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Investigation on concrete filled double skin steel tubes (CFDSTs) under pure torsion
Journal of Constructional Steel Research 90 (2013) 221–234
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Journal of Constructional Steel Research
Investigation on concrete filled double skin steel tubes (CFDSTs) under pure torsion Hong Huang a,b, Lin-Hai Han a,⁎, Xiao-Lin Zhao c,1 a b c
Department of Civil Engineering, Tsinghua University, Beijing, 100084, PR China College of Civil Engineering and Architecture, East of China Jiao Tong University, Nanchang, Jiangxi Province, 330013, PR China Department of Civil Engineering, Monash University, Clayton 3800, Australia
a r t i c l e
i n f o
Article history: Received 21 June 2013 Accepted 30 July 2013 Available online 4 September 2013 Keywords: Concrete filled double skin steel tubes (CFDSTs) Torsion Torsional capacity Failure mode Parametric analysis Design model
a b s t r a c t This paper presents a series of tests on concrete filled double skin steel tubular (CFDST) members subjected to pure torsion. Two types of combinations are included, i.e., CFDST section with circular hollow section (CHS) as both inner and outer tubes, and section with CHS as the inner tube and square hollow section (SHS) as the outer tube. Finite element method was used to analyze typical failure mode and complete torque–rotation curve of the specimens, as well as interaction between the steel tubes and the sandwiched concrete of CFDSTs. It was found that the results calculated by finite element method show reasonable agreement with those of the test results. Six important parameters influencing the torque versus torsional rotation curves are identified, i.e. nominal steel ratio, yield strength of outer steel tubes and inner steel tubes, concrete cube compressive strength, width to thickness ratio of inner steel tubes and hollow section ratio. Finally, design formulas are proposed for calculating torsional capacities of CFDSTs. © 2013 Elsevier Ltd. All rights reserved.
1. Introduction Concrete filled double skin steel tubular (CFDST) members consist of steel hollow sections with concrete annulus filled in. Since the 1990s, many research works have been done on CFDST members with various cross-section shapes subjected to different loading conditions [1]. Both experimental and analytical studies have been focused on the behavior of CFDST stub columns, such as Wei et al. [2], Zhao et al. [3,4], Zhao and Grzebieta [5], Elchalakani et al. [6], Huang et al. [7], Uenaka et al. [8] and Hu and Su [9]. The behavior of the CFDST beam-columns under static or cyclic loading has been intensively investigated (e.g. [10–14]). Lu et al. [15] reported fire performance of CFDST columns exposed to standard fire. The effects of preload on steel tubes to the ultimate strength of CFDST columns were discussed by Li et al. [16] and the experimental behavior of CFDST stub columns subjected to partial compression was reported by Yang et al. [17]. In practice, CFDST members may be subjected to torsional load, such as the transmitting poles of electricity, the pier of viaduct, and the columns of a high rise building under earthquake. Therefore it is necessary to investigate the torsional behavior of CFDST members. Research on torsional properties of concrete filled steel tubular (CFST) members has been carried out for example by Beck and Kiyomiya [18], Xu et al. [19] who carried out tests on CFST members
with circular sections under torsion. The tests showed that the core concrete plays an important role in the torsional resistance of the composite members that exhibited good ductility. Han et al. [20] simulated torque versus rotation angle curves of the CFST members using finite element method, and put forward formulas to predict the ultimate torsional strength of the CFST members with circular and square sections. This paper reports experimental and theoretical research of CFDST members under pure torsion. Two types of combinations are included, i.e., CFDST section with circular hollow section (CHS) as inner and outer tubes, and section with CHS as the inner tube and square hollow section (SHS) as the outer tube. The main parameters varied in the tests are section shape; nominal steel ratio and hollow ratio defined in Section 2.1 of this paper. A finite element analysis (FEA) model was developed on CFDST members in the state of torsion. The FEA model was verified by test results in this paper. Insight into the behavior of CFDST members under torsional load was obtained through analyzing typical failure modes, complete torque versus rotation angle curve and interaction between the steel tubes and the sandwiched concrete. Key parameters, which influence torque versus torsional angle relation curves of CFDST members, were identified. Finally, design formulas are proposed to calculate the torsional capacities of CFDST. 2. Experimental investigations 2.1. Test specimens
⁎ Corresponding author. Tel./fax: +86 10 62797067. E-mail addresses: [email protected], [email protected] (L.-H. Han). 1 National “1000-talent” Chair Professor at Tsinghua University. 0143-974X/$ – see front matter © 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jcsr.2013.07.035
A total of 12 specimens, including 6 CFDST members with CHS inner and CHS outer, one double skin hollow steel tubes (DSHT), 4 CFDST
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Nomenclature Ac Ace
Asco Asc Asi Aso B d D fck fcu fc′ fsyi fsyo T Tuc1 Tuc2 Tue Wsct
W0sct Wsi Wso
tso tsi α αn χ ε θ τscy τy τyi τyo ξ
Cross-sectional area of the sandwiched concrete Nominal core concrete cross-sectional area of concrete (=(B − 2tso)2 for square section; π(D − 2tso)2 / 4 for circular section) Cross-sectional area of the outer steel tube and the sandwiched concrete (=Aso + Ac) Cross-sectional area of CFDST (=Aso + Ac + Asi) Cross-sectional area of inner steel tube Cross-sectional area of outer steel tube Outer dimension of outer steel tube with square section Outer diameter of inner steel tube Outer dimension of outer steel tube with circular section Characteristic concrete strength (fck = 0.67fcu for normal strength concrete) Characteristic 28-day concrete cube strength Concrete cylinder strength Yield strength of inner steel tube Yield strength of outer steel tube Torque Torsional capacity predicted by FEA model Torsional capacity predicted by formula Measured torsion capacity Torsional section modulus of outer steel tube and concrete, given by π(D4 − d4)/(16D) and kW0sct for the composite members with circular and square sections, respectively Torsional section modulus of CFST member with square sections, given by 0.208B3 Torsional section modulus of inner steel tube, given by π(d4 − (d − 2tsi)4)/(16d) Torsional section modulus of outer steel tube, given by π(D4 − (D − 2tso)4)/(16D) and 2tso(B − tso)2 for the members with circular and square sections, respectively Wall thickness of outer steel tube Wall thickness of inner steel tube Steel ratio, given by α = Aso / Ac Nominal steel ratio, given by αn = Aso / Ace Hollow ratio, given by d/(B − 2tso) (for square member) and d/(D − 2tso) (for circular member) Strain Torsional rotation angle Strength of the composite section of outer steel tube and concrete under torsion Shear yield strength of steel The shear yield strength of inner steel tube The shear yield strength of outer steel tube Confinement factor (=αnfsyo / fck)
members with CHS inner and SHS outer and one square CFST member were tested. The two sides of outer and inner steel tubes of all specimens, including the DSHT member, are connected to the bottom and top endplates. The length of all the test specimens is 550 mm. The information of the specimens is listed in Table 1, where D (d) is the outside diameter of outer (inner) circular steel tube; B is the outside diameter of outer square steel tube; tso (tsi) is the wall thickness of outer (inner) steel tube. Six different sizes of steel tubes are used as the outer skin and three different sizes of steel tubes are used as the inner skin. The main parameters varied in the tests are: tube shape (circular and square); hollow ratio, χ (from 0 to 0.48); and nominal steel ratio αn (from 0.08 to 0.14). Nominal steel ratio αn is given by αn = Aso / Ace. Ace is the nominal cross-sectional area of the sandwiched
concrete, which is given by Ace ¼ π4 ðD−2t so Þ2 for section with CHS inner and CHS outer, and Ace = (D − 2tso)2 for section with CHS inner and SHS outer. Aso is the cross-sectional area of outer steel tube. Hollow ratio χ is defined as d/(D − 2tso) (for circular section) and d/(B − 2tso) (for square section), where d and D (or B) are the major dimensions of the inner and outer tubes, respectively, and tso is the thickness of the outer tube. At the time of tests the measured compressive cube strength (fcu) was 50 MPa for circular members and 60 MPa for square members. 2.2. Test setup Fig. 1 shows an overview of the test setup. The bottom endplate of the specimen was fixed on the ground. The upper endplate of the specimen was bolted with a steel square plate upon which a long loading steel arm was welded. The wall thickness of the steel square plate and the loading steel arm is 25 mm. The torque was realized by a pair of equal and opposite forces, which were applied on two sides of the steel arm by two jacks. Generally the loading was terminated when the jacks are about to reach the maximum travel stroke. For monitoring the torsional angle (θ) of the specimen, a thin steel wire with a suspended hammer on the end was winded around the specimen perimeter as seen in Fig. 1(b). To obtain the shear strain (γ), strain rosettes were fixed to the outer surface of the steel tube, as shown in Fig. 1(a). 2.3. Test results and discussion At the initial loading stage of all specimens the load versus torsional rotation angle relationship was observed to be linear. The growth rate of torsional rotation angle was greater than the growth rate of load when the load exceeded about 70% of the ultimate load, and occasionally, the clap sound could be heard. Fig. 2 shows failure modes of the tested specimens. For specimens with circular outer sections, the maximum torsional rotation angle is 7.8°. It was found that all the specimens had no obvious damage from their appearance, and the specimens bonded well with the top plate and bottom plate. In order to observe the failure pattern of the sandwiched concrete, the outer steel tube was removed, as shown in Fig. 2(2a). For circular specimens, obvious cracks with an approximately 45 degree inclination to axial line can be seen on the surface of concrete; even so the concrete still maintained an intact cylinder. There was no sliding trace on the inner wall of the outer steel tube, which showed that there's no slipping between the concrete and outer steel tube, the concrete bonded well with the outer steel tube. For square specimens, the maximum torsional rotation angle is 5.5°. Fig. 2(1b) shows that all specimens with square sections had no obvious damage except that part of the welding of specimen No. SO4I3 cracked. It can be found from Fig. 2(2b) that many cracks along 45 degree direction appeared on the surface of sandwich concrete, and the surface of sandwiched concrete was broken. Fig. 3 shows measured torque (T) versus rotation angle (θ) curves of all specimens. The following findings were observed for circular specimens from Fig. 3(1): (1) the torsional capacity increases obviously with the increasing of hollow ratio. (2) the torsional capacity and elastic stiffness increase with the increasing of nominal steel ratio. (3) the torsion capacity of CFDST improves around 20% comparing with that of the reference double skin hollow steel tubes (DSHT), which shows that concrete played a significant role in resisting the torsional loading. For square specimens, it can be seen from Fig. 3(2a) that the torsional capacity and elastic stiffness increase as nominal steel ratio increases. Torque (T) versus torsional rotation angle (θ) curves of the two CFDST specimens and CFST specimen which have the same outer steel tube and concrete are shown in Fig. 3(2b). The torsional capacities of specimens (Tue), which are determined as the values of torque corresponding to the points where the maximum
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Table 1 Information of CFDST specimens. Section type
No.
