published by Elsevier Ltd. All rights reserved.

Structures 24 (2020) 754–765

V.I. Patel, et al.

Fig. 1. Cross-section of circular DCFSST column.

loading was conducted by Li et al. [1]. It was reported that the ductility of DCFSST columns increased due to the addition of the internal stainless-steel tube. In addition, the external stainless-steel tube was subjected to a greater lateral strain than the inner one. The main reason for this is that the inward expansion of sandwiched concrete was balanced by the hoop compression in the internal hollow tube. The test results indicated that the DCFSST column had a greater energy absorption capacity than its hollow counterpart. The typical failure modes of DCFSST columns included the outward local buckling of the internal and external tubes and crushing of the sandwiched concrete at the buckled regions. The sea-based constructional materials have been used to construct concrete-filled stainless steel tubular (CFSST) composite columns and their structural behavior has been experimentally investigated by a number of researchers [12–16]. The economic use of stainless steel was proposed by Wang et al. [17] using an outer thinwalled stainless steel tube and an inner high-strength carbon steel tube in a DCFST column. Numerical modeling techniques based on the finite and fiber element methods have been utilized to determine the performance of concentrically compressed short circular DCFST columns [18–24]. In the numerical models given by Huang et al. [18] and Wang et al. [19], the concrete confinement model for circular CFST columns was adopted for the sandwiched concrete in DCFST composite columns. Hu and Su [20] employed the Abaqus program to investigate the ultimate loads of short circular DCFST columns loaded axially. Based on experimental and finite element analysis results, Hu and Su [20] derived a confinement model for estimating the lateral confining pressures on the sandwiched concrete. Liang [3] developed strength degradation factors that quantify the strength and ductility of sandwiched concrete in DCFST columns of circular sections. The confinement model of Hu and Su [20] and the strength degradation factors proposed by Liang [3] were incorporated in the fiber-based mathematical model developed by Liang [3], which has been shown to capture well the responses of short and slender DCFST columns [20,24]. The Abaqus program was employed by Hassanein et al. [21] and Pagoulatou et al. [22] to model the load-axial strain responses of circular short DCFST columns with an outer stainless steel tube. A design equation considering concrete confinement and steel strain hardening was proposed by Hassanein et al. [21], which estimated well the strengths of circular DCFST columns. Li et al. [25] developed the axial load–strain relations for numerically determining the behavior of DCFSST columns. Limited research has been undertaken on the structural characteristics of DCFSST columns loaded concentrically. This paper is concerned with the computational modeling, behavior, and design of concentrically compressed circular short DCFSST columns. A computational model is developed, which can predict the load-axial strain

Fig. 2. Typical fiber discretization of cross-section of circular DCFSST column.

responses of DCFSST stub columns made of circular stainless-steel tubes loaded concentrically to failure. The model considers the confinement induced by the double-skins on the sandwiched-concrete in addition to the strain hardening of stainless steel. The fundamental behavior of DCFSST stub columns with various parameters is investigated using the validated computational model. The applicability of the design methods given in current design codes and by Liang [3] to the design of circular DCFSST columns is assessed by undertaking a comparative study against experimental data. Throughout this paper, the abbreviation DCFST column is used to represent double-skin concrete-filled carbon steel tubular column whereas the abbreviation DCFSST column is used to represent double-skin concrete-filled stainless steel tubular column. 2. Computational model based on the theory of fiber analysis 2.1. Theory The computational model is proposed based on the theory of fiber analysis, in which the cross-section of a circular DCFSST column is meshed by many small fiber elements. The discretization technique adopts the mathematical model proposed by Liang [3]. Fig. 2 presents the typical fiber mesh for the cross-section of a circular DCFSST column. In the fiber simulation, the sandwiched concrete and stainless-steel tubes are discretized into layers through their thickness. Their discretization in the radial direction is undertaken based on the layer size of the tube and the sandwiched concrete. The origin O of the coordinate system coincides with the cross-section centroid. The coordinates and area of each fiber element are calculated based on the mesh generated in the discretization. The computational model assumes that: (a) no slippage between the stainless-steel tubes and the sandwiched concrete occurs, which implies that the concrete and stainless-steel fibers are under the same axial strain for each load increment; (b) the concrete confinement provided by double-skins is explicitly considered in the constitutive model for sandwiched concrete; (c) the influence of concrete creep and shrinkage is ignored; (e) the column fails when the concrete compressive strain exceeds the specified ultimate strain. The material properties of stainless steel are given to stainless-steel fibers and concrete fibers are provided with concrete properties. The material uniaxial stress–strain laws are incorporated to compute the fiber stress from axial strain. The internal axial force (P) is obtained by integrating the fiber stresses over the entire cross-section as follows: 755

Structures 24 (2020) 754–765

V.I. Patel, et al. nso

nsi

P=

so, i Aso, i

+

i=1

nsc si, j Asi, j

j =1

+

sc, k Asc, k k=1

(1)

where so, i , si, j and sc, k represent the stresses at the outer stainless steel, internal stainless steel, and sandwiched-concrete element, respectively; Aso, i , Asi, j and Asc, k are the areas of the outer stainless-steel tube, internal stainless-steel tube, and sandwiched concrete, respectively and nso , nsi and nsc are the number of fiber elements in the outer stainlesssteel tube, internal stainless-steel tube, and sandwiched concrete, respectively. 2.2. Computational procedure The structural behavior of a concentrically compressed short DCFSST column is characterized by its axial load–strain responses, from which its ultimate axial strength and strain ductility performance can be quantified. For a short DCFSST column subjected to increasing concentric loading, the internal and external stainless-steel tubes as well as the sandwiched concrete undergo the same axial strain. To capture the full axial load–strain responses of the column, the strain in the axial direction is incrementally increased. For a given axial strain, the fiber element stresses are computed from the axial strain using the stress–strain relations of concrete and stainless steel. The internal axial force (P) for the given strain is determined by the summation of the fiber element stresses over the entire cross-section and is taken as the axial load applied to the column. The complete load-axial strain curve is obtained by repeating the above procedure until the stopping criteria specified is satisfied. The stopping criteria are that the axial load falls to 50% of the ultimate axial strength of the column or the axial strain exceeds the specified ultimate concrete strain [23].

