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Study on the behavior of concrete-filled square double-skin steel tubular stub columns under axial loading
Structures 23 (2020) 665–676
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Study on the behavior of concrete-filled square double-skin steel tubular stub columns under axial loading
T
⁎
Fa-xing Dinga,b, Wen-jun Wanga, De-ren Lua, , Xue-mei Liuc a
School of Civil Engineering, Central South University, Changsha, Hunan Province, 410075, PR China Engineering Technology Research Center for Prefabricated Construction Industrialization of Hunan Province, 410075, PR China c Department of Infrastructure Engineering, The University of Melbourne, Parkville, VIC 3010 Australia b
A R T I C LE I N FO
A B S T R A C T
Keywords: Concrete-filled square double-skin steel tubular (CFDST) stub columns Confinement coefficient Finite element analyses Large hollow ratio Practical calculation formula
This paper presents a numerical, experimental, and theoretical study on the behavior of concrete-filled square double-skin steel tubular (CFDST) stub columns under axial compressive loading. Firstly, three-dimensional solid model of CFDST stub columns was established by ABAQUS finite element software and verified through the existing experimental results. Then a full-scale model was established to investigate the influence of various parameters on ultimate bearing capacity and internal and external compressive stress of concrete. By considering the confinement coefficient, the practical calculation formula for the bearing capacity of CFDST stub columns was proposed. Finally, the experimental research on the mechanical properties of two large hollow ratio CFDST stub columns under axial compression was carried out. And the experimental research further verified the applicability of the FE model and calculation formula of the CFDST stub column with large hollow ratio under axial compression.
1. Introduction Compared with ordinary concrete filled steel tubular (CFST) [1], concrete filled double-skin steel tubular (CFDST) stub columns have not only the characteristics of high bearing capacity, good seismic performance and convenient construction, but also the advantages of light weight, high bending rigidity and good fire resistance and so on [2,3]. Therefore, CFDST columns have good mechanical properties and wide applicability, especially when subjected to an eccentric compressive load [4] or cyclic loading [5,6]. At present, the research on CFDST columns mainly focuses on their static performance. The researched cross-section forms mainly include CHS (circular hollow section) outer and CHS inner, CHS outer and SHS (square hollow section) inner, SHS outer and SHS inner, SHS outer and CHS inner. The existing research results show that the CFDSTs with CHS outer are suitable for the high bridge pier across the deep valley and the offshore platform structure to reduce the water flow or the wind load. The CFDSTs with SHS outer are suitable for the frame giant column or shear wall of the high-rise building. In terms of bearing capacity, the SHS is slightly inferior to the CHS, but it is more beneficial to utilize the internal space. Therefore, the SHS is more valuable and economic in the field of building structure. In recent years, four main types of CFDST have been developed
⁎
using a combination of circular hollow section (CHS) and square hollow section (SHS): Pagoulatou et al.[7], Uenaka et al. [8], Tao et al. [9,10], Elchalakani et al. [11], Han et al. [12], Zhao et al. [13] studied the mechanical behavior of CFDST stub columns with SHS and CHS as outer or inner tubes under axial compression, respectively. These studies focused on the effects of the composite section types, the depth-tothickness ratios of the steel tubes, and the hollow ratio and slenderness ratio on the mechanical properties of CFDST under axial compression. Xie et al. [14] carried out experimental study on the compressionbending-shear-torsion performance of the CFDST (SHS outer and CHS inner) stub columns and the result show that the shear resistance of CFDST (SHS outer and CHS inner) stub columns were higher than that of square CFST column while the ductility of CFDST (SHS outer and CHS inner) stub columns were lower at ultimate stage. Huang et al. [15,16] conducted a preliminary study on the working mechanism of the CFDST stub columns under axial compression, and compared the advantages and disadvantages of different cross-section forms. It was found that the CFDST (SHS outer and CHS inner) stub columns had higher bearing capacity and ductility, and the calculation formula for the ultimate bearing capacity of the CFDST (SHS outer and CHS inner) stub columns was proposed. Zhao et al. [17] conducted an experimental study on the axial compression and bending resistance of the CFDST (SHS outer and SHS inner) stub columns and increased ductility and
Corresponding author. E-mail address: [email protected] (D.-r. Lu).
https://doi.org/10.1016/j.istruc.2019.12.008 Received 5 July 2019; Received in revised form 2 December 2019; Accepted 7 December 2019 2352-0124/ © 2019 Institution of Structural Engineers. Published by Elsevier Ltd. All rights reserved.
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Nomenclature
Nso Nsi Nc Nu Nu,c εL σL,s σθ,s σr,c Asc Ac Ac1 Ac2 Asi Aso σr,c0σθ,so
Symbols Bo Bi b L to ti fso fsi fcfcu Nu,FE Nu,e χ χ0 ρ Nsc
Outer diameter of the outer steel tube Inner diameter of the inner steel tube Outer side length of the core concrete Inner side length of the core concrete Length of the test piece Wall thickness of the outer steel tube Wall thickness of the inner steel tube Yield strength of the outer steel tube Yield strength of the inner steel tubethe compressive cubic strength of concrete Cubic compressive strength of concrete Ultimate bearing capacity of FE results Ultimate bearing capacity of experimental results Hollow ratio of the section Hollow ratio of concrete Steel ratio of the section
k K
Total ultimate capacity Ultimate capacity of the outer tube Ultimate capacity of the inner tube Ultimate capacity of the concrete Ultimate bearing capacity Ultimate bearing capacity calculated by Eq. (10) Axial strain Longitudinal stress Transverse stress Radial stress Total area of cross section Sectional area of the whole core concrete Unconstrained concrete area Constrained concrete area Cross-sectional area of the inner steel tube Cross-sectional area of the outer steel tubeRadial stress of core concrete in constraint area Transverse stress of outer steel tube Coefficient of lateral pressureConfinement coefficient
are established and the parametric analysis are carried out to investigate the confinement effect of inner and outer steel tubes and core concrete under axial compression. (3) Based on the balance of the limit state force and the simplification of the stress cloud diagram, a practical design formula for the ultimate bearing capacity of the CFDST (SHS outer and SHS inner) stub columns considering the influence of the hollow ratio on the confinement coefficient is proposed. (4) A series of compression tests were carried out on two CFDST (SHS outer and SHS inner) stub columns which hollow ratio is large. This experiment makes up for the insufficiency of the existing research and further verifies the rationality of the FE model and bearing capacity calculation formula for large-size stub columns with large hollow ratio under axial compression.
energy absorption had been observed of CFDST subjected to compression. Liang et al. [18] carried out an experimental investigation of the mechanical behavior and working mechanism of the CFDST (SHS outer and SHS inner) with stiffeners. The above research status indicates that the axial compression performance of the CFDST (SHS outer and SHS inner) stub columns still lacks in-depth studies. The constraint effect between the steel tubes and the laminated concrete under axial load is yet to be revealed, and the confinement coefficient of the CFDST (SHS outer and SHS inner) stub columns under axial compression is not clear. In the previous research, the research group proposed a concrete triaxial plastic-damage constitutive model which is suitable for CFST columns with different cross-sections [19–23]. The model was used in the FE analysis of the CFST stub columns in the form of circular, round, octagonal, hexagonal and rectangular sections. Practical design formulas for bearing capacity considering the influence of section shape on the confinement coefficient were proposed. The model and method can be further applied to the three-dimensional solid FE analysis of CFDST (SHS outer and SHS inner) stub columns. Therefore, the main contents of this paper include: (1) finite 3D solid element models of CFDST (SHS outer and SHS inner) stub columns are established by adopting a triaxial plastic-damage constitutive model of concrete under axial compression, and a set of test results reported by different researches are used to verify the FE models. (2) A large number of full-scale models
2. Finite element model and verification 2.1. Finite element modeling and parameter selection Non-linear FE models for CFDST stub columns under axial compression were established using ABAQUS version 6.14 (2014). In the numerical models, the 8-node reduced integral format 3D solid element (C3D8R) is applied to model the inner and outer steel tube, core concrete and loading plates for all specimens. The structured meshing
Fig. 1. Mesh generation of FE models. 666
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Coulomb friction coefficient of 0.5 in the tangential direction is used to simulate the interfacial behavior between the steel tube and the core concrete. The “tie” option is adopted for the constraint between the steel tube and the cover plate so that no relative motion occurs between them. Other parameters setting and stress–strain relationship of concrete tri-axial compression and elasto-plastic hardening stress–strain relationship of steel tube are detailed explained in Ref. [24].
technique is adopted as shown in Fig. 1. The surface-to-surface contact is adopted for the interaction between steel tube and core concrete, in which the surface of steel tube is the master surface meanwhile the corresponding surface of core concrete is slave surface. Limited glide is employed in the sliding formulation as well as the discretization method is surface-to-surface. The tangential behavior and normal behavior are defined in the contact characteristics, and the interface bond-slip relationship between the steel tube and the core concrete is simulated. The normal behavior is set to “hard” contact allowing separation after contact. The tangential friction equation is established by using the penalty function. The
2.2. Comparative analysis of calculation results In this paper, the FE models of the CFDST stub columns under axial
Fig. 2. Comparison of FE and experimental load–strain curves. 667
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Table 1 Comparison of test results in references and FE results. Specimens Label
Bo/mm
Bi/mm
to(ti)/mm
χ
fso(fsi)/MPa
fcu/MPa
Nu,e/kN
Nu,FE/kN
Nu,c/kN
Nu,FE /Nu,e
Nu,c/Nu,e
references
D-SS-a CS1S5A CS1S5B CS2S5A CS2S5B CS3S5A CS3S5B CS4S5A CS4S5B
160 99.74 99.74 100.49 100.49 100.18 100.18 100.46 100.46
53 50 50 50 50 50 50 50 50
3.62(2.71) 5.97(2.44) 5.97(2.44) 4.01(2.44) 4.01(2.44) 2.94(2.44) 2.94(2.44) 2.06(2.44) 2.06(2.44)
0.11 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25
374(3 0 4) 485(4 7 7) 485(4 7 7) 445(4 7 7) 445(4 7 7) 464(4 7 7) 464(4 7 7) 453(4 7 7) 453(4 7 7)
50.5 57.8 57.8 57.8 57.8 57.8 57.8 57.8 57.8
1819 1545 1614 1194 1210 1027 1060 820 839
1820 1689 1689 1253 1253 1088.4 1088.4 862.9 862.9
1908 1566 1566 1253 1253 1066 1066 852 852
1.000 1.093 1.046 1.059 1.036 1.060 1.027 1.052 1.028
1.049 1.013 0.970 1.050 1.036 1.038 1.005 1.039 1.015
[11] [12]
*Note: Nu,
c
is the bearing capacity calculated by Eq. (10).