Specimen label
Outer tube dimensions D(B) × tso (mm)
Inner tube dimensions d × tsi (mm)
χ
fsyo (MPa)
fsyi (MPa)
fcu (MPa)
αn
Tue (kN · m)
Tuc1 (kN · m)
Tuc1 / Tue
Tuc2 (kN · m)
Tuc2 / Tue
1 2 3 4 5 6 7 1 2 3 4 5
CO1I1 CO1I2 CO2I1 CO2I2 CO3I1 CO3I2 HCO3I2 SO4I3 SO5I3-1 SO5I3-2 SO6I3 SO5
Φ165 Φ165 Φ165 Φ165 Φ165 Φ165 Φ165 □-160 □-160 □-160 □-160 □-160
Φ42 Φ75 Φ42 Φ75 Φ42 Φ75 Φ75 Φ60 Φ60 Φ60 Φ60 –
0.27 0.48 0.27 0.48 0.27 0.48 – 0.4 0.4 0.4 0.4 0
260.0 260.0 286.4 286.4 365.6 365.6 365.6 281 281 281 281 281
326.6 355.4 326.6 355.4 326.4 355.4 355.4 275 275 275 275 –
50 50 50 50 50 50 – 60 60 60 60 60
0.08 0.08 0.10 0.10 0.12 0.12 – 0.08 0.11 0.11 0.14 0.11
24.6 33.2 32.3 42.1 48.8 54.3 43.6 34.8 44.4 47.0 48.8 38.0
25.4 33.8 31.8 40.0 46.3 52.2 44.7 33.2 41.6 41.6 46.6 43.9
1.033 1.018 0.985 0.950 0.949 0.961 1.025 0.954 0.937 0.885 0.955 1.155 0.984 0.0693
24.9 31.2 33.0 39.2 45.0 51.2 45.6 32.7 40.1 40.1 47.8 38.3
1.013 0.939 1.020 0.930 0.922 0.943 1.046 0.940 0.902 0.852 0.979 1.008 0.958 0.0588
× × × × × × × × × × × ×
3 3 4 4 4.6 4.6 4.6 3 4 4 5 4
× × × × × × × × × × ×
3 5 3 5 3 5 5 3 3 3 3
Mean COV
shear strain of the cross section is 0.01 [20], are listed in Table 1. Comparing the specimens CO3I2 and HCO3I2, it can be found that the Tue for CFDST specimen is about 24.5% higher than for the respective unfilled one. In order to investigate the effects of torsional carried capacity by filling with concrete, the ratios of the ultimate torque of specimens filled with concrete (Tue) and the ultimate torque of corresponding outer steel tubes (Tuc,outer) are shown in Fig. 4, where the ultimate
8
torque of corresponding outer steel tubes (Tuc,outer) can be calculated by Wsoτyo, Wso is torsional section modulus of outer steel tube, given by π(D4 − (D − 2tso)4)/(16D) and 2tso(B − tso)2 for circular and square sections, respectively. The shear yield strength of outer steel tube is given by τ yo ¼ p1ffiffi3 f yo . It was found that, within the limitation of the current test, the Tue for CFDST specimens with circular section is about 20%–80% higher than that for the unfilled ones and for specimens with square section the improved torsional capacity is about 20%–50% higher.
9
7 2
2 3
3
5 13
2
4
10
6 13
2
5 11
12
1
(a) Schematics view of the test setup
(b) The measurementof angles
(c) A picture of the testsetup Fig. 1. Overview of the test setup.
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CO1I1 CO1I2 CO2I1
CO2I2
CO3I1
CO3I2
HCO3I2 SO4I3
Partial enlargement
SO5I3-1
SO5I3-2
SO6I3
SO5
Partial enlargement
Weld cracking
(a) Circular sections
(b) Square sections
(1) Outer steel tube of CFDST specimen
cracks
(a) Circular sections
(b) Square sections (2)After removal of partial outer steel tube Fig. 2. Failure modes of tested specimens.
3. FEA model and analysis 3.1. FEA model A FEA model was established by Han et al. [20] for the analysis of CFST members under torsion based on the commercial FEA package, ABAQUS. The same model is used to investigate the torsion behavior of CFDST columns in this paper. In the mode, both the steel tubes and the sandwiched concrete of the CFDST members were discretized by 8-node brick elements. The adopted element meshes for both circular and square sections and boundary conditions are shown in Fig. 5, where all the degrees of bottom end plate are constrained, and the top end plate is free. The torsional loading in the z direction is applied to the top surface in an appointed torsional angle. The contact model for CFST column was used for CFDST column in Huang et al. [7], and a fairly good agreement was obtained with test results. This contact model is also used in this paper. In normal direction hard contact is applied, and in the tangential direction the Mohr–Coulomb friction model is adopted. Details of the contact model can be found in Huang et al. [7]. 3.2. Verifications of the FEA model The measured torque (T) versus rotation angle (θ) curves are compared in Fig. 6 with the ones calculated from the results of the FEA
analyses. It can be seen that, generally good agreement is obtained between the calculated and tested results. As there is no descending branch in the curves, the torque corresponding to the point where the shearing strain reaches the value of 0.01 [20], is regarded as torsional capacity Tue. The torsional capacity predicted by FEA model (Tuc1) and the measured value (Tue) are listed in Table 1. For circular members, the mean value and the standard deviation of Tuc1 / Tue are 0.989 and 0.037, respectively, and for square members, the values are 0.980 and 0.104, respectively. 3.3. Typical failure mode Fig. 7 shows the predicted typical failure modes of outer and inner steel tubes of CFDST member as well as the corresponding double skin hollow steel tubes (DSHT) subjected to pure torsion, respectively. The data of CFDST specimens used for calculations are: D(B) = 400 mm, d = 191 mm, tso = 9.3 mm, tsi = 3.18 mm, λ = 40, χ = 0.5, αn = 0.1, fsyo = fsyi = 345 MPa, fcu = 60 MPa. It can be seen from Fig. 7 that there is a significant difference between failure modes of CFDST and DSHT, i.e., no obvious buckling occurs in inner and outer steel tubes of CFDST member, which shows more ductile behavior. Inward buckling was observed for the outer steel tube of DSHT, whereas inward buckling is prevented by the concrete in the CFDST members.
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60 50
CO1I1 CO1I2
T (kN·m)
40
CO2I1
30
CO2I2 CO3I1
20 CO3I2 HCO3I2
10 0 0
2
4
6
8
10
12
θ (°)
60
60
45
45
T (kN·m)
T (kN·m)
(1) Circular sections
30 SO4I3 ( α n= 0.08) SO5I3-1 (α n= 0.11) SO6I3 ( α n= 0.14)
15
30 SO5I3-1(CFDST) SO5I3-2(CFDST) SO5(CFST)
15
0
0 0
1
2
3
4
5
0
1
2
3
4
5
θ (°)
θ (°)
(a) Influence of nominal steel ratio
(b) CFDST and CFST specimens
(2) Square sections Fig. 3. Diagrams of torque versus torsional rotation angle curves for all specimens.
3.4. Complete curves of torque versus rotation angle The typical torque (T) versus torsional rotation (θ) curve of CFDST obtained from the FEA model is shown in Fig. 8. Fig. 9 shows the distributions of the shear stress (S13 in the graphs) in the cross sections of inner and outer steel tubes, as well as the sandwiched concrete at three points above. Fig. 10 shows shear stress (τ) versus torsional angle (θ) curves for typical torsion members in different positions of
the cross sections. The data of CFDST specimens used for calculations are: D(B) = 400 mm, d = 191 mm, tso = 9.3 mm, tsi = 3.18 mm, λ = 40, χ = 0.5, αn = 0.1, fsyo = fsyi = 345 MPa, fcu = 60 MPa. The calculated T versus θ diagram can generally be divided into three stages OA, AB and BC, as shown in Fig. 8. At the end of stage A yielding of outer steel tube occurs and the shear stress of the inner steel tube is half of that of the outer steel tube, as shown in Fig. 9. This is because that the inner steel tube is closer to the center of the cross section. In the first
2
2 CO1I1 CO1I2 CO2I1
1
CO2I2 CO3I1
0.5
CO3I2
0
1.5
Tue/ Tuc,outer
Tue/ Tuc,outer
1.5
SO4I3 SO5I3-1
1
SO5I3-2 SO6I3 SO5
0.5 0
(a) Circular sections
(b) Square sections
Fig. 4. Ratios of the ultimate torque of specimens filled with concrete (Tue) and the ultimate torque of respective outer steel tubes (Tuc,outer).