Fig. 3. Three-stage stress–strain curve for stainless steel in axial compression.

tension can be expressed by the equations proposed by Ramberg and Osgood [28] and Rasmussen [29]. Quach et al. [30] developed a stress–strain model for stainless steels in compression and tension on the basis of experimental results, in which the strain is expressed as a function of stress. Abdella et al. [31] formulated an inversion of the stress–strain laws for stainless steel proposed by Quach et al. [30]. The inversion is convenient for implementation in numerical modeling of stainless steel members. The inversed model given by Abdella et al. [31] together with formulas derived by Quach et al. [30] is incorporated in the present computational model. The first stage of the stress–strain relationship shown in Fig. 3 is expressed by

2.3. Ductility index and stainless-steel contribution ratio

s

The contribution of stainless steel tubes to the ultimate axial load (Pu ) of a DCFSST short column can be calculated using the stainless-steel contribution ratio, which is written by

PIsc =

Pss Pu

(2)

0.2

for

0

s

0.2

(4)

0.2

=

E0

+ 0.002

(5)

In Eq. (4), the parameters C1, C2 , C3 , and C4 were proposed by Abdella et al. [31] as follows:

C1 =

C2

C2 = 1 +

u y

E0 s [1 + C1 r C2 ] 1 + C3 r C4 + C1 r C2

where r is the ratio of s 0.2 , the axial stress of stainless steel is denoted by s , s refers to the stainless steel strain at stress s , E0 denotes the elastic modulus of stainless steel, the stainless steel strain at 0.2 is represented by 0.2 , and the 0.2% proof stress is referred by 0.2 . The equation by Ramberg and Osgood [28] for predicting the 0.2% proof strain is

in which PIsc denotes the stainless steel contribution, and Pss represents the ultimate axial strength of the hollow stainless steel tubular column. The strength Pss is determined by setting the concrete cylinder strength fc to zero in the fiber analysis [26]. The resistance of large plastic deformation without the reduction of strength is known as the ductility of a short DCFSST column. The ductility index predicts the axial ductility of a circular short DCFSST column subjected to concentric loading. The full load-axial strain curve of the DCFSST column is required to evaluate the ductility index, which is defined as

PIsd =

=

(3)

in which PIsd denotes the ductility index, u stands for the axial strain at 90% of the column ultimate axial load in the post-peak response of load-axial strain curve and y is calculated by the ratio of 0.75 0.75, in which 0.75 represents the strain at 75% of the ultimate axial load in the pre-peak response of load-axial strains of the short DCFSST column [3].

(6)

1

B1

(7)

C3 = G0 (1 + C1)

(8)

C4 =

(9)

+ G1

where

=

3. Material constitutive relations

B1 =

3.1. Stainless steel

G0 =

Experiments indicate that stainless steel in compression exhibits significantly higher strain hardening than in tension [26,27]. Fig. 3 represents the relationships of stress and strain for stainless steel material in compression. The stress–strain behavior of stainless steel in

G1 = 756

1+

1 + 4B1 2

G1 E0.2 (n + G0 ) E0

0.002E0

0.2

(11) (12)

0.2 0.2 E0.2 (n

(10)

1)

(13)

Structures 24 (2020) 754–765

V.I. Patel, et al.

where E0.2 represents the tangent modulus corresponding to the stress 0.2 computed by

=

2.0

E0 1 + 0.002 nE0

E0.2 =

1+

in which n denotes the strain-hardening exponent which is expressed by

ln(

=

s

0.2

in which the parameters

= r

=

s

and

for r

0.2

<

s

2.0

s

A=

(17)

0.662 + 1.085 n

=

1.0

= 0.008 + (

0.2

1 E0

1 + E0.2

1.0

0.2

E0.2

+

0.2

(20)

( ) ) H0 H2

ln(1 + A2 ) + ln

C6 = C8 +

ln

(

2.0

0.2

1.0

0.2

(22)

C7 = H0 (1 + C5)

(23)

C8 = 1 + H1

(24)

(n2 1) 2 (H2 H0 ) (1 + n2 H0 ) (1 + n2 H2 ) 0.008 + (

H0 =

H1 =

H2 =

0.2 )

1.0 1.0

(n2

(

1 E0.2

)

E0.2 (26)

0.2

1) (H0 + 1) 1 + n2 H0

E0.2

(

2.0

2.0

0.2

1.0

0.2

(27)

)

(28)

0.2

1.0

=

su

=1

+ 1.145

The equations for predicting the stress Quach et al. [30] are expressed as

and strain

2.0

1

An2 n2 B2

1 E0.2

(30) 2.0

0.2

1.0

0.2

n2

+

0.2

1.0

E0

0.2

0.2

E0

)(1

1

E0 E0.2

1

E0 E0.2

)

(32) (33)

s

for

+

2.0 )

+

su )

s

>

B3

2.0

2.0 (1 2.0

2.0

(34) (35)

+

2.0 )

(36)

(1 +

ut )

1 1+

(37)

2

(38)

ut

fcc (

cc )

c

1+(

c

cc )

(39)

in which considers the concrete brittleness, and it was given by Carreira and Chu [33] as:

(29) 2.0

ut

=

=

0.2

B2

0.2

su

su

c

where the 2.0% proof stress is represented by 2.0 and its corresponding strain is denoted by 2.0 . Quach et al. [30] proposed the material constant n2 , which is written as

E0.2 n2 = 6.399 E0

1 E0

)

The concrete sandwiched by double tubes in a circular DCFST column under increasing axial compression may expand laterally more than the stainless steel tubes. As a result, the radial pressures between the sandwiched concrete and the stainless-steel tubes exist. Liang [3] pointed out that the sandwiched concrete is in a triaxial stress state, the internal tube is subjected to biaxial compression and the external tube is under biaxial stresses. Consequently, the sandwiched concrete may be effectively confined by both the internal and external stainless steel tubes, providing that the depth-to-thickness ratios of the tubes are small. Fig. 4 shows the idealized stress–strain relationship of sandwiched concrete in DCFSST columns composed of circular tubes. The material constitutive model given by Mander et al. [32] for confined concrete is employed to represent Part OA depicted in Fig. 4, which is written by

(25) 1 E0

0.2 )

1.0

1

0.2

3.2. Sandwiched concrete

in which

A2 =

1.0

in which the ultimate stress and strain in tension are denoted by ut and ut , respectively. Quach et al. [30] proposed the equations for predicting ut and ut . For this numerical study, the values of ut and ut reported in the experimental studies of DCFSST columns are adopted.