Table 2 Details of the specimen parameters and analysis results in the parametric study. Specimens Label
Bo × Bi × L/mm
to(ti) /mm
Bo/to
χ
ρ
fcu/MPa
fc/ MPa
fso/MPa
fsi/MPa
Nu,FE/MN
Nu,c/MN
Nu,c/ Nu,FE
SdsA-1 SdsA-2 SdsA-3 SdsA-4 SdsA-5 SdsA-6 SdsA-7 SdsA-8 SdsA-9 SdsA-10 SdsA-11 SdsA-12 SdsA-13
5000 × 0 × 3000 5000 × 2500 × 3000 5000 × 3540 × 3000 5000 × 4330 × 3000 5000 × 3540 × 3000 5000 × 3540 × 3000 5000 × 3540 × 3000 5000 × 3540 × 3000 5000 × 3540 × 3000 5000 × 3540 × 3000 5000 × 3540 × 3000 5000 × 3540 × 3000 5000 × 3540 × 3000
50(50) 50(50) 50(50) 50(50) 40(40) 60(60) 50(50) 50(50) 50(50) 50(50) 50(50) 50(50) 50(50)
100 100 100 100 125 83 100 100 100 100 100 100 100
0 0.25 0.5 0.75 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
0.04 0.08 0.137 0.299 0.11 0.164 0.137 0.137 0.137 0.137 0.137 0.137 0.137
60
47.5
345
345
60
47.5
345
345
40 80 100 60
29.5 66.4 86.1 47.5
345
345
235 420 345
345
1681.8 1450.3 1168.9 874.4 1069.3 1268.7 971.13 1372.8 1579.82 1059.4 1244.6 1083.3 1224.9
1553 1366.5 1121.7 870 1015.8 1227.6 929.1 1325.5 1538.1 1006.0 1200.6 1042.7 1175.6
0.923 0.942 0.960 0.995 0.950 0.968 0.957 0.966 0.974 0.950 0.966 0.963 0.960
235 420
*Note: fc is the compressive cubic strength of concrete, according to reference [23], fc = 0.4fcu7/6.
Fig. 3. Load and stress-axial strain curves of CFDST stub columns under axially loading. 668
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Fig. 4. Stress nephogram of concrete section at each stage.
have a small confinement force on the concrete. Since the Poisson's ratio of the steel tube is larger than that of the concrete, the radial stress of the outer steel tube is negative. It can be seen from the stress nephogram of Fig. 4(a) that the longitudinal stress of the concrete in the middle section is substantially evenly distributed; Elastoplastic stage (AB): The longitudinal stress of concrete increases rapidly at this stage. At point B, the inner and outer steel tubes reach the yield strength, and the longitudinal stress of the concrete approaches the uniaxial compressive strength of concrete. It can be seen from Fig. 3(b) that the rate of decrease of the longitudinal stress at the corner of the outer steel tube and the rate of increase of the transverse stress are greater than the stress of the corresponding middle portion, and the inner steel tube is substantially in an axially compressed state without being bent and unstable. As shown in the stress nephogram of Fig. 4(b), the longitudinal stress value of the corner of the concrete is larger than that of the central part. In summary, the confinement effect of the outer steel tube on the corner concrete is greater than the middle portion. Plastic stage (BC): At this stage, the longitudinal stress of the outer steel tube decreases and the transverse stress increases, while the radial stress of the outer steel tube to the concrete increases gradually. As seen from the stress nephogram of Fig. 4(c), the confinement effect of the outer steel tube on the concrete makes the longitudinal stress of concrete exceeds the uniaxial compressive strength of concrete which value is 47.5 MPa when the compressive cubic strength of concrete is 60 MPa. At the same time, with the increase of the confinement effect of the outer steel tube on the concrete, the longitudinal stress distribution of the cross section of the concrete tends to be uneven due to the greater confinement effect of the outer steel tube on the concrete corner. The inner steel tube always has little confinement effect on the concrete. The details of the comparation about the typical N-εL curves and σr, c-εL curves for the paramedic study are presented in Fig. 5. From the parametric study results, the research findings are summarized below. (1) Fig. 5(a) and (b) compare the effect of different yield strength of outer steel tube on bearing capacity and radial stress. It can be seen that for every 50% increase in the yield strength of the outer steel tube, the bearing capacity is increased by 10%, and the radial stress of the outer steel tube is increased by 20%. The greater yield strength of the outer steel tube, the more confinement effect on the concrete, while the inner steel tube has no obvious confinement on the core concrete. (2) Fig. 5(c) and (d) compare the N-εL curves and the σr,c-εL curves of outer and inner steel tubes under different yield strength of inner steel tube. The results show that the change of the yield strength of the inner steel tube does not cause the change of the radial stress of the outer steel tube to the concrete, nor does it change its own confinement effect on the core concrete. (3) Fig. 5(e) and (f) show the comparison of the N-εL curves and the σr, c-εL curves under different concrete strength. It can be obtained that the radial stress of outer steel tube on concrete is increased by 50% with the increase of concrete strength by 20 MPa. So with the increase of
compression are verified against the experimental results reported by Liang (2019), Huang (2015) and Zhao (2002) [26]. The typical load–strain curves of FE results and experimental results are compared as shown in Fig. 2. Bo is the outer diameter of the outer steel tube, Bi is the inner diameter of the inner steel tube, L is the length of the test piece, fso is the yield strength of the outer steel tube, and fsi is the yield strength of the inner steel tube. fcu is the compressive cubic strength of concrete. The ultimate bearing capacity of FE results (Nu, FE) are compared with the experimental results (Nu, e) in Table 1. to and ti are the wall thickness of the outer and inner steel tube, respectively. χ is the hollow ratio of the section, defined as the ratio of the area of the hollow part to the area enclosed by the outer steel tube, ie χ = Bi2/Bo2. ρ is the steel ratio of the section, defined as the ratio of the sum of the cross-section of inner and outer steel tubes to the cross-sectional area, ie ρ= (4Biti + 4Boto)/(Bo2-Bi2). It is shown that the average value of the ratios (Nu, e/Nu, FE) is 0.959 with the corresponding dispersion coefficient of 0.020. From the above comparisons, it can be found that generally good agreement is achieved between the FE and test results. Therefore, the FE models can be used to carry out further parametric study of the CFDST stub columns beyond the range of test specimens. 2.3. Analysis of influencing factors of full scale examples FE models are established to investigate the mechanical behavior of CFDST stub columns under axial compression. The main parameters affecting the axial bearing capacity of the CFDST stub columns are as follow: the yield strength of outer and inner steel tube fso = fsi = 235 MPa, 345 MPa, and 420 MPa, the compressive cubic strength of concrete fcu = 40 MPa, 60 MPa, 80 MPa and 100 MPa, the steel ratio ρ = 0.04, 0.08, 0.11, 0.137, 0.164 and 0.299. The details of the parameters and results for the parametric study were presented in Table 2. SdsA-3 (Bo = 5000 mm, Bi = 3540 mm, to = ti = 50 mm, fso = fsi = 345 MPa, fcu = 60 MPa, ρ = 0.137, χ = 0.5) was analyzed as a typical specimen. Fig. 3(a) shows the variation of the total axial force (Nsc), the axial force of the inner tube (Nsi), the axial force of the outer tube (Nso), and the axial force of the concrete (Nc) with the longitudinal strain of the specimen. Fig. 3(b) presents the typical longitudinal stress (σL, s)-axial strain (εL) curves and transverse stress (σθ, s)-axial strain (εL) curves of outer and inner steel tube. Fig. 3(c) gives the radial stress (σr, c)-strain curves of outer and inner steel tube. σr, c is the average value of the radial stress of each element in the middle section of the steel tube obtained by finite element extraction. Defining the radial stress from the direction of the steel tube to the concrete is negative. The stress nephogram at midsection of the core concrete at different loading stages was extracted from the FE models as shown in Fig. 4. It can be seen from Figs. 3 and 4 that the loading process can be divided into the following three stages: Elasticity stage (OA): At this stage, the inner and outer steel tubes 669
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Fig. 5. Influence of various parameters on the load bearing capacity and radial stress of steel tube.