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Outer steel tube
Torsional load
Torsional load Y Top end plate X
Z
(Free boundary)
Inner steel tube Concrete
(a) Meshes of circular section
Z
Outer steel tube Y
Y
Z
X X
Bottom end plate Inner steel tube Concrete
(b) Meshes of square section
(Fixed boundary conditions)
(c) General view of circular member
(d) General view of square member
Fig. 5. Element meshes and boundary conditions.
stage the shear stress of sandwiched concrete increases more rapidly as shown in Fig. 10. The torque grows linearly with the increasing of torsional angle. From the yielding at point A an elastic–plastic stage AB occurs and at point B the shear strain of extreme fiber reaches the value around 0.01. During this stage, with the increasing of the torque, the concrete cracks and its volume begins to increase which then leads to the confinement activation provided by the outer steel tube. The confinement effect increases with the increasing torsional deformation. The outward expansion speed of sandwiched concrete is faster than towards inner steel tube, thus no confining compressive stress appears in the concrete. Strain hardening appears in stage BC and torque (T) as well as the shear stress increase moderately, while the torsional angle (θ) increases rapidly. The load is still increasing during this stage as the steel tubes have some reserve in resisting the torque due to the strain hardening of steel. Due to the confinement provided by the outer steel tube, the cracked concrete can still resist torque. The sandwiched concrete resists about 5% of the torque of the composite member, and in addition it provides support to the outer steel tube. From Figs. 9 and 10 it is also obvious that: 1) The shear stress is greatest furthest away from the center of the cross section. 2) Circular and square sections exhibited similar behavior, except that for square sections the diagram is smoother within the strain hardening stage BC. This is attributed to the fact that confinement for sandwiched concrete provided by square section is weaker than that provided by circular section when the warping deformation is very large, especially on the mid-width of the square section, which is similar to the conclusion drawn by Huang et al. [7]. Fig. 11 shows the comparisons of torques (T) versus torsional angle (θ) diagrams for CFDST, sandwiched concrete and steel tubes of CFDST and DSHT, respectively. It can be found that outer and inner steel tubes carry the majority of the torsional loads, while the sandwiched concrete carries 5 to 6% of the torsional loads. Comparing the curves of steel tubes of CFDST and DSHT, the torsional capacity of steel tubes of CFDST is higher than that of DSHT, although they have the same dimensions and materials. This is due to the sandwiched concrete that effectively prevents the buckling of outer steel tube of CFDST.
Comparing the torque diagrams of the composite members with different hollow ratios shown in Fig. 12, it is seen that torques carried by inner and outer steel tubes increase with the increasing of hollow ratio and the contribution of the concrete decreases. The reason is that the area of concrete reduces, and the area as well as the torsional section modulus of inner steel tube increase with the increasing of hollow ratio. 3.5. Interaction between the steel tubes and the sandwiched concrete Fig. 13 shows the confinement stress (p1) versus torsional angle (θ) curves of the composite sections for different hollow ratios. It can be seen that, 1) for circular sections, p1 increases with the increasing of θ in the whole loading process. The confinement stress (p1) of circular section is caused by outward expansion of sandwiched concrete. The increase of torsional angle (θ) will lead to larger deformation of sandwiched concrete. The outer circular steel tube can provide enough confinement to the sandwiched concrete. 2) For square sections, the confinement stress (p1) is obviously greater in the section corners than in the mid-width of the section. The outer steel tube provides less confinement to the sandwiched concrete at locations farther away from the corner of the square section. 3) Confinement stress (p1) decreases with the increasing hollow ratio, because the reduced concrete area causes reduction of expansion in the volume of concrete. 4. Parametric analysis and simplified model 4.1. Parametric analysis Possible parameters that influence torque (T) versus rotation angle (θ) relationship of CFDST columns include hollow ratio (χ), nominal steel ratio (αn), strength of outer steel tube (fsyo), strength of concrete (fcu), strength of inner steel tube (fsyi) and width to thickness ratio of inner steel tube (d / tsi). Fig. 14 shows the effects of different parameters on the T versus θ relations of columns with circular inner and outer hollow sections. The basic data of these examples for calculations
2
4
6
Calculated Measured
0
8
2
4
6
227
60 50 40 30 20 10 0
Calculated Measured
0
8
2
4
6
θ (°)
θ (°)
θ (°)
(a) CO1I1
(b) CO1I2
(c) CO2I1
60 50 40 30 20 10 0
Calculated Measured
0
60 50 40 30 20 10 0
2
4
6
60 50 40 30 20 10 0
Calculated Measured
0
8
T (kN·m)
T (kN·m)
0
T (kN·m)
Calculated Measured
T (kN·m)
60 50 40 30 20 10 0
T (kN·m)
T (kN·m)
H. Huang et al. / Journal of Constructional Steel Research 90 (2013) 221–234
2
4
6
60 50 40 30 20 10 0
Calculated Measured
0
8
2
4
6
θ (°)
θ (°)
θ (°)
(d) CO2I2
(e) CO3I1
(f) CO3I2
60 50 40 30 20 10 0
8
8
Calculated Measured
0
2
4
6
8
θ (°)
(g) HCO3I2
Calculated Measured
1
2
3
4
Calculated Measured
0
5
1
2
3
4
60 50 40 30 20 10 0
Calculated Measured
0
5
1
2
3
4
θ (°)
θ (°)
θ (°)
(a) SO4I3
(b) SO5I3-1
(c) SO5I3-2
60 50 40 30 20 10 0
T (kN·m)
0
60 50 40 30 20 10 0
T (kN·m)
T (kN·m)
60 50 40 30 20 10 0
T (kN·m)
T (kN·m)
(1) Circular sections
Calculated Measured
0
1
2
3
4
5
60 50 40 30 20 10 0
Calculated Measured
0
1
2
3
θ (°)
θ (°)
(d) SO6I3
(e) SO5 (2) Square sections
Fig. 6. Comparison of calculated and tested T–θ curves.
4
5
5
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(a) Outer steel tube of double skin hollow tubes
(c) Inner steel tube of double skin hollow tubes
(b) Outer steel tube of CFDST
(d) Inner steel tube of CFDST
(1) Circular sections
(a) Outer steel tube of double skin hollow tubes
(b) Outer steel tube of CFDST
(c) Inner steel tube of double skin hollow tubes
(d) Inner steel tube of CFDST
(2) Square sections Fig. 7. Comparisons of failure mode between CFDST and double skin hollow steel tubes subjected to pure torsion.
are as follows: D = 400 mm, tso = 9.3 mm, d = 191 mm, tsi = 3.18 mm, λ = 40, fsyo = fsyi = 345 MPa, fcu = 60 MPa, χ = 0.5. Some explanations are given below on the influence of six parameters on torque versus rotation angle curves with columns of circular inner and outer hollow sections as an example. Similar conclusions can be drawn for square members.
T
B
A
O Fig. 8. Typical T–θ curve.
C
Torsional capacity increases as the nominal steel ratio (αn) and the strength of outer steel tube (fsyo) increase. The increasing of nominal steel ratio (αn) can also improve the elastic stiffness. With the increasing the strength of concrete (fcu) torsional capacity increases only slightly, and this is attributable to the contribution of the sandwiched concrete taking only 5 to 6% of the torque. For columns with bigger hollow ratio (χ), such as χ is equal to 0.75, the effect of the strength of concrete (fcu) on torsional capacity is weaker, for the reason of the decreased proportion of the sandwiched concrete. When hollow ratio (χ) is less than 0.5, strength (fsyi) and width to thickness ratio (d / tsi) of inner steel tube have little effect on T versus θ curves. The load carried by the inner steel tube increases with the increasing hollow ratio (χ). Thus when hollow ratio (χ) exceeds 0.5, torsional capacity of member increases with the increasing strength of the inner steel tube (fsyi) and the decreasing width to thickness ratio of the inner steel tube (d / tsi). It can be concluded from Fig. 14 that hollow ratio (χ) has a significant effect on torsional capacities of CFDST columns. Compared with the torque carried by concrete, the torque carried by the inner steel tube is greater. When hollow ratio (χ) increases, torsional capacity of component increases due to the increasing of the area of inner steel tube.
H. Huang et al. / Journal of Constructional Steel Research 90 (2013) 221–234 S,S13 (Average: 75%)
S,S13 (Average: 75%)
(a) Point A
229
S,S13 (Average: 75%)
(b) Point B
(c) Point C
(1) Inner and outer steel tubes of circular sections S,S13 (Average: 75%)
S,S13 (Average: 75%)
(a) Point A
S,S13 (Average: 75%)
(b) Point B
(c) Point C
(2) Concrete core of circular sections S,S13 (Average: 75%)
S,S13 (Average: 75%)
S,S13 (Average: 75%)
(a) Point A
(b) Point B
(c) Point C
(3) Inner and outer steel tubes of square sections S,S13 (Average: 75%)
S,S13 (Average: 75%)
(a) Point A
S,S13 (Average: 75%)
(b) Point B
(c) Point C
(4) Concrete core of square sections Fig. 9. The distributions of shear stress (τ) of steel tubes and concrete (unit: MPa) at three stages (A, B and C) defined in Fig. 8.
4.2. Design formulas Based on the parametric study presented above, the formula for calculating composite member strength under torsion can be obtained by regression analysis. Torsional capacity of the CFDST can be calculated by Eq. (1), in which γtWsctτscy is the torque carried by outer steel tube and concrete, and Wsiτyi is the torque carried by the inner steel tube. τscy is strength of the composite section of outer steel tube and concrete under torsion, which can be calculated by Eqs. (2a) and (2b). When the hollow ratio χ is equal to 0, a CFST member follows and Eq. (1) becomes the same as the
formula for calculating the torsional strength of CFST given in Han et al. [20]. T uc2 ¼ γt W sct τ scy þ W si τyi
ð1Þ
For CFDST members with circular sections, 2:33 0:134 ξ f scy : τscy ¼ 0:422 þ 0:313α n
ð2aÞ
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H. Huang et al. / Journal of Constructional Steel Research 90 (2013) 221–234
20
3 2
τ (MPa)
15
3 2
Point 1 Point 2
1
Point 3 10 5
Point 1 Point 2
1
15
τ (MPa)
20
Point 3 10 5
0 0
A
2
B
C
4
0 6
0
A
B
2
C
4
θ (°)
θ (°)
(a) Circular sections
(b) Square sections
6
Fig. 10. Shear stress (τ) versus rotation angle (θ) relation in different position of the cross sections.