(21)

1

)(

where the ultimate strain and stress in compression are represented by su and su respectively. The equations of Quach et al. [30] are considered herein:

1 C6

2.0 (1 su (1

B3 =

The material parameters C5 , C6 , C7 and C8 in Eq. (16) proposed by Abdella et al. [31] are computed by

C5 =

( )(

A3 + B3 1 s

A3 =

(19)

0.2 )

1.0

0.008 +

=

s

where the 1.0% proof stress is denoted by 1.0 and corresponding strain is represented by 1.0 . The stress 1.0 and strain 1.0 are determined by using the following equations of Quach et al. [30]: 1.0

1

The stainless steel stresses in the third-stage are computed from the axial strain as follows:

(18)

0.2

E0 E0.2

+ 0.008 + (

B2 = 0.018 +

are expressed as

0.2

1.0

0.2

E0

1

1 An2

0.2

in which

(16)

0.2

( )(

)

1.0

(31)

in which the 0.01% proof stress is denoted by 0.01. The second stage of the stress–strain curve illustrated in Fig. 3 is expressed by using the following equation by Abdella et al. [31]:

E0.2 [1 + C5 r C6 ] + 1 + C7 r C8 + C5 r C6

0.2

E0.2

(15)

0.01 )

0.2

2.0

=

2.0

ln(20)

n=

0.2

(14)

0.2

(

1+

Ec

Ec (fcc

cc )

(40)

where the sandwiched concrete axial stress is represented by c , the corresponding axial strain is denoted by c , the peak stress of doubleskin confined sandwiched concrete is represented by fcc , the strain is

proposed by 757

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V.I. Patel, et al.

c

=

c f cc

+ (fcc

c fcc )

(

cu

c

cu

cc

c f cc

)

for

cc

<

c

for

c

>

cu

cu

(47)

where c reflects the effect of confinement on the post-yield response of the concrete stress–strain behavior. It depends on both the tube diameter-to-thickness ratios of Do to and Di ti . Liang [3] proposed the equations for predicting the factor c : c =

1.0 k3 0.0000339(Do to )2

for for

0.010085(Do to ) + 1.349 for

Do to 40 Do to > 40

k3 < 0

(48)

in which k3 was given by Hu and Su [20] as

( ) 0.04731 ( ) 0.00036 ( ) + 0.00134 ( )( ) 0.00058 ( ) 0

k3 = 1.73916

Do to

Fig. 4. Idealized stress–strain curve for sandwiched concrete confined by double-skins.

c fc

+ 6900 (MPa)

cu

(41)

where fc represents the compressive strength of the concrete cylinder, and c the strength reduction factor considering the influence of concrete quality, loading rate, and column size on the actual strength of concrete in columns, proposed by Liang [3] as c

= 1.85tc

0.135

(0.85

cc

=

c fc

c

+ k1 frp

1 + k2

(43)

frp c fc

(44)

in which frp is the lateral pressure on the sandwiched concrete; the constants of k1 = 4.1 and k2 = 20.5 suggested by Richart et al. [35] are incorporated in the numerical model; the strain c at the stress fc is determined using the equation provided by Liang [24] as follows:

0.002 c

= 0.002 +

for fc fc

28

54000

0.003

28 MPa

for 28 < fc

82 MPa

for fc > 82 MPa

(45)

The formula derived by Hu and Su [20] for finding the lateral pressure ( frp ) on the concrete sandwiched by double tubes is adopted in the present computational model as suggested by Liang [3], which is expressed as

( ) 0.00897 ( ) + 0.00125 ( ) + 0.00246 ( )( ) 0.0055 ( ) 0

frp = 8.525

0.166

Do to

Do to

Do 2 to

Di ti

Di ti

Di 2 ti

Di 2 ti

Di ti

(49)

0.03 = 0.023 + 0.000175(100 0.02

Do to)

for for for

Do / to 60 60 < Do / to Do / to > 100

100 (50)

The experimental results on concentrically loaded DCFSST stub columns presented by Li et al. [1] were employed to verify the theoretical model. The dimensions of the cross-sections as well as material properties of the tested columns are reproduced in Table 1. The experimental ultimate axial load (Pu,exp ) was determined as either the first peak load from the load-axial strain curve for the specimen with descending post-peak curve or the load at the axial strain of 0.05 for the specimen exhibiting significant strain hardening behavior after the first peak load [1]. This method was also used in the nonlinear analyses of these specimens to determine their ultimate axial loads. The computed ultimate axial loads (Pu . num) are compared against experimental strengths in Table 1. The table clearly shows that the computer model proposed generally calculates reasonably well the ultimate strengths of the tested specimens. A 0.951 mean of Pu . num Pu . exp ratio is obtained. The standard deviation (SD) was calculated as 0.078 and the coefficient of variation (COV) was determined as 0.082. The predicted and experimental load-axial strain responses of Specimen 152 × 1.6–76 × 1.6-D are provided in Fig. 5 for comparison. The computer model essentially predicts well the column initial axial stiffness, the first peak load and the post-yield responses of the specimen up to the axial strain of 0.16. However, when the axial strain is greater than 0.16, the experimental curve departs significantly from the computed one as shown in Fig. 5. This is likely due to the local failures of the specimen under large axial strains, including the local buckling of the outer tube and concrete crushing which degraded the column strength. The calculated results of Specimen 168 × 3–50 × 1.6-D are compared with measurements in Fig. 6. The predicted initial axial stiffness, first peak load and post-yield behavior of the specimen have a good agreement with test results. However, after the axial strain of 0.15, the measured curve departs slightly from the predicted responses. The computed ultimate axial load is slightly higher than the test data. This discrepancy might be attributed to the fact that the actual concrete strengths of the tested specimens were unknown, and the average concrete strength was employed in the computer simulation.