ultimate load capacity is reached. It can be seen that for every 0.25 increase of the hollow ratio, the radial stress of the outer steel tube is reduced by 20%, and the increase of the hollow ratio also leads to the reduction of the longitudinal stress of the corner concrete and the confinement effect of the outer steel tube on the core concrete. The change of the hollow ratio has little effect on the radial stress of the inner steel tube.
concrete strength, the proportion of load carried by concrete increases, the transverse deformation coefficient of outer steel tube increases, and the radial stress of outer steel tube to concrete increases, while the value of radial stress of inner steel tube to concrete is always small. (4) Fig. 5(g) and (h) compare the effect of different steel ratio on bearing capacity and radial stress. It can be seen that the larger the steel ratio, the radial stress of the outer steel tube slightly increases, while it has little effect on the radial stress of the inner steel tube. (5) Fig. 5(i) and (j) show the comparison of the N-εL curves and the σr, c-εL curves under different hollow ratio and Fig. 6 presents that the stress nephogram of concrete under different hollow ratios when the 670
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Fig. 5. (continued)
3. Practical calculation formula for bearing capacity
σL, s = 0.97fs
3.1. Stress analysis
According to the Von-Mises yield condition for steel material, the transverse stress of the outer steel tube can be expressed as
To derive the calculation formula of bearing capacity, a range of parameters such as concrete strength, yield strength of steel, steel ratio, and hollow ratio are further investigated by FE analysis. The values of these parameters are chosen based on the engineering practice. A total of 72 groups of optimized column specimens are included in the numerical study, in which Q235 steel matches C40 and C60 concrete, Q345 steel matches C60 and C80 concrete, while Q420 steel matches C80 and C100 concrete. Specific parameters and matching principles are shown in Table 3. The longitudinal stress of the steel tube at three locations (endpoint, 1/4 point and midpoint of the middle section of the steel tube) is extracted from FE calculation results when the specimen reaches the ultimate bearing capacity. The relationship between the ratio of longitudinal stress and yield strength of steel tube with ultimate strength (fsc = Nu/Asc,Asc = Ac + As, Asc is the total area of cross section) is shown in Fig. 7. According to the analysis of static performance of the CFDST stub columns under axial compression, it is considered that the restraining effect between the outer steel tube and the core concrete is the same as that of the ordinary CFST stub columns, and the inner steel tube does not have the restraining effect on the core concrete. Therefore, only the force of the outer steel tube is considered in the analysis. It can be seen from Fig. 7 that when the specimens reach the ultimate strength, the average value of the ratio of the longitudinal stress (pressure) and the yield strength of the outer steel tube can be expressed as
σθ, s = 0.09fs
(1)
(2)
3.2. Simplification of section force The results of FE analysis show that the core concrete of the CFDST specimens with different hollow ratio has different constraint area. According to the stress nephogram of core concrete under ultimate bearing capacity in Fig. 8, the stress distribution of CFDST stub columns can be simplified to Fig. 9 for calculation. It is assumed that the core concrete in the unconstrained area is not bound by the outer steel tube, and the core concrete in the constraint area is uniformly bound by the outer steel tube. The dimensions of the core concrete are defined as follows: B is the outer side length of the core concrete (B = Bo-2to), b is the inner side length of the core concrete (b = Bi + 2to), χ0 is the hollow ratio of concrete, χ0 = [Bo2 (Bi + 2to)2]/[Bi2(Bo-2to)2]χ = b2/ B2, it can be seen that: When χ0 ≤ 0.44 , which is equivalent to χ0 ≤ 0.44 , the unconstrained area is assumed to be the circumscribed circle of the inner steel tube. When χ0 > 0.44 , which is equivalent to χ0 > 0.44 , the constraint of the outer steel tube on the core concrete is more pronounced at the corner, and the constraint area is the square area of the corner. Therefore, according to the different hollow ratio of concrete, the relationship between the area of the unconstrained area and the area of the core concrete can be defined as 671
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Fig. 6. Stress nephogram of concrete section under different hollow ratios. Table 3 Details of parameters of the specimen used to derive calculation formula. Bo × Bi/mm
to(ti)/mm
χ
ρ
Q235
5000 × 2240 5000 × 2740 5000 × 3160 5000 × 3540 5000 × 3870 5000 × 4180
30–50
0.2 0.3 0.4 0.5 0.6 0.7
0.072–0.243
C40
Q345 C60
C60
Q420 C80
C80
C100
where Ac1 is the unconstrained concrete area; Ac is the sectional area of the whole core concrete, Ac = B2-b2=(1-χ0)B2. The relationship between the area of the constraint area and the area of the core concrete can be expressed as 1 − 1.6χ
Ac2 =
0 Ac χ0 ≤ 0.44 ⎧ ⎪ 1 − χ0 2) ( B b − ⎨A = A χ0 > 0.44 ⎪ c2 (1 − χ0 ) B 2 c ⎩
(4)
where Ac2 is the constrainted concrete area, Ac1 + Ac2 = Ac. 3.3. Formula establishment According to the limit equilibrium theory, the transverse force (2toσθ,so) of the outer steel tube is in equilibrium with the equivalent radial force (Bσr,c0) of steel tube on concrete in constraint area, that is Fig. 7. Average ratio of axial compressive stress to yield strength of outer steel tube.
⎧ A c1 =
0.6χ0 A 1 − χ0 c
σr , c 0 =
(5)
where σr,c0 is the radial stress of core concrete in constraint area; σθ,so is the transverse stress of outer steel tube. According to the literature [22], the axial compressive stress of constrained core concrete can be given as
χ0 ≤ 0.44
⎨ 2Bb − b2 A χ > 0.44 c 0 ⎩ (1 − χ0 )
2tσθ, so B
(3) 672
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Fig. 8. Stress nephogram of concrete section under different hollow ratio of concrete.
σL, C = fc + Kσr , c
(6)
fc Ac + (1.15 − 0.2χ0 ) fso Aso + fsi Asi χ0 ≤ 0.44 Nu = ⎧ ⎨ fc Ac + (1.2 + 0.15χ0 = 0.3 χ0 ) fso Aso + fsi Asi χ0 > 0.44 ⎩
where k is the coefficient of lateral pressure, k = 3.4 according to Ding et al.[25] On the basis of static equilibrium method, the ultimate bearing capacity Nu of axially-loaded CFDST stub columns can be expressed as
Nu = f0 Ac1 + σl, C Ac 2 + σL, S Aso + fsi Asi
The ultimate bearing capacity formula can also be written as
Nu = fc Ac + Kfso Aso + fsi Asi
(7)
4t° Ac (1 − χ0 ) B
(10)
where K is the confinement coefficient of CFDST (SHS outer and SHS inner) stub columns. According to Eq. (9), the relationship between K and hollow ratio of concrete is shown in Fig. 10. It can be seen that in the interval of the hollow ratio of 0.1–0.44, the difference between the two types of combined action coefficients is not large. To simplify the formula, the confinement coefficient K is uniformly taken as
where Asi is the cross-sectional area of the inner steel tube, Aso is the cross-sectional area of the outer steel tube, Aso≈4Bto. The relationship between the cross-sectional area of the outer steel tube and the core concrete area can be expressed as
Aso =
(9)
K = 1.2 + 0.15χ0 − 0.3 χ0
(8)
0 ≤ χ0 ≤ 0.77
When χ0 = 0, Eq. (11) is simplified to
Substituting Eqs. (1)–(6) and (8) into (7), Nu can be obtained as 673
(11)
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Fig. 9. Stress area division of concrete section of CFDST stub columns.
of Nu, e to Nu, c is 1.031 with the corresponding dispersion coefficient of 0.021 and the average ratio of Nu, FE to Nu, c is 0.962 with the corresponding dispersion coefficient of 0.016. It can be seen from the Fig. 11 that the predicted results agree well with the FE modelling results which is slightly larger than the experimental results, and the error is within 10%, which is generally in good agreement. 4. Further experimental verification Table 1 shows that the the hollow ratio of the research of CFDST stub columns under axial loading was below 0.25 in the existing literatures [16], [17] and [18]. Therefore, the author carried out two test specimens with large-diameter to further verify the rationality of the finite element method and formula calculation results. The concrete was pumped with commercial concrete at the mixing station, and the design strength was C40. The compressive strength fcu of the concrete cube measured by the 150 mm cube test block of natural conservation was 39.8 MPa. The yield strength of the 3 mm thick steel tube was 353 MPa as measured by the tensile test. Table 4 lists the basic parameters and bearing capacity calculation results of the test specimen. The experiment on large-diameter CFDST Stub Columns under axial loading was carried out on the 2000 t triaxial test machine of the National Engineering Laboratory of High-speed Railway Construction Technology of Central South University. The loading control mode: the load of each stage is equivalent to 1/10 ultimate bearing capacity in the elastic stage and the load of each stage is equivalent to 1/20 of the ultimate bearing capacity in the elastoplastic stage. Each level is about 3–5 min.
Fig. 10. Relationship between confinement coefficient of outer steel tube and hollow ratio of concrete.