800
800
700
700
CFDST
600
500
T (kN·m)
T (kN·m)
600
CFDST
Steel tubes of CFDST
400
Steel tubes of DSHT
300 200
500
Steel tubes of CFDST Steel tubes of DSHT
400 300 200
Sandwiched concrete
100
Sandwiched concrete
100
0
0 0
2
4
6
0
2
4
θ (°)
θ (°)
(a) Circular sections
(b) Square sections
6
Fig. 11. Comparisons of the torques (T) carried by CFDST, sandwiched concrete, and steel tubes of CFDST and DSHT respectively versus rotation angle (θ) relations.
For CFDST members with square sections,
ð2bÞ
700
800
600
700
500
600
T (kN·m)
T (kN·m)
2:33 0:25 ξ f scy τscy ¼ 0:455 þ 0:313α n
where, fscy is axial compression strength of outer steel tube and concrete, fscy = C1χ2fyo + C2(1.14 + 1.02ξ)fck for circular sections; fscy = C1χ2fyo + C2(1.18 + 0.85ξ)fck for square sections. Coefficient C1 and C2 are equal to α / (1 + α) and (1 + αn) / (1 + α), respectively. α is steel ratio of member, which is given by (α = Aso / Ac).
=0.75
400 300 200 100
=0.5
Steel tubes of CFDST
=0 =0 =0.5 =0.75
Concrete
=0.75
500
Steel tubes of CFDST
=0.5
400
=0
300
=0 =0.5 =0.75
200
Concrete
100
0
0 0
2
4
6
0
2
4
θ (°)
θ (°)
(a) Circular sections
(b) Square sections
Fig. 12. The comparisons of torque (T) carried by concrete and steel tubes with different hollow ratios.
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H. Huang et al. / Journal of Constructional Steel Research 90 (2013) 221–234
40
30 p1
25
35
20
p 1(MPa)
p 1(MPa)
30
15 10
=0
5
=0 =0.5 =0.75
On the corner
=0 =0.5 =0.75
On the mid-width
25 20 15 10
=0.5
231
p1
5
=0.75
0
0 0
2
4
6
0
2
4
θ (°)
θ (°)
(a) Circular sections
(b) Square sections
6
Fig. 13. Confinement stress p1 between outer steel tube and concrete in the cross section of columns with different hollow ratios.
Wsct is torsional section modulus of outer steel tube and concrete, given by π(D4 − d4)/(16D) and kW0sct for the composite members with circular and square sections, respectively. W0sct is torsional section
modulus of CFST member with square sections, given by 0.208B3 [20]. Coefficient k is related to hollow ratio, and it can be incorporated in coefficient γt. Wsi is torsional section modulus of inner steel tube, given
Fig. 14. Effects of different parameters on T versus θ relations (circular section as an example).
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Fig. 14 (continued).
by π(d4 − (d − 2tsi)4)/(16d). The shear yield strength of inner steel tube is given by τ yi ¼ p1ffiffi3 f yi . Fig. 15 shows the relations of factor γt with the confinement factor (ξ) and hollow ratio (χ). Formulae for γt can be obtained by using the regression analysis method. For CFDST members with circular sections, γ t ¼ ð−0:22χ þ 0:273Þ ln ðξÞ−0:133χ þ 1:29:
ð3aÞ
For CFDST members with square sections, 2
γ t ¼ ð−0:333χ þ 0:26Þ ln ðξÞ−1:124χ þ 0:364χ þ 1:434:
ð3bÞ
The validity limits of Eq. (1) are: χ = 0 to 0.75; αn = 0.05 to 0.2; fyo = 235 MPa to 700 MPa; fyi = 235 MPa to 700 MPa, d / tsi = 30 to 90; and fcu = 30 MPa to 90 MPa. For the DSHT specimen, torsional capacity (Tuc2) can be calculated by Eq. (4), in which Wyoτyo is the torque carried by outer steel tube, and Wsiτyi is the torque carried by the inner steel tube. T uc2 ¼ W so τyo þ W si τyi
ð4Þ
Wso is torsional section modulus of outer steel tube, given by π(D4 − (D − 2tso)4)/(16D). The shear yield strength of outer steel tube is given by τ yo ¼ p1ffiffi3 f yo . Figs. 16 and 17 respectively show comparisons between torsional capacity calculated by simplified model (Tuc2) and FEA model (Tuc1), and comparisons between simplified model (Tuc2) and test results (Tue). The values of Tue, Tuc1 and Tuc2 are also listed in Table 1. The mean value and the coefficient of variation (COV) of Tuc1 / Tue are 0.984 and 0.0693, whereas the mean value and the COV of Tuc2 / Tue are 0.958 and 0.0588. The torsional capacity (Tuc2) of the DSHT specimen calculated by Eq. (4) and the torsional capacity (Tuc1) predicted by FEA model are listed in Table 1. The values of Tuc1 and Tuc2 overestimate the measured value by 3% and 5%, respectively. 5. Conclusions Based on the results of present study, the following conclusions can be drawn: (1) The present experimental results show that the torsion capacity of CFDST improves about 20% comparing with that of DSHT, due to the existence of sandwiched concrete. With the increasing of hollow ratio and nominal steel ratio, torsional capacity increases.
2
1.5
1.5
1
1
0.5
1000
0.5
0
0 0
0.5
1
1.5
2
0
0.5
2
1.5
1.5
1
1
t
t
1
1.5
2
(b)
(a) 2
0.5
800 600 400 200 0 0
200
0.5
1
1.5
2
600
800
1000 1200
(a) Circular sections
0 0
400
T uc1(kN·m)
0.5
0
233
1200
T uc2(kN·m)
2
t
t
H. Huang et al. / Journal of Constructional Steel Research 90 (2013) 221–234
1400 0
0.5
1
1.5
2
1200
(d)
1000
T uc2(kN·m)
(c) (1) Circular sections 2
2
1.5
1.5
1
1
800 600
t
t
400 0.5
200
0.5
0
0
0 0
0.5
1
1.5
2
0
0.5
1
1.5
0
2
200 400 600 800 1000 1200 1400
T uc1(kN·m)
(b)
2
2
1.5
1.5
1
1
t
0.5
(b) Square sections Fig. 16. Comparisons of torsional capacity estimated by the simplified and FEA models.
0.5
0
0 0
0.5
1
1.5
2
0
(c)
0.5
1
1.5
2
of the strength (fsyi) and width to thickness ratio of inner steel tube (d / tsi) become significant. (4) Simplified models were derived in this paper to predict the torsional capacity of CFDST members. The capacities predicted by the simplified method are in good agreement with the experimental results and those calculated using FEA modeling.
(d)
Fig. 15. γt versus ξ relations.
(2) The torque versus torsional angle curves calculated by finite element method in this paper show good agreement with test results. Torque versus torsional rotation curve of CFDST can be generally divided into three stages, and outer steel tube provides enough confinement to the sandwiched concrete. (3) Six important parameters that influence the torque versus torsional rotation curves of the composite members were investigated. It was found that nominal steel ratio (αn), strength of outer steel tube (fsyo) and hollow ratio (χ) have important influence on the curves. When hollow ratio (χ) exceeds 0.5, the effect
T uc2(kN·m)
(2) Square sections
80
80
60
60
T uc2(kN·m)
t
(a)
40 20 0
40 20 0
0
20
40
60
80
0
20
40
60
80
T ue(kN·m)
T ue(kN·m)
(a) Circular sections
(b) Square sections
Fig. 17. Comparisons of torsional capacity from the test results and estimated by the simplified model.
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Acknowledgments The research reported in the paper was supported by the National Natural Science Foundation of China (No. 51008122) as well as by the Tsinghua University Initiative Scientific Research Program (No. 2011THZ03). The financial support are highly appreciated. References [1] Zhao XL, Han LH. Double skin composite construction. Prog Struct Eng Mater 2006;8(3):93–102. [2] Wei S, Mau ST, Vipulanandan C, Mantrala SK. Performance of new sandwich tube under axial loading: experiment. J Struct Eng ASCE 1995;121(12):1806–14. [3] Zhao XL, Grzebieta RH, Elchalakani M. Tests of concrete-filled double skin CHS composite stub columns. Steel Compos Struct Int J 2002;2(2):129–46. [4] Zhao XL, Han BK, 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] Zhao XL, Grzebieta RH. Strength and ductility of concrete filled double skin (SHS inner and SHS outer) tubes. Thin-Walled Struct 2002;40(2):199–233. [6] Elchalakani M, Zhao XL, Grzebieta R. Tests on concrete filled double-skin (CHS outer and SHS inner) composite short columns under axial compression. Thin-Walled Struct 2002;40(5):415–41. [7] 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. [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] 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. [10] Lin ML, Tsai KC. Behavior of double-skinned composite steel tubular columns subjected to combined axial and flexural loads. Proceedings of the First International Conference on Steel & Composite Structures, Pusan, Korea; 2001. p. 1145–52. [11] 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. [12] Han LH, Tao Z, Huang H, Zhao XL. Concrete-filled double skin (SHS outer and CHS inner) steel tubular beam-columns. Thin-Walled Struct 2004;42(9):1329–55. [13] Han LH, Tao Z, Zhao XL. Concrete-filled double skin steel tubular (CFDST) beamcolumns subjected to cyclic bending. Eng Struct 2006;28(12):1698–714. [14] Uenaka K, Kitoh H. Mechanical behavior of concrete filled double skin tubular circular deep beams. Thin-Walled Struct 2011;49(2):256–63. [15] Lu H, Zhao XL, Han LH. FE modeling and fire resistance design of concrete filled double skin tubular columns. J Constr Steel Res 2011;67(11):1733–48. [16] Li W, Han LH, Zhao XL. Axial strength of concrete-filled double skin steel tubular (CFDST) columns with preload on steel tubes. Thin-Walled Struct 2012;56(7): 9–20. [17] Yang YF, Han LH, Sun BH. Experimental behaviour of partially loaded concrete filled double-skin steel tube (CFDST) sections. J Constr Steel Res 2012;71(4):63–73. [18] Beck J, Kiyomiya O. Fundamental pure torsional properties of concrete filled circular steel tubes. J Mater Constr Struct Pavements JSCE 2003;60:285–96. [19] Xu JS, Zhou J, Lee G. Experimental studies on concrete filled steel tubular medium and long columns under compression and torsion. Proceedings of the Third International Conference on Steel–Concrete Composite Structures (I), ASCCS, Fukuoka, Japan; 1991. p. 159–64. [20] Han LH, Yao GH, Tao Z. Performance of concrete-filled thin-walled steel tubes under pure torsion. Thin-Walled Struct 2007;45(1):24–36.