where tc denotes the thickness of the sandwiched-concrete shown in Fig. 1 and it is determined as tc = Do 2 to Di 2 , in which Do and Di represent the diameters of the external and internal tubes, respectively, and to stands for the outer tube thickness. The compressive strength (fcc ) and its corresponding strain ( cc ) of the sandwiched concrete confined by double-skins are estimated by the equations suggested by Mander et al. [32] with strength reduction factor c as follows:

fcc =

Do 2 to

Di ti

4. Experimental verification

(42)

1.0)

c

Do to

In Eq. (47), the concrete strain cu is determined by the expressions proposed by Liang [3] based on experimental data as follows:

denoted by cc , and the pre-peak modulus is denoted by Ec , which is obtained using the recommendation by ACI Committee 363R-92 [34]:

Ec = 3320

0.00862

(46)

where ti denotes the thickness of the inner stainless steel tube as indicated in Fig. 1. It should be noted that Eq. (46) is applicable to circular DCFSST columns with 20 Do to 100 and 15 Do to 55. The linear branches AB and BC of the concrete stress–strain relationship illustrated in Fig. 4 are determined using the following equations:

5. Fundamental behavior The computational modeling technique proposed was employed to ascertain the influences of the sandwiched concrete strength, stainless758

Structures 24 (2020) 754–765

[1] 0.918 0.962 1.106 0.942 1.074 0.935 0.892 0.958 0.847 0.879 0.948 0.959 0.075 0.079 535 610 656 850 1071 771 1399 1402 1147 1159 1083 583 634 593 902 997 825 1569 1464 1354 1319 1142 195 195 195 195 193.2 186.6 195 176.2 192.6 199.3 189.0 706.0 706.0 656.4 617.8 659.8 659.8 615.8 615.8 615.8 615.8 653.1

186.6 186.6 192.6 199.3 189.0 189.0 190.3 190.3 190.3 190.3 189.6

376.5 228.9 376.5 228.9 398.9 353.3 376.5 259.2 226.0 281.2 314.5

656.8 562.1 656.8 562.1 732.4 706.0 656.8 587.8 656.4 617.8 659.8

Pu,exp (kN)

353.3 353.3 226.0 281.2 314.5 314.5 281.5 281.5 281.5 281.5 304.0

Fig. 6. Comparison of experimental and computational load–strain responses of Specimen 168 × 3–50 × 1.6-D.

steel grades, and tube geometry on the fundamental behavior of short DCFSST columns composed of circular sections loaded axially.

42 42 42 42 42 42 42 42 42 42 42

suo

(MPa) 0.2o

f’c (MPa)

Fig. 5. Comparison of experimental and computational load–strain responses of Specimen 152 × 1.6–76 × 1.6-D.

49.6 × 1.53 50.9 × 3.07 49.6 × 1.53 50.9 × 3.07 76.2 × 1.66 101.8 × 1.70 49.6 × 1.53 89.2 × 3.22 101.9 × 2.79 114.1 × 2.79 152.6 × 1.60 101.8 101.8 101.9 114.1 152.6 152.6 168.4 168.4 168.4 168.4 202.7 101 × 1.6–50 × 1.6-D 101 × 1.6–50 × 3-D 101 × 3–50 × 1.6-D 114 × 3–50 × 3-D 152 × 1.6–76 × 1.6-D 152 × 1.6–101 × 1.6-D 168 × 3–50 × 1.6-D 168 × 3–89 × 3-D 168 × 3–101 × 3-D 168 × 3–114 × 3-D 203 × 2–152 × 1.6-D Mean Standard deviation (SD) Coefficient of variation (COV)

1.70 1.70 2.79 2.79 1.60 1.60 3.22 3.22 3.22 3.22 1.99

The significance of sandwiched concrete strength on the load-axial strain responses, strain ductility index and stainless steel contribution ratio were evaluated by means of undertaking numerical analyses on Columns DC1-DC5 given in Table 2. The sandwiched concrete strengths under consideration ranged from 40 MPa to 100 MPa. Fig. 7 shows the calculated load-axial strain curves of DCFSST composite columns made of concrete with different strengths. As demonstrated, the ultimate load and initial stiffness of DCFSST column are improved by increasing the concrete strength. The percentage increases in the column ultimate strengths are 12%, 30%, and 72%, respectively when increasing the concrete strength from 40 MPa to 50 MPa, 65 MPa and 100 MPa. The post-peak behavior of the axial load–strain curve becomes steeper due to the use of higher strength concrete that has a brittle behavior. The calculated strain ductility indices of the columns filled with concrete having various strengths are given in Fig. 8. The higher concrete strength, the lower the strain ductility of the column. It is discovered that the strain ductility decreases more when increasing the concrete strength from 40 MPa to 50 MPa than when increasing the concrete

× × × × × × × × × × ×

Do × to (mm)

Di × ti (mm)

5.1. Effect of sandwiched concrete strength

Specimens

Table 1 Geometric and material properties and ultimate axial strengths of circular DCFSST short columns.

(MPa)

E0o (GPa)

0.2i

(MPa)

sui

(MPa)

E0i (GPa)

Pu, num (kN)

Pu, num Pu,exp

Ref.

V.I. Patel, et al.

759

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V.I. Patel, et al.

Table 2 Circular DCFSST short columns employed in the parameter study. Column

Do × to (mm)

Do to

Di × ti (mm)

Di ti

DC1 DC2 DC3 DC4 DC5 DC6 DC7 DC8 DC9 DC10 DC11 DC12 DC13 DC14 DC15 DC16 DC17 DC18 DC19 DC20 DC21 DC22

300 300 300 300 300 400 400 400 400 500 500 500 500 600 600 600 600 600 600 600 600 200

50 50 50 50 50 50 50 50 50 40 40 40 40 50 50 50 50 40 50 60 70 50

150 150 150 150 150 200 200 200 200 150 200 300 400 120 120 120 120 120 120 120 120 100

30 30 30 30 30 40 40 40 40 15 20 30 40 20 30 40 50 30 30 30 30 20

× × × × × × × × × × × × × × × × × × × × × ×

6 6 6 6 6 8 8 8 8 8 8 8 8 12 12 12 12 15 12 10 8.6 4

× × × × × × × × × × × × × × × × × × × × × ×

5 5 5 5 5 5 5 5 5 10 10 10 10 6 4 3 2.4 4 4 4 4 5

0.2o , 0.2i

(MPa)

205 205 205 205 205 205 275 350 430 275 275 275 275 430 430 430 430 430 430 430 430 280

suo , sui

520 520 520 520 520 520 450 520 590 450 450 450 450 590 590 590 590 590 590 590 590 435

Fig. 7. Effect of concrete compressive strength on load-axial strain responses.