Nu = fc Ac + 1.2fs As
(12)
Eq. (12) is the formula for calculating the ultimate bearing capacity of squrare CFST stub columns [25]. 3.4. Verification and comparison The FE model results (Nu, FE) and experimental results (Nu, e) for all CFDST stub columns were compared with the predicted results (Nu, c) by Eq. (10), as shown in Fig. 11. The results show that the average ratio
Fig. 11. Comparisons from FE and test results versus Eq. (13). 674
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Table 4 Geometric and material parameters for test specimen. Specimens Label
B0 × Bi × to(ti) × d/mm
L/mm
fcu/MPa
fs/MPa
ρ/%
Bo/to
χ
Nu,e/kN
Nu,FE/kN
Nu,c/kN
Nu,e/Nu,FE
Nu,e/Nu,c
X-0.49 X-0.64
500 × 350 × 3(3) × 0 500 × 400 × 3(3) × 0
1000
39.8
353
8 12
167 167
0.49 0.64
6939 6090
7228.67 6238.86
7159.42 6234.67
0.960 0.976
0.970 0.977
Fig. 12. Experimental instrumentation for all specimens.
Fig. 13. Comparisons from FE and test results versus Eq. (13).
steel tube surface and the strain curve was close to linearity. Elastic-plastic stage: When the test piece enters the elastic–plastic working state, the steel tube began to yield. For the X-0.64 specimen, the restraining effect of the steel tube on the core concrete is weak due to the large hollow ratio, and the upward trend of the load–strain curve is slower than the corresponding X-0.49 specimen.
When the ultimate bearing capacity was approached, the specimens were loaded slowly and continuously until failure. The compressive process of the specimens was divided into three stage until failure including elastic stage, elastic–plastic stage, and plastic stage. Elastic stage: In the early loading period, the test specimen was in stable working condition. There was no obvious deformation at the
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Acknowledgments
Plastic stage: When reaching the ultimate loading, the buckling portion is concentrated at the upper end of the test specimen due to the concrete coarse aggregate sinking at the upper end of the test specimen during the pouring process. The X-0.49 specimen showed slight local bulging at the height of two-thirds. The upper end of the X-0.64 specimen showed obvious local bulging, so that the experimental bearing capacity value is lower than the FE calculation value. Then with the destruction of concrete and steel tube, the strain value becomes larger and grows rapidly, which may contribute to the difference between the modeling and experimental curves. The test loading and the failure mode of the final test piece are shown in Fig. 12. The comparison between the measured curve of the load-axial strain relationship of the axial compression and the finite element calculation curve and the comparison between the measured value of the axial bearing capacity and the calculated value of the finite element and the calculated value of the formula (10) are shown in Fig. 13. It can be seen that the finite element curve agrees well with the experimental curve in the elastic phase and the limit state, and in the failure phase, since the defect of the steel pipe is not considered in the finite element calculation, the failure buckling of the test piece cannot be better simulated. Therefore, the curve after the limit state is deviated from the finite element calculation curve. The mean value of the ratio of the experimental value to the finite element value is 0.953, and the mean value of the ratio of the experimental value to the calculated value of the formula (10) is 0.974. In general, the finite element result and the calculation result of the formula (10) agree well with the experimental results.
This research was financially supported by the National Natural Science Foundation of China (Grant No. 51578548), the National Key Research Program of China (Grant No. 2017YFC0703404), and Science Fund for Distinguished Young Scholars in Hunan Province (Grant No. 2019JJ20029). References [1] Zhi-wu Yu, Fa-xing Ding, et al. Experimental behavior of circular concrete-filled steel tube stub columns. J Constr Steel Res 2007;63(2):165–74. [2] Chen J, Ni Y-Y, Jin W-L. Column tests of dodecagonal section double skin concretefilled steel tubes. Thin-Walled Struct 2015;88:28–40. [3] Yuan W-B, Yang J-J. Experimental and numerical studies of short concrete-filled double skin composite tube columns under axially compressive loads. J Constr Steel Res 2013;80:23–31. [4] Li W, Han L-H, Ren Q-X, et al. Behavior and calculation of tapered CFDST columns under eccentric compression. J Constr Steel Res 2013;83:127–36. [5] Han L-H, Huang H, Zhao X-L. Analytical behavior of concrete-filled double skin steel tubular (CFDST) beam-columns under cyclic loading. Thin-Walled Struct 2009;47(6–7):668–80. [6] Zhou F, Xu W. Cyclic loading tests on concrete-filled double-skin (SHS outer and CHS inner) stainless steel tubular beam-columns. Eng Struct 2016;127:304–18. [7] Pagoulatou M, Sheehan T, Dai XH, et al. Finite element analysis on the capacity of circular concrete-filled double-skin steel tubular (CFDST) stub columns. Eng Struct 2014;72(102):112. [8] Uenaka K, Kitoh H, Sonoda K. Concrete filled double skin circular stub columns under compression. Steel Const 2010;48(1):19–24. [9] Zhong Tao, Lin-hai Han, Xiao-ling Zhao. 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. [10] Zhong Tao, Lin-hai Han. Behaviour of concrete-filled double skin rectangular steel tubular beam–columns. J Constr Steel Res 2006;62(7):631–46. [11] Elchalakani M, Xiao-ling Zhao, Grzebieta R. Tests on concrete filled double-skin (CHS outer and SHS inner) composite short columns under axial compression. ThinWalled Struct 2002;40(5):415–41. [12] Lin-Hai Han, Zhong Tao, Hong Huang, et al. Concrete-filled double skin (SHS outer and CHS inner) steel tubular beam-columns. Thin-Walled Struct 2004;42(9):1329–55. [13] Xiao-Ling Zhao, Grzebieta RH, Ukur A, et al. Tests of concrete-filled double skin (SHS outer and CHS inner) composite stub columns. Adv Steel Struct 2002;2(2):567–74. [14] Li Xie, Boyang Lin, Fang Yuan, et al. Experimental study on mechanical performance of square concrete filled double-skin steel tubular columns under compression-bending-shear loading conditions. J Build Struct 2015;36(suppl. 1):230–4. (in Chinese). [15] Hong Huang, Lin-hai Han, Zhong Tao, et al. Analytical behaviour of concrete-filled double skin steel tubular (CFDST) stub columns. J Constr Steel Res 2012;57(4):37–48. [16] Hong Huang, Baojun Cha, Mengcheng Chen, et al. Comparative test study on mechanical behavior of concrete-filled double-skin steel tubular with hollow-centered square section short columns under axial compression. Railway Eng 2015;10:85–9. (in Chinese). [17] Grzebieta R. Strength and Ductility of Concrete-Filled Double Skin (SHA inner and SHA outer) Tubes. Thin-Walled Struct 2002;40:199. [18] Liang W, Dong J, Wang Q. Mechanical behaviour of concrete-filled double-skin steel tube (CFDST) with stiffeners under axial and eccentric loading. Thin-Walled Struct 2019;138:215–30. [19] Fa-xing Ding, Zhe Li, et al. Composite action of hexagonal concrete-filled steel tubular stub columns under axial loading. Thin-Walled Struct 2016;107(11):453–61. [20] Fa-xing Ding, Zhe Li, et al. Composite action of octagonal concrete-filled steel tubular stub columns under axial loading. Thin-Walled Struct 2016;107:453–61. [21] Fa-xing Ding, Jiang Zhu, et al. Comparative study of stirrup-confined circular concrete-filled steel tubular stub columns under axial loading. Thin-Walled Struct 2018;123:294–304. [22] Gong Yong-zhi Fu, Lei Ding Fa-xing, et al. Bearing capacity of axially loaded stirrup confined concrete-filled square steel tubular stub columns. J Build Struct 2016. [23] Ding Fa-xing Lu, De-ren Bai Yu, et al. Comparative study of square stirrup-confined concrete-filled steel tubular stub columns under axial loading. Thin-Walled Struct 2018;98:443–53. [24] Fa-xing Ding, Xiao-yong Ying, Lin-chao Zhou, et al. Unified calculation method and its application in determining the uniaxial mechanical properties of concrete. Front Arch Civil Eng China 2011;5(3):381–93. [25] Fa-xing Ding, Chang-jing Fang, Bai Yu, et al. Mechanical performance of stirrupconfined concrete-filled steel tubular stub columns under axial loading. J Constr Steel Res 2014;98(98):146–57. [26] Zhao XL, Han B, Grzebieta RH. Plastic mechanism analysis of concrete-filled double-skin (SHS inner and SHS outer) stub columns. Thin-Walled Struct 2002;40(10):815–33.