Contents lists available at ScienceDirect
Journal of Constructional Steel Research
Investigation on concrete filled double skin steel tubes (CFDSTs) under pure torsion Hong Huang a,b, Lin-Hai Han a,⁎, Xiao-Lin Zhao c,1 a b c
Department of Civil Engineering, Tsinghua University, Beijing, 100084, PR China College of Civil Engineering and Architecture, East of China Jiao Tong University, Nanchang, Jiangxi Province, 330013, PR China Department of Civil Engineering, Monash University, Clayton 3800, Australia
a r t i c l e
i n f o
Article history: Received 21 June 2013 Accepted 30 July 2013 Available online 4 September 2013 Keywords: Concrete filled double skin steel tubes (CFDSTs) Torsion Torsional capacity Failure mode Parametric analysis Design model
a b s t r a c t This paper presents a series of tests on concrete filled double skin steel tubular (CFDST) members subjected to pure torsion. Two types of combinations are included, i.e., CFDST section with circular hollow section (CHS) as both inner and outer tubes, and section with CHS as the inner tube and square hollow section (SHS) as the outer tube. Finite element method was used to analyze typical failure mode and complete torque–rotation curve of the specimens, as well as interaction between the steel tubes and the sandwiched concrete of CFDSTs. It was found that the results calculated by finite element method show reasonable agreement with those of the test results. Six important parameters influencing the torque versus torsional rotation curves are identified, i.e. nominal steel ratio, yield strength of outer steel tubes and inner steel tubes, concrete cube compressive strength, width to thickness ratio of inner steel tubes and hollow section ratio. Finally, design formulas are proposed for calculating torsional capacities of CFDSTs. © 2013 Elsevier Ltd. All rights reserved.
1. Introduction Concrete filled double skin steel tubular (CFDST) members consist of steel hollow sections with concrete annulus filled in. Since the 1990s, many research works have been done on CFDST members with various cross-section shapes subjected to different loading conditions [1]. Both experimental and analytical studies have been focused on the behavior of CFDST stub columns, such as Wei et al. [2], Zhao et al. [3,4], Zhao and Grzebieta [5], Elchalakani et al. [6], Huang et al. [7], Uenaka et al. [8] and Hu and Su [9]. The behavior of the CFDST beam-columns under static or cyclic loading has been intensively investigated (e.g. [10–14]). Lu et al. [15] reported fire performance of CFDST columns exposed to standard fire. The effects of preload on steel tubes to the ultimate strength of CFDST columns were discussed by Li et al. [16] and the experimental behavior of CFDST stub columns subjected to partial compression was reported by Yang et al. [17]. In practice, CFDST members may be subjected to torsional load, such as the transmitting poles of electricity, the pier of viaduct, and the columns of a high rise building under earthquake. Therefore it is necessary to investigate the torsional behavior of CFDST members. Research on torsional properties of concrete filled steel tubular (CFST) members has been carried out for example by Beck and Kiyomiya [18], Xu et al. [19] who carried out tests on CFST members
with circular sections under torsion. The tests showed that the core concrete plays an important role in the torsional resistance of the composite members that exhibited good ductility. Han et al. [20] simulated torque versus rotation angle curves of the CFST members using finite element method, and put forward formulas to predict the ultimate torsional strength of the CFST members with circular and square sections. This paper reports experimental and theoretical research of CFDST members under pure torsion. Two types of combinations are included, i.e., CFDST section with circular hollow section (CHS) as inner and outer tubes, and section with CHS as the inner tube and square hollow section (SHS) as the outer tube. The main parameters varied in the tests are section shape; nominal steel ratio and hollow ratio defined in Section 2.1 of this paper. A finite element analysis (FEA) model was developed on CFDST members in the state of torsion. The FEA model was verified by test results in this paper. Insight into the behavior of CFDST members under torsional load was obtained through analyzing typical failure modes, complete torque versus rotation angle curve and interaction between the steel tubes and the sandwiched concrete. Key parameters, which influence torque versus torsional angle relation curves of CFDST members, were identified. Finally, design formulas are proposed to calculate the torsional capacities of CFDST. 2. Experimental investigations 2.1. Test specimens
⁎ Corresponding author. Tel./fax: +86 10 62797067. E-mail addresses: [email protected], [email protected] (L.-H. Han). 1 National “1000-talent” Chair Professor at Tsinghua University. 0143-974X/$ – see front matter © 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jcsr.2013.07.035
A total of 12 specimens, including 6 CFDST members with CHS inner and CHS outer, one double skin hollow steel tubes (DSHT), 4 CFDST
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Nomenclature Ac Ace
Asco Asc Asi Aso B d D fck fcu fc′ fsyi fsyo T Tuc1 Tuc2 Tue Wsct
W0sct Wsi Wso
tso tsi α αn χ ε θ τscy τy τyi τyo ξ
Cross-sectional area of the sandwiched concrete Nominal core concrete cross-sectional area of concrete (=(B − 2tso)2 for square section; π(D − 2tso)2 / 4 for circular section) Cross-sectional area of the outer steel tube and the sandwiched concrete (=Aso + Ac) Cross-sectional area of CFDST (=Aso + Ac + Asi) Cross-sectional area of inner steel tube Cross-sectional area of outer steel tube Outer dimension of outer steel tube with square section Outer diameter of inner steel tube Outer dimension of outer steel tube with circular section Characteristic concrete strength (fck = 0.67fcu for normal strength concrete) Characteristic 28-day concrete cube strength Concrete cylinder strength Yield strength of inner steel tube Yield strength of outer steel tube Torque Torsional capacity predicted by FEA model Torsional capacity predicted by formula Measured torsion capacity Torsional section modulus of outer steel tube and concrete, given by π(D4 − d4)/(16D) and kW0sct for the composite members with circular and square sections, respectively Torsional section modulus of CFST member with square sections, given by 0.208B3 Torsional section modulus of inner steel tube, given by π(d4 − (d − 2tsi)4)/(16d) Torsional section modulus of outer steel tube, given by π(D4 − (D − 2tso)4)/(16D) and 2tso(B − tso)2 for the members with circular and square sections, respectively Wall thickness of outer steel tube Wall thickness of inner steel tube Steel ratio, given by α = Aso / Ac Nominal steel ratio, given by αn = Aso / Ace Hollow ratio, given by d/(B − 2tso) (for square member) and d/(D − 2tso) (for circular member) Strain Torsional rotation angle Strength of the composite section of outer steel tube and concrete under torsion Shear yield strength of steel The shear yield strength of inner steel tube The shear yield strength of outer steel tube Confinement factor (=αnfsyo / fck)
members with CHS inner and SHS outer and one square CFST member were tested. The two sides of outer and inner steel tubes of all specimens, including the DSHT member, are connected to the bottom and top endplates. The length of all the test specimens is 550 mm. The information of the specimens is listed in Table 1, where D (d) is the outside diameter of outer (inner) circular steel tube; B is the outside diameter of outer square steel tube; tso (tsi) is the wall thickness of outer (inner) steel tube. Six different sizes of steel tubes are used as the outer skin and three different sizes of steel tubes are used as the inner skin. The main parameters varied in the tests are: tube shape (circular and square); hollow ratio, χ (from 0 to 0.48); and nominal steel ratio αn (from 0.08 to 0.14). Nominal steel ratio αn is given by αn = Aso / Ace. Ace is the nominal cross-sectional area of the sandwiched
concrete, which is given by Ace ¼ π4 ðD−2t so Þ2 for section with CHS inner and CHS outer, and Ace = (D − 2tso)2 for section with CHS inner and SHS outer. Aso is the cross-sectional area of outer steel tube. Hollow ratio χ is defined as d/(D − 2tso) (for circular section) and d/(B − 2tso) (for square section), where d and D (or B) are the major dimensions of the inner and outer tubes, respectively, and tso is the thickness of the outer tube. At the time of tests the measured compressive cube strength (fcu) was 50 MPa for circular members and 60 MPa for square members. 2.2. Test setup Fig. 1 shows an overview of the test setup. The bottom endplate of the specimen was fixed on the ground. The upper endplate of the specimen was bolted with a steel square plate upon which a long loading steel arm was welded. The wall thickness of the steel square plate and the loading steel arm is 25 mm. The torque was realized by a pair of equal and opposite forces, which were applied on two sides of the steel arm by two jacks. Generally the loading was terminated when the jacks are about to reach the maximum travel stroke. For monitoring the torsional angle (θ) of the specimen, a thin steel wire with a suspended hammer on the end was winded around the specimen perimeter as seen in Fig. 1(b). To obtain the shear strain (γ), strain rosettes were fixed to the outer surface of the steel tube, as shown in Fig. 1(a). 2.3. Test results and discussion At the initial loading stage of all specimens the load versus torsional rotation angle relationship was observed to be linear. The growth rate of torsional rotation angle was greater than the growth rate of load when the load exceeded about 70% of the ultimate load, and occasionally, the clap sound could be heard. Fig. 2 shows failure modes of the tested specimens. For specimens with circular outer sections, the maximum torsional rotation angle is 7.8°. It was found that all the specimens had no obvious damage from their appearance, and the specimens bonded well with the top plate and bottom plate. In order to observe the failure pattern of the sandwiched concrete, the outer steel tube was removed, as shown in Fig. 2(2a). For circular specimens, obvious cracks with an approximately 45 degree inclination to axial line can be seen on the surface of concrete; even so the concrete still maintained an intact cylinder. There was no sliding trace on the inner wall of the outer steel tube, which showed that there's no slipping between the concrete and outer steel tube, the concrete bonded well with the outer steel tube. For square specimens, the maximum torsional rotation angle is 5.5°. Fig. 2(1b) shows that all specimens with square sections had no obvious damage except that part of the welding of specimen No. SO4I3 cracked. It can be found from Fig. 2(2b) that many cracks along 45 degree direction appeared on the surface of sandwich concrete, and the surface of sandwiched concrete was broken. Fig. 3 shows measured torque (T) versus rotation angle (θ) curves of all specimens. The following findings were observed for circular specimens from Fig. 3(1): (1) the torsional capacity increases obviously with the increasing of hollow ratio. (2) the torsional capacity and elastic stiffness increase with the increasing of nominal steel ratio. (3) the torsion capacity of CFDST improves around 20% comparing with that of the reference double skin hollow steel tubes (DSHT), which shows that concrete played a significant role in resisting the torsional loading. For square specimens, it can be seen from Fig. 3(2a) that the torsional capacity and elastic stiffness increase as nominal steel ratio increases. Torque (T) versus torsional rotation angle (θ) curves of the two CFDST specimens and CFST specimen which have the same outer steel tube and concrete are shown in Fig. 3(2b). The torsional capacities of specimens (Tue), which are determined as the values of torque corresponding to the points where the maximum
H. Huang et al. / Journal of Constructional Steel Research 90 (2013) 221–234
223
Table 1 Information of CFDST specimens. Section type
No.