(MPa)

E0o, E0i (GPa)

no, ni

f’c (MPa)

PIsd

PIsc

195 195 195 195 195 195 185 200 200 185 185 185 185 200 200 200 200 200 200 200 200 195

7.5 7.5 7.5 7.5 7.5 4 8.5 8.5 5.5 8.5 8.5 8.5 8.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 9

40 50 65 80 100 80 80 80 80 50 50 50 50 65 65 65 65 65 65 65 65 65

21.5 9.5 7.3 6.1 5.1 5.6 5.6 6.3 7.7 4.5 5.2 8.8 20.7 7.7 8.0 8.0 6.0 12.5 8.0 5.9 4.1 9.7

0.63 0.57 0.49 0.43 0.37 0.46 0.48 0.55 0.63 0.42 0.47 0.64 0.91 0.50 0.52 0.58 0.58 0.52 0.52 0.46 0.40 0.54

Fig. 9. Effect of concrete compressive strength on stainless steel contribution ratio.

strength from 50 MPa to 100 MPa. The strain ductility index is 21.5, 9.5, 7.3, 6.1 and 5.1 for DCFSST column filled with 40 MPa, 50 MPa, 65 MPa, 80 MPa and 100 MPa, respectively. Fig. 9 represents the contribution ratios of the stainless-steel tube in DCFSST columns having various strengths of concrete. It would appear that increasing the concrete strength considerably decreases the stainless-steel contribution ratio. 5.2. Effect of stainless steel grades Stainless steels are usually classified into three grades in AS/NZS 4673:2001 [36] based on their different material properties for the structural use, including duplex stainless steels, ferritic stainless steels and austenitic stainless steels. The geometric configurations and material strengths of Columns DC6-DC9 were employed to evaluate the effect of stainless steel strength on their structural behavior. Fig. 10 compares the load-axial strain curves for columns that had different stainless steel grades. As shown in the figure, the proof stress has a slight influence on the initial axial stiffness of the column due to the different elastic modulus of stainless steel grades given in Table 2. The

Fig. 8. Effect of concrete compressive strength on strain ductility index.

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with proof stresses ranged from 205 MPa to 275 MPa exhibits similar stress–strain behavior. However, stainless steel with proof stresses ranged from 275 MPa to 430 MPa has significant strain-hardening behavior, which contributes to the ductility of the DCFFST column. The DCFSST column with a proof stress of 275 MPa has a ductility indicator of 5.6 while the index becomes 7.7 when the 430 MPa stainless steel grade is used. It is demonstrated in Fig. 12 that the contribution ratio of the stainless-steel tube increases from 0.46 to 0.63 when increasing the proof stress from 275 MPa to 430 MPa. The numerical predictions reveal that the duplex stainless steel Grade S31803 recommended in AS/ NZS 4673:2001 [36] should be used to improve the ultimate axial loads and ductility of DCFSST columns. 5.3. Effect of Di Do ratio The Di Do ratio is an important feature that markedly influences the behavior of circular DCFSST columns. Columns DC10-DC13 given in Table 2 were analyzed by using the developed computer model to assess the significance of the Di Do ratio on their structural characteristics. The Di Do ratio was ranged from 0.3 to 0.8 by altering the diameter of the inner tube (Di) and all other parameters were not changed. Fig. 13 shows that the ratio of Di Do has a minor influence on the column initial stiffness. However, the post-yield load-axial strain behavior is significantly affected by the ratio of Di Do . The ductility of DCFSST columns decreases with an increase in the Di Do ratio. The ultimate load noticeably decreases as the Di Do ratio increases from 0.4 to 0.8. On the other hand, the ductility indicator increases from 4.5 to 20.7 when changing the ratio of Di Do from 0.3 to 0.8 as illustrated in Fig. 14. Fig. 15 indicates that the ratio of stainless-steel contribution increases from 0.42 to 0.91 as the Di Do ratio increases from 0.3 to 0.8, respectively.

Fig. 10. Effect of stainless steel grades on the load-axial strain responses.

5.4. Effect of Di Do ratio The effect of the internal stainless steel tube in terms of Di ti ratio was investigated by analyzing Columns DC14-DC17 given in Table 2. The different Di ti ratio was determined by altering the inner tube thickness ti for the same inner tube diameter Di. The predicted loadaxial strain responses of DCFSST columns with the variation of Di ti ratio have been plotted in Fig. 16. It can be seen that the initial axial stiffness of the column is not sensitive to the variation of the ratio of Di ti , but the column ultimate strength considerably decreases with an increase in the Di ti ratio. The reason for this is that the double-skin lateral confining pressure reduces as the ratio of Di ti increases. Increasing the ratio of Di ti from 20 to 30, 40 and 50 leads to the strength reductions by 8.4%, 17.8% and 18.9%, respectively. The ductility

Fig. 11. Effect of stainless steel grades on strain ductility index.

Fig. 12. Effect of stainless steel grades on stainless steel contribution ratio.

column ultimate load increases by 30% when the duplex stainless steel with 430 MPa proof stress is used instead of the austenitic stainless steel having proof stress of 205 MPa. As indicated in Fig. 11, the strain ductility index is not sensitive to the stainless steel proof stress ranged from 205 MPa to 275 MPa, but significantly increases as the proof stress increases from 275 MPa to 430 MPa. This is because the stainless steel

Fig. 13. Effect of Di Do ratio on load-axial strain responses. 761

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Fig. 14. Effect of Di Do ratio on strain ductility index.

Fig. 17. Effect of Di ti ratio on strain ductility index.