5. Conclusions This paper presents a combined numerical, experimental, and theoretical study on the behavior of the CFDST (SHS outer and SHS inner) stub columns under axial compressive loading. FE models are also developed for the CFDST (SHS outer and SHS inner) columns and validated through experimental results. Comprehensive parametric studies were also conducted using the validated FE models. A design formula for predicting the load bearing capacity of CFDST (SHS outer and SHS inner) columns is proposed based on the above results and further confirmed by the experimental results from two additional specimens. The FE models were also further confirmed the results. Based on the studies, the following conclusions could be drawn: (1) The FE results are in good agreement with experimental results by other scholars. (2) The results of finite element parameter analysis show that the constraint of the outer steel tube on the core concrete is mainly concentrated in the corner area, while the inner steel tube has no obvious constraint on the core concrete. As the hollow ratio increases, the constraint effect of the outer steel tube on the concrete is weakened. (3) Based on the ultimate equilibrium principle, a practical formula for the ultimate bearing capacity of CFDST columns under axial loading is proposed. According to the range of parameter analysis, the formula is applicable to the calculation of bearing capacity of square CFDST columns with hollow ratio ranging from 0 to 0.7, concrete strength ranging from 40 MPa to 100 MPa and steel yield strength ranging from 235 MPa to 420 MPa. The predicted results show very good agreement with the experimental and numerical results. (4) Through further supplementary experiment, the results show that the finite element model and calculation formula are still applicable to the CFDST stub column with large hollow ratio under axial compression. Declaration of Competing Interest 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. 676
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Study on the behavior of concrete-filled square double-skin steel tubular stub columns under axial loading
T
⁎
Fa-xing Dinga,b, Wen-jun Wanga, De-ren Lua, , Xue-mei Liuc a
School of Civil Engineering, Central South University, Changsha, Hunan Province, 410075, PR China Engineering Technology Research Center for Prefabricated Construction Industrialization of Hunan Province, 410075, PR China c Department of Infrastructure Engineering, The University of Melbourne, Parkville, VIC 3010 Australia b
A R T I C LE I N FO
A B S T R A C T
Keywords: Concrete-filled square double-skin steel tubular (CFDST) stub columns Confinement coefficient Finite element analyses Large hollow ratio Practical calculation formula
This paper presents a numerical, experimental, and theoretical study on the behavior of concrete-filled square double-skin steel tubular (CFDST) stub columns under axial compressive loading. Firstly, three-dimensional solid model of CFDST stub columns was established by ABAQUS finite element software and verified through the existing experimental results. Then a full-scale model was established to investigate the influence of various parameters on ultimate bearing capacity and internal and external compressive stress of concrete. By considering the confinement coefficient, the practical calculation formula for the bearing capacity of CFDST stub columns was proposed. Finally, the experimental research on the mechanical properties of two large hollow ratio CFDST stub columns under axial compression was carried out. And the experimental research further verified the applicability of the FE model and calculation formula of the CFDST stub column with large hollow ratio under axial compression.
1. Introduction Compared with ordinary concrete filled steel tubular (CFST) [1], concrete filled double-skin steel tubular (CFDST) stub columns have not only the characteristics of high bearing capacity, good seismic performance and convenient construction, but also the advantages of light weight, high bending rigidity and good fire resistance and so on [2,3]. Therefore, CFDST columns have good mechanical properties and wide applicability, especially when subjected to an eccentric compressive load [4] or cyclic loading [5,6]. At present, the research on CFDST columns mainly focuses on their static performance. The researched cross-section forms mainly include CHS (circular hollow section) outer and CHS inner, CHS outer and SHS (square hollow section) inner, SHS outer and SHS inner, SHS outer and CHS inner. The existing research results show that the CFDSTs with CHS outer are suitable for the high bridge pier across the deep valley and the offshore platform structure to reduce the water flow or the wind load. The CFDSTs with SHS outer are suitable for the frame giant column or shear wall of the high-rise building. In terms of bearing capacity, the SHS is slightly inferior to the CHS, but it is more beneficial to utilize the internal space. Therefore, the SHS is more valuable and economic in the field of building structure. In recent years, four main types of CFDST have been developed
⁎
using a combination of circular hollow section (CHS) and square hollow section (SHS): Pagoulatou et al.[7], Uenaka et al. [8], Tao et al. [9,10], Elchalakani et al. [11], Han et al. [12], Zhao et al. [13] studied the mechanical behavior of CFDST stub columns with SHS and CHS as outer or inner tubes under axial compression, respectively. These studies focused on the effects of the composite section types, the depth-tothickness ratios of the steel tubes, and the hollow ratio and slenderness ratio on the mechanical properties of CFDST under axial compression. Xie et al. [14] carried out experimental study on the compressionbending-shear-torsion performance of the CFDST (SHS outer and CHS inner) stub columns and the result show that the shear resistance of CFDST (SHS outer and CHS inner) stub columns were higher than that of square CFST column while the ductility of CFDST (SHS outer and CHS inner) stub columns were lower at ultimate stage. Huang et al. [15,16] conducted a preliminary study on the working mechanism of the CFDST stub columns under axial compression, and compared the advantages and disadvantages of different cross-section forms. It was found that the CFDST (SHS outer and CHS inner) stub columns had higher bearing capacity and ductility, and the calculation formula for the ultimate bearing capacity of the CFDST (SHS outer and CHS inner) stub columns was proposed. Zhao et al. [17] conducted an experimental study on the axial compression and bending resistance of the CFDST (SHS outer and SHS inner) stub columns and increased ductility and
Corresponding author. E-mail address: [email protected] (D.-r. Lu).
https://doi.org/10.1016/j.istruc.2019.12.008 Received 5 July 2019; Received in revised form 2 December 2019; Accepted 7 December 2019 2352-0124/ © 2019 Institution of Structural Engineers. Published by Elsevier Ltd. All rights reserved.
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Nomenclature
Nso Nsi Nc Nu Nu,c εL σL,s σθ,s σr,c Asc Ac Ac1 Ac2 Asi Aso σr,c0σθ,so
Symbols Bo Bi b L to ti fso fsi fcfcu Nu,FE Nu,e χ χ0 ρ Nsc
Outer diameter of the outer steel tube Inner diameter of the inner steel tube Outer side length of the core concrete Inner side length of the core concrete Length of the test piece Wall thickness of the outer steel tube Wall thickness of the inner steel tube Yield strength of the outer steel tube Yield strength of the inner steel tubethe compressive cubic strength of concrete Cubic compressive strength of concrete Ultimate bearing capacity of FE results Ultimate bearing capacity of experimental results Hollow ratio of the section Hollow ratio of concrete Steel ratio of the section
k K
Total ultimate capacity Ultimate capacity of the outer tube Ultimate capacity of the inner tube Ultimate capacity of the concrete Ultimate bearing capacity Ultimate bearing capacity calculated by Eq. (10) Axial strain Longitudinal stress Transverse stress Radial stress Total area of cross section Sectional area of the whole core concrete Unconstrained concrete area Constrained concrete area Cross-sectional area of the inner steel tube Cross-sectional area of the outer steel tubeRadial stress of core concrete in constraint area Transverse stress of outer steel tube Coefficient of lateral pressureConfinement coefficient
are established and the parametric analysis are carried out to investigate the confinement effect of inner and outer steel tubes and core concrete under axial compression. (3) Based on the balance of the limit state force and the simplification of the stress cloud diagram, a practical design formula for the ultimate bearing capacity of the CFDST (SHS outer and SHS inner) stub columns considering the influence of the hollow ratio on the confinement coefficient is proposed. (4) A series of compression tests were carried out on two CFDST (SHS outer and SHS inner) stub columns which hollow ratio is large. This experiment makes up for the insufficiency of the existing research and further verifies the rationality of the FE model and bearing capacity calculation formula for large-size stub columns with large hollow ratio under axial compression.
energy absorption had been observed of CFDST subjected to compression. Liang et al. [18] carried out an experimental investigation of the mechanical behavior and working mechanism of the CFDST (SHS outer and SHS inner) with stiffeners. The above research status indicates that the axial compression performance of the CFDST (SHS outer and SHS inner) stub columns still lacks in-depth studies. The constraint effect between the steel tubes and the laminated concrete under axial load is yet to be revealed, and the confinement coefficient of the CFDST (SHS outer and SHS inner) stub columns under axial compression is not clear. In the previous research, the research group proposed a concrete triaxial plastic-damage constitutive model which is suitable for CFST columns with different cross-sections [19–23]. The model was used in the FE analysis of the CFST stub columns in the form of circular, round, octagonal, hexagonal and rectangular sections. Practical design formulas for bearing capacity considering the influence of section shape on the confinement coefficient were proposed. The model and method can be further applied to the three-dimensional solid FE analysis of CFDST (SHS outer and SHS inner) stub columns. Therefore, the main contents of this paper include: (1) finite 3D solid element models of CFDST (SHS outer and SHS inner) stub columns are established by adopting a triaxial plastic-damage constitutive model of concrete under axial compression, and a set of test results reported by different researches are used to verify the FE models. (2) A large number of full-scale models
2. Finite element model and verification 2.1. Finite element modeling and parameter selection Non-linear FE models for CFDST stub columns under axial compression were established using ABAQUS version 6.14 (2014). In the numerical models, the 8-node reduced integral format 3D solid element (C3D8R) is applied to model the inner and outer steel tube, core concrete and loading plates for all specimens. The structured meshing
Fig. 1. Mesh generation of FE models. 666
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Coulomb friction coefficient of 0.5 in the tangential direction is used to simulate the interfacial behavior between the steel tube and the core concrete. The “tie” option is adopted for the constraint between the steel tube and the cover plate so that no relative motion occurs between them. Other parameters setting and stress–strain relationship of concrete tri-axial compression and elasto-plastic hardening stress–strain relationship of steel tube are detailed explained in Ref. [24].
technique is adopted as shown in Fig. 1. The surface-to-surface contact is adopted for the interaction between steel tube and core concrete, in which the surface of steel tube is the master surface meanwhile the corresponding surface of core concrete is slave surface. Limited glide is employed in the sliding formulation as well as the discretization method is surface-to-surface. The tangential behavior and normal behavior are defined in the contact characteristics, and the interface bond-slip relationship between the steel tube and the core concrete is simulated. The normal behavior is set to “hard” contact allowing separation after contact. The tangential friction equation is established by using the penalty function. The
2.2. Comparative analysis of calculation results In this paper, the FE models of the CFDST stub columns under axial
Fig. 2. Comparison of FE and experimental load–strain curves. 667
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Table 1 Comparison of test results in references and FE results. Specimens Label
Bo/mm
Bi/mm
to(ti)/mm
χ
fso(fsi)/MPa
fcu/MPa
Nu,e/kN
Nu,FE/kN
Nu,c/kN
Nu,FE /Nu,e
Nu,c/Nu,e
references
D-SS-a CS1S5A CS1S5B CS2S5A CS2S5B CS3S5A CS3S5B CS4S5A CS4S5B
160 99.74 99.74 100.49 100.49 100.18 100.18 100.46 100.46
53 50 50 50 50 50 50 50 50
3.62(2.71) 5.97(2.44) 5.97(2.44) 4.01(2.44) 4.01(2.44) 2.94(2.44) 2.94(2.44) 2.06(2.44) 2.06(2.44)
0.11 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25
374(3 0 4) 485(4 7 7) 485(4 7 7) 445(4 7 7) 445(4 7 7) 464(4 7 7) 464(4 7 7) 453(4 7 7) 453(4 7 7)
50.5 57.8 57.8 57.8 57.8 57.8 57.8 57.8 57.8
1819 1545 1614 1194 1210 1027 1060 820 839
1820 1689 1689 1253 1253 1088.4 1088.4 862.9 862.9
1908 1566 1566 1253 1253 1066 1066 852 852
1.000 1.093 1.046 1.059 1.036 1.060 1.027 1.052 1.028
1.049 1.013 0.970 1.050 1.036 1.038 1.005 1.039 1.015
[11] [12]
*Note: Nu,
c
is the bearing capacity calculated by Eq. (10).