Specimen label
Outer tube dimensions D(B) × tso (mm)
Inner tube dimensions d × tsi (mm)
χ
fsyo (MPa)
fsyi (MPa)
fcu (MPa)
αn
Tue (kN · m)
Tuc1 (kN · m)
Tuc1 / Tue
Tuc2 (kN · m)
Tuc2 / Tue
1 2 3 4 5 6 7 1 2 3 4 5
CO1I1 CO1I2 CO2I1 CO2I2 CO3I1 CO3I2 HCO3I2 SO4I3 SO5I3-1 SO5I3-2 SO6I3 SO5
Φ165 Φ165 Φ165 Φ165 Φ165 Φ165 Φ165 □-160 □-160 □-160 □-160 □-160
Φ42 Φ75 Φ42 Φ75 Φ42 Φ75 Φ75 Φ60 Φ60 Φ60 Φ60 –
0.27 0.48 0.27 0.48 0.27 0.48 – 0.4 0.4 0.4 0.4 0
260.0 260.0 286.4 286.4 365.6 365.6 365.6 281 281 281 281 281
326.6 355.4 326.6 355.4 326.4 355.4 355.4 275 275 275 275 –
50 50 50 50 50 50 – 60 60 60 60 60
0.08 0.08 0.10 0.10 0.12 0.12 – 0.08 0.11 0.11 0.14 0.11
24.6 33.2 32.3 42.1 48.8 54.3 43.6 34.8 44.4 47.0 48.8 38.0
25.4 33.8 31.8 40.0 46.3 52.2 44.7 33.2 41.6 41.6 46.6 43.9
1.033 1.018 0.985 0.950 0.949 0.961 1.025 0.954 0.937 0.885 0.955 1.155 0.984 0.0693
24.9 31.2 33.0 39.2 45.0 51.2 45.6 32.7 40.1 40.1 47.8 38.3
1.013 0.939 1.020 0.930 0.922 0.943 1.046 0.940 0.902 0.852 0.979 1.008 0.958 0.0588
× × × × × × × × × × × ×
3 3 4 4 4.6 4.6 4.6 3 4 4 5 4
× × × × × × × × × × ×
3 5 3 5 3 5 5 3 3 3 3
Mean COV
shear strain of the cross section is 0.01 [20], are listed in Table 1. Comparing the specimens CO3I2 and HCO3I2, it can be found that the Tue for CFDST specimen is about 24.5% higher than for the respective unfilled one. In order to investigate the effects of torsional carried capacity by filling with concrete, the ratios of the ultimate torque of specimens filled with concrete (Tue) and the ultimate torque of corresponding outer steel tubes (Tuc,outer) are shown in Fig. 4, where the ultimate
8
torque of corresponding outer steel tubes (Tuc,outer) can be calculated by Wsoτyo, Wso is torsional section modulus of outer steel tube, given by π(D4 − (D − 2tso)4)/(16D) and 2tso(B − tso)2 for circular and square sections, respectively. The shear yield strength of outer steel tube is given by τ yo ¼ p1ffiffi3 f yo . It was found that, within the limitation of the current test, the Tue for CFDST specimens with circular section is about 20%–80% higher than that for the unfilled ones and for specimens with square section the improved torsional capacity is about 20%–50% higher.
9
7 2
2 3
3
5 13
2
4
10
6 13
2
5 11
12
1
(a) Schematics view of the test setup
(b) The measurementof angles
(c) A picture of the testsetup Fig. 1. Overview of the test setup.
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CO1I1 CO1I2 CO2I1
CO2I2
CO3I1
CO3I2
HCO3I2 SO4I3
Partial enlargement
SO5I3-1
SO5I3-2
SO6I3
SO5
Partial enlargement
Weld cracking
(a) Circular sections
(b) Square sections
(1) Outer steel tube of CFDST specimen
cracks
(a) Circular sections
(b) Square sections (2)After removal of partial outer steel tube Fig. 2. Failure modes of tested specimens.
3. FEA model and analysis 3.1. FEA model A FEA model was established by Han et al. [20] for the analysis of CFST members under torsion based on the commercial FEA package, ABAQUS. The same model is used to investigate the torsion behavior of CFDST columns in this paper. In the mode, both the steel tubes and the sandwiched concrete of the CFDST members were discretized by 8-node brick elements. The adopted element meshes for both circular and square sections and boundary conditions are shown in Fig. 5, where all the degrees of bottom end plate are constrained, and the top end plate is free. The torsional loading in the z direction is applied to the top surface in an appointed torsional angle. The contact model for CFST column was used for CFDST column in Huang et al. [7], and a fairly good agreement was obtained with test results. This contact model is also used in this paper. In normal direction hard contact is applied, and in the tangential direction the Mohr–Coulomb friction model is adopted. Details of the contact model can be found in Huang et al. [7]. 3.2. Verifications of the FEA model The measured torque (T) versus rotation angle (θ) curves are compared in Fig. 6 with the ones calculated from the results of the FEA
analyses. It can be seen that, generally good agreement is obtained between the calculated and tested results. As there is no descending branch in the curves, the torque corresponding to the point where the shearing strain reaches the value of 0.01 [20], is regarded as torsional capacity Tue. The torsional capacity predicted by FEA model (Tuc1) and the measured value (Tue) are listed in Table 1. For circular members, the mean value and the standard deviation of Tuc1 / Tue are 0.989 and 0.037, respectively, and for square members, the values are 0.980 and 0.104, respectively. 3.3. Typical failure mode Fig. 7 shows the predicted typical failure modes of outer and inner steel tubes of CFDST member as well as the corresponding double skin hollow steel tubes (DSHT) subjected to pure torsion, respectively. The data of CFDST specimens used for calculations are: D(B) = 400 mm, d = 191 mm, tso = 9.3 mm, tsi = 3.18 mm, λ = 40, χ = 0.5, αn = 0.1, fsyo = fsyi = 345 MPa, fcu = 60 MPa. It can be seen from Fig. 7 that there is a significant difference between failure modes of CFDST and DSHT, i.e., no obvious buckling occurs in inner and outer steel tubes of CFDST member, which shows more ductile behavior. Inward buckling was observed for the outer steel tube of DSHT, whereas inward buckling is prevented by the concrete in the CFDST members.
H. Huang et al. / Journal of Constructional Steel Research 90 (2013) 221–234
225
60 50
CO1I1 CO1I2
T (kN·m)
40
CO2I1
30
CO2I2 CO3I1
20 CO3I2 HCO3I2
10 0 0
2
4
6
8
10
12
θ (°)
60
60
45
45
T (kN·m)
T (kN·m)
(1) Circular sections
30 SO4I3 ( α n= 0.08) SO5I3-1 (α n= 0.11) SO6I3 ( α n= 0.14)
15
30 SO5I3-1(CFDST) SO5I3-2(CFDST) SO5(CFST)
15
0
0 0
1
2
3
4
5
0
1
2
3
4
5
θ (°)
θ (°)
(a) Influence of nominal steel ratio
(b) CFDST and CFST specimens
(2) Square sections Fig. 3. Diagrams of torque versus torsional rotation angle curves for all specimens.