Fig. 15. Effect of Di Do ratio on stainless steel contribution ratio. Fig. 18. Effect of Di ti ratio on stainless steel contribution ratio.

with the Di ti ratios of 20, 30, 40 and 50 are 0.49, 0.52, 0.58 and 0.58, respectively. 5.5. Effect of Do to ratio The nonlinear analyses on Columns DC18-DC21 given in Table 2 were undertaken and the numerical results obtained are presented in Figs. 19–21. As demonstrated in Fig. 19, the initial stiffness of the column is slightly influenced by the variation of the Do to ratio. The use of a larger Do to ratio, however, markedly reduces the column ultimate load. The column ultimate load decreases by18.9%, 21.6% and 21.8%, respectively when increasing the Do to ratio from 40 to 50, 60 and 70. The ratio of Do to has a remarkable influence on the post-peak responses as indicated in Fig. 19. Fig. 20 presents the effects of Do to ratio on the ductility indicators of DCFSST columns. As shown in Fig. 20, the ductility indices of DCFSST columns having the Do to ratios of 40, 50, 60 and 70 are 12.5, 8.0, 5.9 and 4.1, respectively. The stainless steel contribution ratio as presented in Fig. 21 slightly decreases with increasing the Do to ratio. The stainless steel contribution ratio is slightly affected by varying the Do to ratio 40 to 50. The stainless steel contribution ratio reduces from 0.52 to 0.46 and 0.40 as the Do to ratio increases from 50 to 60 and 70, respectively.

Fig. 16. Effect of Di ti ratio on load-axial strain responses.

indicators of the columns having various ratios of Di ti are shown in Fig. 17. It is indicated that the strain ductility index increases slightly when the ratio of Di ti is changed from 20 to 40. However, when the ratio of Di ti is changed from 40 to 50, the ductility performance index reduces from 8.0 to 6.0. The contribution ratios of the stainless-steel tubes are provided in Fig. 18. The ratios of stainless-steel contribution 762

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Fig. 19. Effect of Do to ratio on load-axial strain responses.

Fig. 22. Load-axial strain responses of DCFST and DCFSST columns.

structural characteristics of circular short DCFST and DCFSST columns. The same geometry and yield strengths of both columns were employed for the comparison purpose. The mathematical model given by Liang [3] was utilized to determine the nonlinear load–strain response of circular DCFST column. The predicted load–strain responses are given in Fig. 22. Both columns have almost the same curve before attaining their ultimate loads. However, the DCFSST column has a higher capacity than the DCFST column. The significant difference in the post-yield behavior of nonlinear load–strain curves between DCFSST and DCFST columns can be observed from Fig. 22. The energy absorption capacity, which is the area under the load–strain curve, of a DCFSST column is slightly greater than that of a DCFST column. The slope of the load–strain curve of a DCFST column after attending the peak load is found to be steeper than that of a DCFSST column. This indicates that the DCFSST column exhibits higher ductility than the DCFST column. The reason for this is that stainless steel has more significant strain-hardening behavior than carbon steel.

Fig. 20. Effect of Do to ratio on strain ductility index.

6. Current design models for CFST columns There are several standards for the design of CFST composite short columns composed of circular tubes including Eurocode 4 [4] and ANSI/AISC 360-16 [5]. Nevertheless, these codes have not provided guidelines for the design circular short DCFSST composite columns loaded concentrically. The ultimate axial loads predicted using these design standards are compared against experimental data to evaluate their accuracy for the design of DCFSST columns. 6.1. Eurocode 4 The equation given in Eurocode 4 [4] is used for the design of composite columns including concrete-encased sections, partially encased sections, circular CFST columns and rectangular CFST columns. For examining the applicability of Eurocode 4 [4] equation, the confinement effect on the strength calculations of circular CFST columns is considered in Eurocode 4 [4]. For short DCFSST composite columns with circular section, the design expression given in Eurocode 4 [4] for the design of short CFST circular columns is modified as follows:

Fig. 21. Effect of Do to ratio on stainless steel contribution ratio.

+

a Aso 0.2o

+ Asc fc 1 +

0.2o

Pu .EC4 =

As the stress–strain behaviors of carbon steel and stainless steel are significantly different, the structural characteristics of DCFST and DCFSST columns were investigated to evaluate their possible differences. Column DC22 given in Table 2 was used to compare the

where Asi and Aso are the cross-sectional areas of the internal and external steel tubes, respectively; Asc refers to the cross-sectional area of sandwiched concrete. The steel strength reduction factor a and the concrete strength factor c are determined by 763

a Asi 0.2i

to Do

5.6. Comparison of DCFST and DCFSST columns

c

fc

(51)

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Table 3 Comparison of computed ultimate axial loads with experimental results. Specimens

L

101 × 1.6–50 × 3-D 101 × 1.6–50 × 3-D 101 × 3–50 × 1.6-D 114 × 3–50 × 3-D 152 × 1.6–76 × 1.6-D 152 × 1.6–101 × 1.6-D 168 × 3–50 × 1.6-D 168 × 3–89 × 3-D 168 × 3–101 × 3-D 168 × 3–114 × 3-D 203 × 2–152 × 1.6-D DC1 DC2 DC3 DC4 DC5 DC6 DC7 DC8 DC9 DC10 DC11 DC12 DC13 DC14 DC15 DC16 DC17 DC18 DC19 DC20 DC21 DC22 Mean Standard deviation (SD) Coefficient of variation (COV)

a

= 0.25(3 + 2 ¯ )

c

= 4.9

(mm)

300 300 300 350 450 450 450 450 450 450 400 900 900 900 900 900 1200 1200 1200 1200 1500 1500 1500 1500 1800 1800 1800 1800 1800 1800 1800 1800 600

1

a

18.5 ¯ + 17 ¯ 2

c

0

Pu

(kN)

583 634 593 902 997 825 1569 1464 1354 1319 1142 3927 4397 5109 5826 6767 9405 10,319 11,267 12,239 15,388 14,970 12,959 10,451 29,172 26,722 23,992 23,651 32,952 26,722 25,834 25,775 2843

Eurocode 4 [4]

AISC 316-16 [5]

Pu, EC 4 (kN)

Pu, EC 4 Pu

Pu, AISC (kN)

Pu, AISC Pu

Pu, Liang (kN)