Table 2 Details of the specimen parameters and analysis results in the parametric study. Specimens Label
Bo × Bi × L/mm
to(ti) /mm
Bo/to
χ
ρ
fcu/MPa
fc/ MPa
fso/MPa
fsi/MPa
Nu,FE/MN
Nu,c/MN
Nu,c/ Nu,FE
SdsA-1 SdsA-2 SdsA-3 SdsA-4 SdsA-5 SdsA-6 SdsA-7 SdsA-8 SdsA-9 SdsA-10 SdsA-11 SdsA-12 SdsA-13
5000 × 0 × 3000 5000 × 2500 × 3000 5000 × 3540 × 3000 5000 × 4330 × 3000 5000 × 3540 × 3000 5000 × 3540 × 3000 5000 × 3540 × 3000 5000 × 3540 × 3000 5000 × 3540 × 3000 5000 × 3540 × 3000 5000 × 3540 × 3000 5000 × 3540 × 3000 5000 × 3540 × 3000
50(50) 50(50) 50(50) 50(50) 40(40) 60(60) 50(50) 50(50) 50(50) 50(50) 50(50) 50(50) 50(50)
100 100 100 100 125 83 100 100 100 100 100 100 100
0 0.25 0.5 0.75 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
0.04 0.08 0.137 0.299 0.11 0.164 0.137 0.137 0.137 0.137 0.137 0.137 0.137
60
47.5
345
345
60
47.5
345
345
40 80 100 60
29.5 66.4 86.1 47.5
345
345
235 420 345
345
1681.8 1450.3 1168.9 874.4 1069.3 1268.7 971.13 1372.8 1579.82 1059.4 1244.6 1083.3 1224.9
1553 1366.5 1121.7 870 1015.8 1227.6 929.1 1325.5 1538.1 1006.0 1200.6 1042.7 1175.6
0.923 0.942 0.960 0.995 0.950 0.968 0.957 0.966 0.974 0.950 0.966 0.963 0.960
235 420
*Note: fc is the compressive cubic strength of concrete, according to reference [23], fc = 0.4fcu7/6.
Fig. 3. Load and stress-axial strain curves of CFDST stub columns under axially loading. 668
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Fig. 4. Stress nephogram of concrete section at each stage.
have a small confinement force on the concrete. Since the Poisson's ratio of the steel tube is larger than that of the concrete, the radial stress of the outer steel tube is negative. It can be seen from the stress nephogram of Fig. 4(a) that the longitudinal stress of the concrete in the middle section is substantially evenly distributed; Elastoplastic stage (AB): The longitudinal stress of concrete increases rapidly at this stage. At point B, the inner and outer steel tubes reach the yield strength, and the longitudinal stress of the concrete approaches the uniaxial compressive strength of concrete. It can be seen from Fig. 3(b) that the rate of decrease of the longitudinal stress at the corner of the outer steel tube and the rate of increase of the transverse stress are greater than the stress of the corresponding middle portion, and the inner steel tube is substantially in an axially compressed state without being bent and unstable. As shown in the stress nephogram of Fig. 4(b), the longitudinal stress value of the corner of the concrete is larger than that of the central part. In summary, the confinement effect of the outer steel tube on the corner concrete is greater than the middle portion. Plastic stage (BC): At this stage, the longitudinal stress of the outer steel tube decreases and the transverse stress increases, while the radial stress of the outer steel tube to the concrete increases gradually. As seen from the stress nephogram of Fig. 4(c), the confinement effect of the outer steel tube on the concrete makes the longitudinal stress of concrete exceeds the uniaxial compressive strength of concrete which value is 47.5 MPa when the compressive cubic strength of concrete is 60 MPa. At the same time, with the increase of the confinement effect of the outer steel tube on the concrete, the longitudinal stress distribution of the cross section of the concrete tends to be uneven due to the greater confinement effect of the outer steel tube on the concrete corner. The inner steel tube always has little confinement effect on the concrete. The details of the comparation about the typical N-εL curves and σr, c-εL curves for the paramedic study are presented in Fig. 5. From the parametric study results, the research findings are summarized below. (1) Fig. 5(a) and (b) compare the effect of different yield strength of outer steel tube on bearing capacity and radial stress. It can be seen that for every 50% increase in the yield strength of the outer steel tube, the bearing capacity is increased by 10%, and the radial stress of the outer steel tube is increased by 20%. The greater yield strength of the outer steel tube, the more confinement effect on the concrete, while the inner steel tube has no obvious confinement on the core concrete. (2) Fig. 5(c) and (d) compare the N-εL curves and the σr,c-εL curves of outer and inner steel tubes under different yield strength of inner steel tube. The results show that the change of the yield strength of the inner steel tube does not cause the change of the radial stress of the outer steel tube to the concrete, nor does it change its own confinement effect on the core concrete. (3) Fig. 5(e) and (f) show the comparison of the N-εL curves and the σr, c-εL curves under different concrete strength. It can be obtained that the radial stress of outer steel tube on concrete is increased by 50% with the increase of concrete strength by 20 MPa. So with the increase of
compression are verified against the experimental results reported by Liang (2019), Huang (2015) and Zhao (2002) [26]. The typical load–strain curves of FE results and experimental results are compared as shown in Fig. 2. Bo is the outer diameter of the outer steel tube, Bi is the inner diameter of the inner steel tube, L is the length of the test piece, fso is the yield strength of the outer steel tube, and fsi is the yield strength of the inner steel tube. fcu is the compressive cubic strength of concrete. The ultimate bearing capacity of FE results (Nu, FE) are compared with the experimental results (Nu, e) in Table 1. to and ti are the wall thickness of the outer and inner steel tube, respectively. χ is the hollow ratio of the section, defined as the ratio of the area of the hollow part to the area enclosed by the outer steel tube, ie χ = Bi2/Bo2. ρ is the steel ratio of the section, defined as the ratio of the sum of the cross-section of inner and outer steel tubes to the cross-sectional area, ie ρ= (4Biti + 4Boto)/(Bo2-Bi2). It is shown that the average value of the ratios (Nu, e/Nu, FE) is 0.959 with the corresponding dispersion coefficient of 0.020. From the above comparisons, it can be found that generally good agreement is achieved between the FE and test results. Therefore, the FE models can be used to carry out further parametric study of the CFDST stub columns beyond the range of test specimens. 2.3. Analysis of influencing factors of full scale examples FE models are established to investigate the mechanical behavior of CFDST stub columns under axial compression. The main parameters affecting the axial bearing capacity of the CFDST stub columns are as follow: the yield strength of outer and inner steel tube fso = fsi = 235 MPa, 345 MPa, and 420 MPa, the compressive cubic strength of concrete fcu = 40 MPa, 60 MPa, 80 MPa and 100 MPa, the steel ratio ρ = 0.04, 0.08, 0.11, 0.137, 0.164 and 0.299. The details of the parameters and results for the parametric study were presented in Table 2. SdsA-3 (Bo = 5000 mm, Bi = 3540 mm, to = ti = 50 mm, fso = fsi = 345 MPa, fcu = 60 MPa, ρ = 0.137, χ = 0.5) was analyzed as a typical specimen. Fig. 3(a) shows the variation of the total axial force (Nsc), the axial force of the inner tube (Nsi), the axial force of the outer tube (Nso), and the axial force of the concrete (Nc) with the longitudinal strain of the specimen. Fig. 3(b) presents the typical longitudinal stress (σL, s)-axial strain (εL) curves and transverse stress (σθ, s)-axial strain (εL) curves of outer and inner steel tube. Fig. 3(c) gives the radial stress (σr, c)-strain curves of outer and inner steel tube. σr, c is the average value of the radial stress of each element in the middle section of the steel tube obtained by finite element extraction. Defining the radial stress from the direction of the steel tube to the concrete is negative. The stress nephogram at midsection of the core concrete at different loading stages was extracted from the FE models as shown in Fig. 4. It can be seen from Figs. 3 and 4 that the loading process can be divided into the following three stages: Elasticity stage (OA): At this stage, the inner and outer steel tubes 669
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Fig. 5. Influence of various parameters on the load bearing capacity and radial stress of steel tube.