3.4. Complete curves of torque versus rotation angle The typical torque (T) versus torsional rotation (θ) curve of CFDST obtained from the FEA model is shown in Fig. 8. Fig. 9 shows the distributions of the shear stress (S13 in the graphs) in the cross sections of inner and outer steel tubes, as well as the sandwiched concrete at three points above. Fig. 10 shows shear stress (τ) versus torsional angle (θ) curves for typical torsion members in different positions of
the cross sections. The data of CFDST specimens used for calculations are: D(B) = 400 mm, d = 191 mm, tso = 9.3 mm, tsi = 3.18 mm, λ = 40, χ = 0.5, αn = 0.1, fsyo = fsyi = 345 MPa, fcu = 60 MPa. The calculated T versus θ diagram can generally be divided into three stages OA, AB and BC, as shown in Fig. 8. At the end of stage A yielding of outer steel tube occurs and the shear stress of the inner steel tube is half of that of the outer steel tube, as shown in Fig. 9. This is because that the inner steel tube is closer to the center of the cross section. In the first
2
2 CO1I1 CO1I2 CO2I1
1
CO2I2 CO3I1
0.5
CO3I2
0
1.5
Tue/ Tuc,outer
Tue/ Tuc,outer
1.5
SO4I3 SO5I3-1
1
SO5I3-2 SO6I3 SO5
0.5 0
(a) Circular sections
(b) Square sections
Fig. 4. Ratios of the ultimate torque of specimens filled with concrete (Tue) and the ultimate torque of respective outer steel tubes (Tuc,outer).
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Outer steel tube
Torsional load
Torsional load Y Top end plate X
Z
(Free boundary)
Inner steel tube Concrete
(a) Meshes of circular section
Z
Outer steel tube Y
Y
Z
X X
Bottom end plate Inner steel tube Concrete
(b) Meshes of square section
(Fixed boundary conditions)
(c) General view of circular member
(d) General view of square member
Fig. 5. Element meshes and boundary conditions.
stage the shear stress of sandwiched concrete increases more rapidly as shown in Fig. 10. The torque grows linearly with the increasing of torsional angle. From the yielding at point A an elastic–plastic stage AB occurs and at point B the shear strain of extreme fiber reaches the value around 0.01. During this stage, with the increasing of the torque, the concrete cracks and its volume begins to increase which then leads to the confinement activation provided by the outer steel tube. The confinement effect increases with the increasing torsional deformation. The outward expansion speed of sandwiched concrete is faster than towards inner steel tube, thus no confining compressive stress appears in the concrete. Strain hardening appears in stage BC and torque (T) as well as the shear stress increase moderately, while the torsional angle (θ) increases rapidly. The load is still increasing during this stage as the steel tubes have some reserve in resisting the torque due to the strain hardening of steel. Due to the confinement provided by the outer steel tube, the cracked concrete can still resist torque. The sandwiched concrete resists about 5% of the torque of the composite member, and in addition it provides support to the outer steel tube. From Figs. 9 and 10 it is also obvious that: 1) The shear stress is greatest furthest away from the center of the cross section. 2) Circular and square sections exhibited similar behavior, except that for square sections the diagram is smoother within the strain hardening stage BC. This is attributed to the fact that confinement for sandwiched concrete provided by square section is weaker than that provided by circular section when the warping deformation is very large, especially on the mid-width of the square section, which is similar to the conclusion drawn by Huang et al. [7]. Fig. 11 shows the comparisons of torques (T) versus torsional angle (θ) diagrams for CFDST, sandwiched concrete and steel tubes of CFDST and DSHT, respectively. It can be found that outer and inner steel tubes carry the majority of the torsional loads, while the sandwiched concrete carries 5 to 6% of the torsional loads. Comparing the curves of steel tubes of CFDST and DSHT, the torsional capacity of steel tubes of CFDST is higher than that of DSHT, although they have the same dimensions and materials. This is due to the sandwiched concrete that effectively prevents the buckling of outer steel tube of CFDST.
Comparing the torque diagrams of the composite members with different hollow ratios shown in Fig. 12, it is seen that torques carried by inner and outer steel tubes increase with the increasing of hollow ratio and the contribution of the concrete decreases. The reason is that the area of concrete reduces, and the area as well as the torsional section modulus of inner steel tube increase with the increasing of hollow ratio. 3.5. Interaction between the steel tubes and the sandwiched concrete Fig. 13 shows the confinement stress (p1) versus torsional angle (θ) curves of the composite sections for different hollow ratios. It can be seen that, 1) for circular sections, p1 increases with the increasing of θ in the whole loading process. The confinement stress (p1) of circular section is caused by outward expansion of sandwiched concrete. The increase of torsional angle (θ) will lead to larger deformation of sandwiched concrete. The outer circular steel tube can provide enough confinement to the sandwiched concrete. 2) For square sections, the confinement stress (p1) is obviously greater in the section corners than in the mid-width of the section. The outer steel tube provides less confinement to the sandwiched concrete at locations farther away from the corner of the square section. 3) Confinement stress (p1) decreases with the increasing hollow ratio, because the reduced concrete area causes reduction of expansion in the volume of concrete. 4. Parametric analysis and simplified model 4.1. Parametric analysis Possible parameters that influence torque (T) versus rotation angle (θ) relationship of CFDST columns include hollow ratio (χ), nominal steel ratio (αn), strength of outer steel tube (fsyo), strength of concrete (fcu), strength of inner steel tube (fsyi) and width to thickness ratio of inner steel tube (d / tsi). Fig. 14 shows the effects of different parameters on the T versus θ relations of columns with circular inner and outer hollow sections. The basic data of these examples for calculations
2
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6
Calculated Measured
0
8
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4
6
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θ (°)
θ (°)
θ (°)
(a) CO1I1
(b) CO1I2
(c) CO2I1
60 50 40 30 20 10 0
Calculated Measured
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60 50 40 30 20 10 0
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60 50 40 30 20 10 0
Calculated Measured
0
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T (kN·m)
T (kN·m)
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T (kN·m)
Calculated Measured
T (kN·m)
60 50 40 30 20 10 0
T (kN·m)
T (kN·m)
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6
60 50 40 30 20 10 0
Calculated Measured
0
8
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θ (°)
θ (°)
θ (°)
(d) CO2I2
(e) CO3I1
(f) CO3I2
60 50 40 30 20 10 0
8
8
Calculated Measured
0
2
4
6
8
θ (°)
(g) HCO3I2
Calculated Measured
1
2
3
4
Calculated Measured
0
5
1
2
3
4
60 50 40 30 20 10 0
Calculated Measured
0
5
1
2
3
4
θ (°)
θ (°)
θ (°)
(a) SO4I3
(b) SO5I3-1
(c) SO5I3-2
60 50 40 30 20 10 0
T (kN·m)
0
60 50 40 30 20 10 0
T (kN·m)
T (kN·m)
60 50 40 30 20 10 0
T (kN·m)
T (kN·m)
(1) Circular sections
Calculated Measured
0
1
2
3
4
5
60 50 40 30 20 10 0
Calculated Measured
0
1
2
3
θ (°)
θ (°)
(d) SO6I3
(e) SO5 (2) Square sections
Fig. 6. Comparison of calculated and tested T–θ curves.
4
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5
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(a) Outer steel tube of double skin hollow tubes
(c) Inner steel tube of double skin hollow tubes
(b) Outer steel tube of CFDST
(d) Inner steel tube of CFDST
(1) Circular sections
(a) Outer steel tube of double skin hollow tubes
(b) Outer steel tube of CFDST
(c) Inner steel tube of double skin hollow tubes
(d) Inner steel tube of CFDST
(2) Square sections Fig. 7. Comparisons of failure mode between CFDST and double skin hollow steel tubes subjected to pure torsion.
are as follows: D = 400 mm, tso = 9.3 mm, d = 191 mm, tsi = 3.18 mm, λ = 40, fsyo = fsyi = 345 MPa, fcu = 60 MPa, χ = 0.5. Some explanations are given below on the influence of six parameters on torque versus rotation angle curves with columns of circular inner and outer hollow sections as an example. Similar conclusions can be drawn for square members.
T
B
A
O Fig. 8. Typical T–θ curve.
C
Torsional capacity increases as the nominal steel ratio (αn) and the strength of outer steel tube (fsyo) increase. The increasing of nominal steel ratio (αn) can also improve the elastic stiffness. With the increasing the strength of concrete (fcu) torsional capacity increases only slightly, and this is attributable to the contribution of the sandwiched concrete taking only 5 to 6% of the torque. For columns with bigger hollow ratio (χ), such as χ is equal to 0.75, the effect of the strength of concrete (fcu) on torsional capacity is weaker, for the reason of the decreased proportion of the sandwiched concrete. When hollow ratio (χ) is less than 0.5, strength (fsyi) and width to thickness ratio (d / tsi) of inner steel tube have little effect on T versus θ curves. The load carried by the inner steel tube increases with the increasing hollow ratio (χ). Thus when hollow ratio (χ) exceeds 0.5, torsional capacity of member increases with the increasing strength of the inner steel tube (fsyi) and the decreasing width to thickness ratio of the inner steel tube (d / tsi). It can be concluded from Fig. 14 that hollow ratio (χ) has a significant effect on torsional capacities of CFDST columns. Compared with the torque carried by concrete, the torque carried by the inner steel tube is greater. When hollow ratio (χ) increases, torsional capacity of component increases due to the increasing of the area of inner steel tube.
H. Huang et al. / Journal of Constructional Steel Research 90 (2013) 221–234 S,S13 (Average: 75%)
S,S13 (Average: 75%)
(a) Point A
229
S,S13 (Average: 75%)
(b) Point B
(c) Point C
(1) Inner and outer steel tubes of circular sections S,S13 (Average: 75%)
S,S13 (Average: 75%)
(a) Point A
S,S13 (Average: 75%)
(b) Point B
(c) Point C
(2) Concrete core of circular sections S,S13 (Average: 75%)
S,S13 (Average: 75%)
S,S13 (Average: 75%)
(a) Point A
(b) Point B
(c) Point C
(3) Inner and outer steel tubes of square sections S,S13 (Average: 75%)
S,S13 (Average: 75%)
(a) Point A
S,S13 (Average: 75%)
(b) Point B
(c) Point C
(4) Concrete core of square sections Fig. 9. The distributions of shear stress (τ) of steel tubes and concrete (unit: MPa) at three stages (A, B and C) defined in Fig. 8.