Pu, Liang Pu

552 562 550 748 980 828 1526 1393 1263 1206 1157 3764 4225 4919 5616 6546 9819 10,825 11,917 13,051 13,954 13,487 11,833 9149 29,860 29,633 29,516 29,445 32,419 29,633 27,745 26,411 2583

0.947 0.886 0.928 0.829 0.983 1.004 0.972 0.952 0.933 0.914 1.013 0.958 0.961 0.963 0.964 0.967 1.044 1.049 1.058 1.066 0.907 0.901 0.913 0.875 1.024 1.109 1.230 1.245 0.984 1.109 1.074 1.025 0.909 0.991 0.093 0.094

502 517 497 668 911 802 1302 1268 1163 1159 1128 3407 3858 4534 5211 6113 9062 9966 10,934 11,968 12,510 12,289 11,288 9540 25,848 25,551 25,398 25,305 27,540 25,551 24,213 23,272 2410

0.861 0.815 0.838 0.740 0.914 0.972 0.830 0.866 0.859 0.879 0.988 0.868 0.877 0.887 0.894 0.903 0.964 0.966 0.970 0.978 0.813 0.821 0.871 0.913 0.886 0.956 1.059 1.070 0.836 0.956 0.937 0.903 0.848 0.901 0.072 0.080

568 639 575 857 1069 797 1489 1494 1252 1227 1095 3997 4472 5184 5896 6846 9613 10,590 11,637 12,753 15,303 14,889 12,961 9897 29,378 27,366 25,324 25,217 30,271 27,366 25,884 25,306 2893

0.974 1.008 0.969 0.950 1.072 0.966 0.949 1.020 0.924 0.931 0.959 1.018 1.017 1.015 1.012 1.012 1.022 1.026 1.033 1.042 0.995 0.995 1.000 0.947 1.007 1.024 1.056 1.066 0.919 1.024 1.002 0.982 1.018 0.999 0.039 0.039

(52)

6.2. ANSI/AISC 360-16

(53)

The design code ANSI/AISC 360-16 [5] completely ignores the wellappeared concrete confinement in the calculations of the cross-section capacity of short CFST circular columns. The design equation provided in ANSI/AISC 360-16 [5] for CFST columns is slightly modified to predict the axial capacity of DCFSST columns as

where ¯ represents the relative slenderness of the DCFSST column, which is defined as

¯=

Npl . Rk (54)

Ncr

Pu .AISC = Asi

0.2i

+ Aso

0.2o

where the squash load of the column cross-section Npl . Rk is calculated by

Npl . Rk = Asi

0.2i

+ Aso

0.2o

+ fc Asc

(55)

Ncr =

in which L is the column effective length and the effective bending stiffness (EI )eff of a DCFSST column is estimated by (57)

Pu . Liang =

where E0i , E0o are the modulus of elasticity of the internal and external stainless-steel tubes, respectively; the second moments of area of the sandwiched concrete, the internal tube, the external tube are denoted by Isc , Isi , Iso respectively. The Young’s modulus of sandwiched concrete Ecm is estimated by

Ecm = 22000

fc + 8 10

(59)

A simple design model for estimating the cross-section capacity of circular short DCFST composite columns was proposed by Liang [3]. The design model accounts for the effects of noticeable features including the strain-hardening and double-skin concrete confinement in the prediction of the cross-section strength. Liang’s design equation is expressed as

(56)

(EI )eff = E0i Isi + E0o Iso + 0.6Ecm Isc

+ 0.95fc Asc

6.3. Liang’s design model

In Eq. (54), the elastic critical buckling load Ncr is determined by 2 (EI ) eff L2

Liang [3]

si 0.2i Asi

+

so 0.2o Aso

+ ( c fc + 4.1frp ) Asc

(60)

where c and frp are calculated using Eqs. (42) and (46), respectively. Based on the stresses in the stainless steel tubes obtained from the experimental and numerical results, the strain hardening parameters, si and so , are proposed as

0.3

si

(58) 764

= 1.6029

Di ti

0.118

(61)

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V.I. Patel, et al.

so

= 3.5245

Do to

Declaration of Competing Interest

0.299

(62)

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

6.4. Applicability of current design models to DCFSST columns The ultimate axial strengths of short DCFSST columns calculated by the modified methods described in preceding sections are compared against experimental data as well as computational results in Table 3, in which Pu is the ultimate load obtained by either experiments or the numerical model. The mean of the ultimate loads obtained from the design method given in Eurocode 4 [4] to the experimental and numerical values is 0.991. The approach specified in ANSI/AISC 360-16 [5] generally underestimates the column ultimate axial loads. The mean of Pu . AISC Pu ratio is 0.901 with an SD of 0.072 and a COV of 0.080. This is because the ANSI/AISC 360-16 [5] code does not account for the confinement effect. The design model proposed by Liang [3] accurately predicts the cross-section capacity of DCFSST columns. The reason for this is that Liang’s model [3] takes into account the concrete confinement induced by double-skins and steel strain hardening. The mean of Pu . Liang Pu ratios predicted using Liang’s model is 0.999 with a 0.039 SD and a 0.039 COV.