ultimate load capacity is reached. It can be seen that for every 0.25 increase of the hollow ratio, the radial stress of the outer steel tube is reduced by 20%, and the increase of the hollow ratio also leads to the reduction of the longitudinal stress of the corner concrete and the confinement effect of the outer steel tube on the core concrete. The change of the hollow ratio has little effect on the radial stress of the inner steel tube.
concrete strength, the proportion of load carried by concrete increases, the transverse deformation coefficient of outer steel tube increases, and the radial stress of outer steel tube to concrete increases, while the value of radial stress of inner steel tube to concrete is always small. (4) Fig. 5(g) and (h) compare the effect of different steel ratio on bearing capacity and radial stress. It can be seen that the larger the steel ratio, the radial stress of the outer steel tube slightly increases, while it has little effect on the radial stress of the inner steel tube. (5) Fig. 5(i) and (j) show the comparison of the N-εL curves and the σr, c-εL curves under different hollow ratio and Fig. 6 presents that the stress nephogram of concrete under different hollow ratios when the 670
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Fig. 5. (continued)
3. Practical calculation formula for bearing capacity
σL, s = 0.97fs
3.1. Stress analysis
According to the Von-Mises yield condition for steel material, the transverse stress of the outer steel tube can be expressed as
To derive the calculation formula of bearing capacity, a range of parameters such as concrete strength, yield strength of steel, steel ratio, and hollow ratio are further investigated by FE analysis. The values of these parameters are chosen based on the engineering practice. A total of 72 groups of optimized column specimens are included in the numerical study, in which Q235 steel matches C40 and C60 concrete, Q345 steel matches C60 and C80 concrete, while Q420 steel matches C80 and C100 concrete. Specific parameters and matching principles are shown in Table 3. The longitudinal stress of the steel tube at three locations (endpoint, 1/4 point and midpoint of the middle section of the steel tube) is extracted from FE calculation results when the specimen reaches the ultimate bearing capacity. The relationship between the ratio of longitudinal stress and yield strength of steel tube with ultimate strength (fsc = Nu/Asc,Asc = Ac + As, Asc is the total area of cross section) is shown in Fig. 7. According to the analysis of static performance of the CFDST stub columns under axial compression, it is considered that the restraining effect between the outer steel tube and the core concrete is the same as that of the ordinary CFST stub columns, and the inner steel tube does not have the restraining effect on the core concrete. Therefore, only the force of the outer steel tube is considered in the analysis. It can be seen from Fig. 7 that when the specimens reach the ultimate strength, the average value of the ratio of the longitudinal stress (pressure) and the yield strength of the outer steel tube can be expressed as
σθ, s = 0.09fs
(1)
(2)
3.2. Simplification of section force The results of FE analysis show that the core concrete of the CFDST specimens with different hollow ratio has different constraint area. According to the stress nephogram of core concrete under ultimate bearing capacity in Fig. 8, the stress distribution of CFDST stub columns can be simplified to Fig. 9 for calculation. It is assumed that the core concrete in the unconstrained area is not bound by the outer steel tube, and the core concrete in the constraint area is uniformly bound by the outer steel tube. The dimensions of the core concrete are defined as follows: B is the outer side length of the core concrete (B = Bo-2to), b is the inner side length of the core concrete (b = Bi + 2to), χ0 is the hollow ratio of concrete, χ0 = [Bo2 (Bi + 2to)2]/[Bi2(Bo-2to)2]χ = b2/ B2, it can be seen that: When χ0 ≤ 0.44 , which is equivalent to χ0 ≤ 0.44 , the unconstrained area is assumed to be the circumscribed circle of the inner steel tube. When χ0 > 0.44 , which is equivalent to χ0 > 0.44 , the constraint of the outer steel tube on the core concrete is more pronounced at the corner, and the constraint area is the square area of the corner. Therefore, according to the different hollow ratio of concrete, the relationship between the area of the unconstrained area and the area of the core concrete can be defined as 671
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Fig. 6. Stress nephogram of concrete section under different hollow ratios. Table 3 Details of parameters of the specimen used to derive calculation formula. Bo × Bi/mm
to(ti)/mm
χ
ρ
Q235
5000 × 2240 5000 × 2740 5000 × 3160 5000 × 3540 5000 × 3870 5000 × 4180
30–50
0.2 0.3 0.4 0.5 0.6 0.7
0.072–0.243
C40
Q345 C60
C60
Q420 C80
C80
C100
where Ac1 is the unconstrained concrete area; Ac is the sectional area of the whole core concrete, Ac = B2-b2=(1-χ0)B2. The relationship between the area of the constraint area and the area of the core concrete can be expressed as 1 − 1.6χ
Ac2 =
0 Ac χ0 ≤ 0.44 ⎧ ⎪ 1 − χ0 2) ( B b − ⎨A = A χ0 > 0.44 ⎪ c2 (1 − χ0 ) B 2 c ⎩
(4)
where Ac2 is the constrainted concrete area, Ac1 + Ac2 = Ac. 3.3. Formula establishment According to the limit equilibrium theory, the transverse force (2toσθ,so) of the outer steel tube is in equilibrium with the equivalent radial force (Bσr,c0) of steel tube on concrete in constraint area, that is Fig. 7. Average ratio of axial compressive stress to yield strength of outer steel tube.
⎧ A c1 =
0.6χ0 A 1 − χ0 c
σr , c 0 =
(5)
where σr,c0 is the radial stress of core concrete in constraint area; σθ,so is the transverse stress of outer steel tube. According to the literature [22], the axial compressive stress of constrained core concrete can be given as
χ0 ≤ 0.44
⎨ 2Bb − b2 A χ > 0.44 c 0 ⎩ (1 − χ0 )
2tσθ, so B
(3) 672
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Fig. 8. Stress nephogram of concrete section under different hollow ratio of concrete.
σL, C = fc + Kσr , c
(6)
fc Ac + (1.15 − 0.2χ0 ) fso Aso + fsi Asi χ0 ≤ 0.44 Nu = ⎧ ⎨ fc Ac + (1.2 + 0.15χ0 = 0.3 χ0 ) fso Aso + fsi Asi χ0 > 0.44 ⎩
where k is the coefficient of lateral pressure, k = 3.4 according to Ding et al.[25] On the basis of static equilibrium method, the ultimate bearing capacity Nu of axially-loaded CFDST stub columns can be expressed as
Nu = f0 Ac1 + σl, C Ac 2 + σL, S Aso + fsi Asi
The ultimate bearing capacity formula can also be written as
Nu = fc Ac + Kfso Aso + fsi Asi
(7)
4t° Ac (1 − χ0 ) B
(10)
where K is the confinement coefficient of CFDST (SHS outer and SHS inner) stub columns. According to Eq. (9), the relationship between K and hollow ratio of concrete is shown in Fig. 10. It can be seen that in the interval of the hollow ratio of 0.1–0.44, the difference between the two types of combined action coefficients is not large. To simplify the formula, the confinement coefficient K is uniformly taken as
where Asi is the cross-sectional area of the inner steel tube, Aso is the cross-sectional area of the outer steel tube, Aso≈4Bto. The relationship between the cross-sectional area of the outer steel tube and the core concrete area can be expressed as
Aso =
(9)
K = 1.2 + 0.15χ0 − 0.3 χ0
(8)
0 ≤ χ0 ≤ 0.77
When χ0 = 0, Eq. (11) is simplified to
Substituting Eqs. (1)–(6) and (8) into (7), Nu can be obtained as 673
(11)
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Fig. 9. Stress area division of concrete section of CFDST stub columns.
of Nu, e to Nu, c is 1.031 with the corresponding dispersion coefficient of 0.021 and the average ratio of Nu, FE to Nu, c is 0.962 with the corresponding dispersion coefficient of 0.016. It can be seen from the Fig. 11 that the predicted results agree well with the FE modelling results which is slightly larger than the experimental results, and the error is within 10%, which is generally in good agreement. 4. Further experimental verification Table 1 shows that the the hollow ratio of the research of CFDST stub columns under axial loading was below 0.25 in the existing literatures [16], [17] and [18]. Therefore, the author carried out two test specimens with large-diameter to further verify the rationality of the finite element method and formula calculation results. The concrete was pumped with commercial concrete at the mixing station, and the design strength was C40. The compressive strength fcu of the concrete cube measured by the 150 mm cube test block of natural conservation was 39.8 MPa. The yield strength of the 3 mm thick steel tube was 353 MPa as measured by the tensile test. Table 4 lists the basic parameters and bearing capacity calculation results of the test specimen. The experiment on large-diameter CFDST Stub Columns under axial loading was carried out on the 2000 t triaxial test machine of the National Engineering Laboratory of High-speed Railway Construction Technology of Central South University. The loading control mode: the load of each stage is equivalent to 1/10 ultimate bearing capacity in the elastic stage and the load of each stage is equivalent to 1/20 of the ultimate bearing capacity in the elastoplastic stage. Each level is about 3–5 min.
Fig. 10. Relationship between confinement coefficient of outer steel tube and hollow ratio of concrete.
Nu = fc Ac + 1.2fs As
(12)
Eq. (12) is the formula for calculating the ultimate bearing capacity of squrare CFST stub columns [25]. 3.4. Verification and comparison The FE model results (Nu, FE) and experimental results (Nu, e) for all CFDST stub columns were compared with the predicted results (Nu, c) by Eq. (10), as shown in Fig. 11. The results show that the average ratio
Fig. 11. Comparisons from FE and test results versus Eq. (13). 674
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Table 4 Geometric and material parameters for test specimen. Specimens Label
B0 × Bi × to(ti) × d/mm
L/mm
fcu/MPa
fs/MPa
ρ/%
Bo/to
χ
Nu,e/kN
Nu,FE/kN
Nu,c/kN
Nu,e/Nu,FE
Nu,e/Nu,c
X-0.49 X-0.64
500 × 350 × 3(3) × 0 500 × 400 × 3(3) × 0
1000
39.8
353
8 12
167 167
0.49 0.64
6939 6090
7228.67 6238.86
7159.42 6234.67
0.960 0.976
0.970 0.977
Fig. 12. Experimental instrumentation for all specimens.