4.2. Design formulas Based on the parametric study presented above, the formula for calculating composite member strength under torsion can be obtained by regression analysis. Torsional capacity of the CFDST can be calculated by Eq. (1), in which γtWsctτscy is the torque carried by outer steel tube and concrete, and Wsiτyi is the torque carried by the inner steel tube. τscy is strength of the composite section of outer steel tube and concrete under torsion, which can be calculated by Eqs. (2a) and (2b). When the hollow ratio χ is equal to 0, a CFST member follows and Eq. (1) becomes the same as the
formula for calculating the torsional strength of CFST given in Han et al. [20]. T uc2 ¼ γt W sct τ scy þ W si τyi
ð1Þ
For CFDST members with circular sections, 2:33 0:134 ξ f scy : τscy ¼ 0:422 þ 0:313α n
ð2aÞ
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20
3 2
τ (MPa)
15
3 2
Point 1 Point 2
1
Point 3 10 5
Point 1 Point 2
1
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τ (MPa)
20
Point 3 10 5
0 0
A
2
B
C
4
0 6
0
A
B
2
C
4
θ (°)
θ (°)
(a) Circular sections
(b) Square sections
6
Fig. 10. Shear stress (τ) versus rotation angle (θ) relation in different position of the cross sections.
800
800
700
700
CFDST
600
500
T (kN·m)
T (kN·m)
600
CFDST
Steel tubes of CFDST
400
Steel tubes of DSHT
300 200
500
Steel tubes of CFDST Steel tubes of DSHT
400 300 200
Sandwiched concrete
100
Sandwiched concrete
100
0
0 0
2
4
6
0
2
4
θ (°)
θ (°)
(a) Circular sections
(b) Square sections
6
Fig. 11. Comparisons of the torques (T) carried by CFDST, sandwiched concrete, and steel tubes of CFDST and DSHT respectively versus rotation angle (θ) relations.
For CFDST members with square sections,
ð2bÞ
700
800
600
700
500
600
T (kN·m)
T (kN·m)
2:33 0:25 ξ f scy τscy ¼ 0:455 þ 0:313α n
where, fscy is axial compression strength of outer steel tube and concrete, fscy = C1χ2fyo + C2(1.14 + 1.02ξ)fck for circular sections; fscy = C1χ2fyo + C2(1.18 + 0.85ξ)fck for square sections. Coefficient C1 and C2 are equal to α / (1 + α) and (1 + αn) / (1 + α), respectively. α is steel ratio of member, which is given by (α = Aso / Ac).
=0.75
400 300 200 100
=0.5
Steel tubes of CFDST
=0 =0 =0.5 =0.75
Concrete
=0.75
500
Steel tubes of CFDST
=0.5
400
=0
300
=0 =0.5 =0.75
200
Concrete
100
0
0 0
2
4
6
0
2
4
θ (°)
θ (°)
(a) Circular sections
(b) Square sections
Fig. 12. The comparisons of torque (T) carried by concrete and steel tubes with different hollow ratios.
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40
30 p1
25
35
20
p 1(MPa)
p 1(MPa)
30
15 10
=0
5
=0 =0.5 =0.75
On the corner
=0 =0.5 =0.75
On the mid-width
25 20 15 10
=0.5
231
p1
5
=0.75
0
0 0
2
4
6
0
2
4
θ (°)
θ (°)
(a) Circular sections
(b) Square sections
6
Fig. 13. Confinement stress p1 between outer steel tube and concrete in the cross section of columns with different hollow ratios.
Wsct is torsional section modulus of outer steel tube and concrete, given by π(D4 − d4)/(16D) and kW0sct for the composite members with circular and square sections, respectively. W0sct is torsional section
modulus of CFST member with square sections, given by 0.208B3 [20]. Coefficient k is related to hollow ratio, and it can be incorporated in coefficient γt. Wsi is torsional section modulus of inner steel tube, given
Fig. 14. Effects of different parameters on T versus θ relations (circular section as an example).
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Fig. 14 (continued).
by π(d4 − (d − 2tsi)4)/(16d). The shear yield strength of inner steel tube is given by τ yi ¼ p1ffiffi3 f yi . Fig. 15 shows the relations of factor γt with the confinement factor (ξ) and hollow ratio (χ). Formulae for γt can be obtained by using the regression analysis method. For CFDST members with circular sections, γ t ¼ ð−0:22χ þ 0:273Þ ln ðξÞ−0:133χ þ 1:29:
ð3aÞ
For CFDST members with square sections, 2
γ t ¼ ð−0:333χ þ 0:26Þ ln ðξÞ−1:124χ þ 0:364χ þ 1:434:
ð3bÞ
The validity limits of Eq. (1) are: χ = 0 to 0.75; αn = 0.05 to 0.2; fyo = 235 MPa to 700 MPa; fyi = 235 MPa to 700 MPa, d / tsi = 30 to 90; and fcu = 30 MPa to 90 MPa. For the DSHT specimen, torsional capacity (Tuc2) can be calculated by Eq. (4), in which Wyoτyo is the torque carried by outer steel tube, and Wsiτyi is the torque carried by the inner steel tube. T uc2 ¼ W so τyo þ W si τyi
ð4Þ
Wso is torsional section modulus of outer steel tube, given by π(D4 − (D − 2tso)4)/(16D). The shear yield strength of outer steel tube is given by τ yo ¼ p1ffiffi3 f yo . Figs. 16 and 17 respectively show comparisons between torsional capacity calculated by simplified model (Tuc2) and FEA model (Tuc1), and comparisons between simplified model (Tuc2) and test results (Tue). The values of Tue, Tuc1 and Tuc2 are also listed in Table 1. The mean value and the coefficient of variation (COV) of Tuc1 / Tue are 0.984 and 0.0693, whereas the mean value and the COV of Tuc2 / Tue are 0.958 and 0.0588. The torsional capacity (Tuc2) of the DSHT specimen calculated by Eq. (4) and the torsional capacity (Tuc1) predicted by FEA model are listed in Table 1. The values of Tuc1 and Tuc2 overestimate the measured value by 3% and 5%, respectively. 5. Conclusions Based on the results of present study, the following conclusions can be drawn: (1) The present experimental results show that the torsion capacity of CFDST improves about 20% comparing with that of DSHT, due to the existence of sandwiched concrete. With the increasing of hollow ratio and nominal steel ratio, torsional capacity increases.
2
1.5
1.5
1
1
0.5
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0.5
1
1.5
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0.5
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1
1
t
t
1
1.5
2
(b)
(a) 2
0.5
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(a) Circular sections
0 0
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T uc1(kN·m)
0.5
0
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T uc2(kN·m)
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t
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1400 0
0.5
1
1.5
2
1200
(d)
1000
T uc2(kN·m)
(c) (1) Circular sections 2
2
1.5
1.5
1
1
800 600
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t
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200
0.5
0
0
0 0
0.5
1
1.5
2
0
0.5
1
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0
2
200 400 600 800 1000 1200 1400
T uc1(kN·m)
(b)
2
2
1.5
1.5
1
1
t
0.5
(b) Square sections Fig. 16. Comparisons of torsional capacity estimated by the simplified and FEA models.
0.5
0
0 0
0.5
1
1.5
2
0
(c)
0.5
1
1.5
2
of the strength (fsyi) and width to thickness ratio of inner steel tube (d / tsi) become significant. (4) Simplified models were derived in this paper to predict the torsional capacity of CFDST members. The capacities predicted by the simplified method are in good agreement with the experimental results and those calculated using FEA modeling.
(d)
Fig. 15. γt versus ξ relations.
(2) The torque versus torsional angle curves calculated by finite element method in this paper show good agreement with test results. Torque versus torsional rotation curve of CFDST can be generally divided into three stages, and outer steel tube provides enough confinement to the sandwiched concrete. (3) Six important parameters that influence the torque versus torsional rotation curves of the composite members were investigated. It was found that nominal steel ratio (αn), strength of outer steel tube (fsyo) and hollow ratio (χ) have important influence on the curves. When hollow ratio (χ) exceeds 0.5, the effect
T uc2(kN·m)
(2) Square sections
80
80
60
60
T uc2(kN·m)
t
(a)
40 20 0
40 20 0
0
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40
60
80
0
20
40
60
80
T ue(kN·m)
T ue(kN·m)
(a) Circular sections
(b) Square sections
Fig. 17. Comparisons of torsional capacity from the test results and estimated by the simplified model.
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Acknowledgments The research reported in the paper was supported by the National Natural Science Foundation of China (No. 51008122) as well as by the Tsinghua University Initiative Scientific Research Program (No. 2011THZ03). The financial support are highly appreciated. References [1] Zhao XL, Han LH. Double skin composite construction. Prog Struct Eng Mater 2006;8(3):93–102. [2] Wei S, Mau ST, Vipulanandan C, Mantrala SK. Performance of new sandwich tube under axial loading: experiment. J Struct Eng ASCE 1995;121(12):1806–14. [3] Zhao XL, Grzebieta RH, Elchalakani M. Tests of concrete-filled double skin CHS composite stub columns. Steel Compos Struct Int J 2002;2(2):129–46. [4] Zhao XL, Han BK, 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] Zhao XL, Grzebieta RH. Strength and ductility of concrete filled double skin (SHS inner and SHS outer) tubes. Thin-Walled Struct 2002;40(2):199–233. [6] Elchalakani M, Zhao XL, Grzebieta R. Tests on concrete filled double-skin (CHS outer and SHS inner) composite short columns under axial compression. Thin-Walled Struct 2002;40(5):415–41. [7] 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. [8] Uenaka K, Kitoh H, Sonoda K. Concrete filled double skin circular stub columns under compression. Thin-Walled Struct 2010;48(1):19–24.
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