References [1] Li YL, Zhao XL, Singh Raman RK, Yu X. Axial compression tests on seawater and sea sand concrete-filled double-skin stainless steel circular tubes. Eng Struct 2018;176:426–38. [2] Zhao XL, Grzebieta R, Elchalakani M. Tests of concrete-filled double skin CHS composite stub columns. Steel Compos Struct 2002;2(2):129–46. [3] Liang QQ. Nonlinear analysis of circular double-skin concrete-filled steel tubular columns under axial compression. Eng Struct 2017;131:639–50. [4] Eurocode,. 4, Design of composite steel and concrete structures-Part 1–1: general rules and rules for buildings. Brussels, Belgium: European Committee for Standardization, CEN; 2004. [5] ANSI/AISC 360-16. Specification for structural steel buildings. Chicago (IL, USA): American Institute of Steel Construction; 2016. [6] Tao Z, Han LH, Zhao XL. Behaviour of concrete-filled double skin (CHS inner and CHS outer) steel tubular stub columns and beam-columns. J Constr Steel Res 2004;60(8):1129–58. [7] Han LH, Huang H, Tao Z, Zhao XL. Concrete-filled double skin steel tubular (CFDST) beam-columns subjected to cyclic bending. Eng Struct 2006;28(12):1698–714. [8] Uenaka K, Kitoh H, Sonoda K. Concrete filled double skin circular stub columns under compression. Thin-Walled Struct 2010;48(1):19–24. [9] Han LH, Ren QX, Li W. Tests on stub stainless steel-concrete-carbon steel double-skin tubular (DST) columns. J Constr Steel Res 2011;67:437–52. [10] Elchalakani M, Hassanein MF, Karrech A, Fawzia S, Yang B, Patel VI. Experimental tests and design of rubberised concrete-filled double skin circular tubular short columns. Structures 2018;15:196–210. [11] Ekmekyapar T, Alwan OH, Hasan HG, Shehab BA, AL-Eliwi BJM. Comparison of classical, double skin and double section CFST stub columns: experiments and design formulations. J Constr Steel Res 2019;155:192–204. [12] Young B, Ellobody E. Experimental investigation of concrete-filled cold-formed high strength stainless steel tube columns. J Constr Steel Res 2006;62(5):484–92. [13] Lam D, Gardner L. Structural design of stainless steel concrete filled columns. J Constr Steel Res 2008;64(11):1275–82. [14] Uy B, Tao Z, Han LH. Behaviour of short and slender concrete-filled stainless steel tubular columns. J Constr Steel Res 2011;67(3):360–78. [15] Li D, Uy B, Aslani F, Hou C. Behaviour and design of spiral-welded stainless steel tubes subjected to axial compression. J Constr Steel Res 2019;154:67–83. [16] Liao FY, Hou C, Zhang WJ, Ren J. Experimental investigation on sea sand concrete-filled stainless steel tubular stub columns. J Constr Steel Res 2019;155:46–61. [17] Wang F, Young B, Gardner L. Compressive testing and numerical modelling of concretefilled double skin CHS with austenitic stainless steel outer tubes. Thin-Walled Struct 2019;141:345–59. [18] Huang H, Han LH, Tao Z, Zhao XL. Analytical behaviour of concrete-filled double skin steel tubular (CFDST) stub columns. J Constr Steel Res 2010;66(4):542–55. [19] Wang F, Han LH, Li W. Analytical behavior of CFDST stub columns with external stainless steel tubes under axial compression. Thin-Walled Struct 2018;127:756–68. [20] Hu HT, Su FC. Nonlinear analysis of short concrete-filled double skin tube columns subjected to axial compressive forces. Mar Struct 2011;24(4):319–37. [21] Hassanein MF, Kharoob OF, Liang QQ. Circular concrete-filled double skin tubular short columns with external stainless steel tubes under axial compression. Thin-Walled Struct 2013;73:252–63. [22] Pagoulatou M, Sheehan T, Dai XH, Lam D. Finite element analysis on the capacity of circular concrete-filled double-skin steel tubular (CFDST) stub columns. Eng Struct 2014;72:102–12. [23] Liang QQ. Analysis and design of steel and composite structures. Boca Raton and London: CRC Press, Taylor and Francis Group; 2014. [24] Liang QQ. Numerical simulation of high strength circular double-skin concrete-filled steel tubular slender columns. Eng Struct 2018;168:205–17. [25] Li YL, Zhao XL, Raman RKS. Theoretical model for concrete-filled stainless steel circular stub columns under axial compression. J Constr Steel Res 2019;157:426–39. [26] Patel VI, Liang QQ, Hadi MNS. Concrete-filled stainless steel tubular columns. Boca Raton and London: CRC Press, Taylor and Francis; 2018. [27] Patel VI, Liang QQ, Hadi MNS. Nonlinear analysis of axially loaded circular concretefilled stainless steel tubular short columns. J Constr Steel Res 2014;101:9–18. [28] Ramberg W, Osgood WR. Description of stress-strain curves by three parameters. NACA Tech. Note No. 902; 1943. [29] Rasmussen KJR. Full-range stress–strain curves for stainless steel alloys. J Constr Steel Res 2003;59(1):47–61. [30] Quach WM, Teng JG, Chung KF. Three-stage full-range stress-strain model for stainless steels. J Struct Eng 2008;134(9):1518–27. [31] Abdella K, Thannon RA, Mehri AI, Alshaikh FA. Inversion of three-stage stress strain relation for stainless steel in tension and compression. 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7. Conclusions Circular double-skin concrete-filled steel tubular (DCFSST) columns can be constructed by the concrete made of seawater and sea-sand without corrosion. A computational model has been proposed in this paper for computing the load-axial strain responses of such circular DCFSST short columns loaded concentrically. The computer model developed explicitly incorporates the double-skin confinement and significant strain-hardening behavior of stainless steel in compression. The established experimental results on circular DCFSST columns have been used to validate the computational model. The proposed model has been found to yield accurate predictions of the nonlinear load–strain behavior of DCFSST columns. The computer model has been employed to ascertain the significance of various important features on the structural behavior of DCFSST short columns. The important concluding remarks are as follows: (1) The ultimate strength and initial stiffness of short DCFSST columns improve significantly as the concrete strength increases. However, both ductility and stainless steel contribution ratios decrease when increasing the concrete strength. (2) The ultimate axial load of a DCFST column with the 430 MPa duplex stainless steel is higher than that with the 205 MPa austenitic stainless steel. In addition, the stainless steel contribution and ductility increase as the stainless steel proof strength increases. (3) A DCFSST column with a larger Di Do ratio exhibits a lower ultimate axial strength. However, its ductility and stainless steel contribution increase as the Di Do ratio increases. (4) The ultimate strength of DCFSST columns reduces with an increase in the Di ti ratio. The stainless-steel contribution increases as the Di ti ratio increases. The column ductility decreases with increasing the Di ti ratio from 40 to 50. (5) The larger the Do to ratio, the lower the column ultimate load. The ductility and stainless steel contribution decrease as the Do to ratio increases. (6) The DCFSST column has a higher ultimate load, energy absorption capacity and ductility than the DCFST column. (7) The current design codes Eurocode 4 [4] and the model given by Liang [3] accurately calculate the ultimate load of DCFSST columns.

765