Fig. 13. Comparisons from FE and test results versus Eq. (13).
steel tube surface and the strain curve was close to linearity. Elastic-plastic stage: When the test piece enters the elastic–plastic working state, the steel tube began to yield. For the X-0.64 specimen, the restraining effect of the steel tube on the core concrete is weak due to the large hollow ratio, and the upward trend of the load–strain curve is slower than the corresponding X-0.49 specimen.
When the ultimate bearing capacity was approached, the specimens were loaded slowly and continuously until failure. The compressive process of the specimens was divided into three stage until failure including elastic stage, elastic–plastic stage, and plastic stage. Elastic stage: In the early loading period, the test specimen was in stable working condition. There was no obvious deformation at the
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Acknowledgments
Plastic stage: When reaching the ultimate loading, the buckling portion is concentrated at the upper end of the test specimen due to the concrete coarse aggregate sinking at the upper end of the test specimen during the pouring process. The X-0.49 specimen showed slight local bulging at the height of two-thirds. The upper end of the X-0.64 specimen showed obvious local bulging, so that the experimental bearing capacity value is lower than the FE calculation value. Then with the destruction of concrete and steel tube, the strain value becomes larger and grows rapidly, which may contribute to the difference between the modeling and experimental curves. The test loading and the failure mode of the final test piece are shown in Fig. 12. The comparison between the measured curve of the load-axial strain relationship of the axial compression and the finite element calculation curve and the comparison between the measured value of the axial bearing capacity and the calculated value of the finite element and the calculated value of the formula (10) are shown in Fig. 13. It can be seen that the finite element curve agrees well with the experimental curve in the elastic phase and the limit state, and in the failure phase, since the defect of the steel pipe is not considered in the finite element calculation, the failure buckling of the test piece cannot be better simulated. Therefore, the curve after the limit state is deviated from the finite element calculation curve. The mean value of the ratio of the experimental value to the finite element value is 0.953, and the mean value of the ratio of the experimental value to the calculated value of the formula (10) is 0.974. In general, the finite element result and the calculation result of the formula (10) agree well with the experimental results.
This research was financially supported by the National Natural Science Foundation of China (Grant No. 51578548), the National Key Research Program of China (Grant No. 2017YFC0703404), and Science Fund for Distinguished Young Scholars in Hunan Province (Grant No. 2019JJ20029). References [1] Zhi-wu Yu, Fa-xing Ding, et al. Experimental behavior of circular concrete-filled steel tube stub columns. J Constr Steel Res 2007;63(2):165–74. [2] Chen J, Ni Y-Y, Jin W-L. Column tests of dodecagonal section double skin concretefilled steel tubes. Thin-Walled Struct 2015;88:28–40. [3] Yuan W-B, Yang J-J. Experimental and numerical studies of short concrete-filled double skin composite tube columns under axially compressive loads. J Constr Steel Res 2013;80:23–31. [4] Li W, Han L-H, Ren Q-X, et al. Behavior and calculation of tapered CFDST columns under eccentric compression. J Constr Steel Res 2013;83:127–36. [5] Han L-H, Huang H, Zhao X-L. Analytical behavior of concrete-filled double skin steel tubular (CFDST) beam-columns under cyclic loading. Thin-Walled Struct 2009;47(6–7):668–80. [6] Zhou F, Xu W. Cyclic loading tests on concrete-filled double-skin (SHS outer and CHS inner) stainless steel tubular beam-columns. Eng Struct 2016;127:304–18. [7] Pagoulatou M, Sheehan T, Dai XH, et al. Finite element analysis on the capacity of circular concrete-filled double-skin steel tubular (CFDST) stub columns. Eng Struct 2014;72(102):112. [8] Uenaka K, Kitoh H, Sonoda K. Concrete filled double skin circular stub columns under compression. Steel Const 2010;48(1):19–24. [9] Zhong Tao, Lin-hai Han, Xiao-ling Zhao. 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. [10] Zhong Tao, Lin-hai Han. Behaviour of concrete-filled double skin rectangular steel tubular beam–columns. J Constr Steel Res 2006;62(7):631–46. [11] Elchalakani M, Xiao-ling Zhao, Grzebieta R. Tests on concrete filled double-skin (CHS outer and SHS inner) composite short columns under axial compression. ThinWalled Struct 2002;40(5):415–41. [12] Lin-Hai Han, Zhong Tao, Hong Huang, et al. Concrete-filled double skin (SHS outer and CHS inner) steel tubular beam-columns. Thin-Walled Struct 2004;42(9):1329–55. [13] Xiao-Ling Zhao, Grzebieta RH, Ukur A, et al. Tests of concrete-filled double skin (SHS outer and CHS inner) composite stub columns. Adv Steel Struct 2002;2(2):567–74. [14] Li Xie, Boyang Lin, Fang Yuan, et al. Experimental study on mechanical performance of square concrete filled double-skin steel tubular columns under compression-bending-shear loading conditions. J Build Struct 2015;36(suppl. 1):230–4. (in Chinese). [15] Hong Huang, Lin-hai Han, Zhong Tao, et al. Analytical behaviour of concrete-filled double skin steel tubular (CFDST) stub columns. J Constr Steel Res 2012;57(4):37–48. [16] Hong Huang, Baojun Cha, Mengcheng Chen, et al. Comparative test study on mechanical behavior of concrete-filled double-skin steel tubular with hollow-centered square section short columns under axial compression. Railway Eng 2015;10:85–9. (in Chinese). [17] Grzebieta R. Strength and Ductility of Concrete-Filled Double Skin (SHA inner and SHA outer) Tubes. Thin-Walled Struct 2002;40:199. [18] Liang W, Dong J, Wang Q. Mechanical behaviour of concrete-filled double-skin steel tube (CFDST) with stiffeners under axial and eccentric loading. Thin-Walled Struct 2019;138:215–30. [19] Fa-xing Ding, Zhe Li, et al. Composite action of hexagonal concrete-filled steel tubular stub columns under axial loading. Thin-Walled Struct 2016;107(11):453–61. [20] Fa-xing Ding, Zhe Li, et al. Composite action of octagonal concrete-filled steel tubular stub columns under axial loading. Thin-Walled Struct 2016;107:453–61. [21] Fa-xing Ding, Jiang Zhu, et al. Comparative study of stirrup-confined circular concrete-filled steel tubular stub columns under axial loading. Thin-Walled Struct 2018;123:294–304. [22] Gong Yong-zhi Fu, Lei Ding Fa-xing, et al. Bearing capacity of axially loaded stirrup confined concrete-filled square steel tubular stub columns. J Build Struct 2016. [23] Ding Fa-xing Lu, De-ren Bai Yu, et al. Comparative study of square stirrup-confined concrete-filled steel tubular stub columns under axial loading. Thin-Walled Struct 2018;98:443–53. [24] Fa-xing Ding, Xiao-yong Ying, Lin-chao Zhou, et al. Unified calculation method and its application in determining the uniaxial mechanical properties of concrete. Front Arch Civil Eng China 2011;5(3):381–93. [25] Fa-xing Ding, Chang-jing Fang, Bai Yu, et al. Mechanical performance of stirrupconfined concrete-filled steel tubular stub columns under axial loading. J Constr Steel Res 2014;98(98):146–57. [26] Zhao XL, Han B, Grzebieta RH. Plastic mechanism analysis of concrete-filled double-skin (SHS inner and SHS outer) stub columns. Thin-Walled Struct 2002;40(10):815–33.
5. Conclusions This paper presents a combined numerical, experimental, and theoretical study on the behavior of the CFDST (SHS outer and SHS inner) stub columns under axial compressive loading. FE models are also developed for the CFDST (SHS outer and SHS inner) columns and validated through experimental results. Comprehensive parametric studies were also conducted using the validated FE models. A design formula for predicting the load bearing capacity of CFDST (SHS outer and SHS inner) columns is proposed based on the above results and further confirmed by the experimental results from two additional specimens. The FE models were also further confirmed the results. Based on the studies, the following conclusions could be drawn: (1) The FE results are in good agreement with experimental results by other scholars. (2) The results of finite element parameter analysis show that the constraint of the outer steel tube on the core concrete is mainly concentrated in the corner area, while the inner steel tube has no obvious constraint on the core concrete. As the hollow ratio increases, the constraint effect of the outer steel tube on the concrete is weakened. (3) Based on the ultimate equilibrium principle, a practical formula for the ultimate bearing capacity of CFDST columns under axial loading is proposed. According to the range of parameter analysis, the formula is applicable to the calculation of bearing capacity of square CFDST columns with hollow ratio ranging from 0 to 0.7, concrete strength ranging from 40 MPa to 100 MPa and steel yield strength ranging from 235 MPa to 420 MPa. The predicted results show very good agreement with the experimental and numerical results. (4) Through further supplementary experiment, the results show that the finite element model and calculation formula are still applicable to the CFDST stub column with large hollow ratio under axial compression. Declaration of Competing Interest 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. 676