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Behavior of thin-walled dodecagonal section double skin concrete-filled steel tubes under bending
Thin-Walled Structures 98 (2016) 293–300
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Behavior of thin-walled dodecagonal section double skin concrete-filled steel tubes under bending Ju Chen a, Jun Wang a, Fang Xie b,n, Wei-liang Jin a a b
Department of Civil Engineering, Zhejiang University, China Yuanpei college, Shaoxing University, China
art ic l e i nf o
a b s t r a c t
Article history: Received 7 April 2015 Received in revised form 12 August 2015 Accepted 3 October 2015
The behavior of thin-walled dodecagonal section double skin concrete-filled steel tubes under bending was studied in this paper. Both experimental investigation and finite element analysis (FEA) were carried out. A total of 7 specimens were tested with the beam length of 2000 mm. The width to thickness ratio of the outer steel tube ranged from 75 to 133. The load–displacement curves, failure mode and ultimate capacity of test specimens were obtained. A finite element model was developed for the thin-walled dodecagonal section double skin concrete-filled steel tube subjected to bending. The FEA results were verified against the test results and parametric study was conducted using the verified model. In addition, the suitability of Han's method, Uenaka's method and proposed method for thin-walled circular section double skin concrete-filled steel tubes subjected to bending was also evaluated. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Bending Concrete-filled steel tube Dodecagonal section Double skin
1. Introduction Concrete Filled Double Skin Tubes (CFDST) are composite members which consist of an inner and outer steel tubes with the concrete filled between the steel tubes [1]. This kind of composite columns have been recognized to have a series of advantages, such as high strength and bending stiffness, good seismic and fire performance [2]. CFDST columns also holds the characteristics of Concrete-filled steel tubular (CFT), but have less self-weight. For the flexural properties of CFDST, some scholars have made a lot of research work in recent years, Zhao [3] studied the mechanical properties of square section CFDST subjected to pure bending; Uenaka et al. [4,5] reported the behavior of circular section CFDST under pure bending; Shimizu [6] carried out a fourpoint bending test on the circular section CFDST with shear connecters between the inner and outer tubes; Han et al. [7] studied the ductility and energy dissipation ability of CFDST beams with circular and square cross section. There were experimental and analytical studies have been conducted on the bending behavior of concrete-filled steel tubes (CFTs). Moon et al. [8] and Lu et al. [9] preformed finite element analysis (FEA) to study the flexural performance of circular section CFTs. Han et al. [10,11] studied the flexural behavior of rectangular and circular section CFTs and the design method was proposed; Jiang et al. [12] carried out a series of bending tests of thin-walled n
Corresponding author. Fax: þ 86 575 88319253. E-mail address: [email protected] (F. Xie).
http://dx.doi.org/10.1016/j.tws.2015.10.002 0263-8231/& 2015 Elsevier Ltd. All rights reserved.
concrete-filled steel tubes and developed an analytical model. Lu et al. [13] conducted analytical study on the flexural performance of circular section thin-walled CFTs. In retrospection of the former study about the CFDST specimens, investigation mainly focused on the circular and square section specimens. Chen et al. [14] reported the column tests of dodecagonal section double skin concrete-filled steel tubes. The dodecagonal section double skin concrete-filled steel tube is expected to have better local buckling resistance compared with square section specimens. It is also expected to have the advantage of easy fabrication and flat surface for connection compared with circular section specimens. There are practical applications of dodecagonal CFDST in electronic transmission poles in Zhejiang province, China. In this study, the behavior of dodecagonal section double skin concrete-filled steel tube under bending was studied. Both experimental investigation and finite element analysis were carried out. The suitability of current design method of circular section CFDST members were evaluated for dodecagonal section specimens.
2. Experimental investigation 2.1. Test specimens The tested specimens were fabricated by molding a flat steel plate into a dodecagonal shape, and then the ends of the steel tubes were cut to specified length of 2000 mm. The outside surface of inner steel tubes and insides surface of the outer steel tubes
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Nomenclature Ac Ace Asi Aso Di Do E L Mi Mo
cross-sectional area of concrete nominal cross section area of concrete, given by π(Do − 2tso)2 /4 cross-sectional area of inner tube cross-sectional area of outer tube outside diameter of inner tube outside diameter of outer tube elastic modulus of steel length of member ultimate bending capacity of the inner tube; composite ultimate bending capacity of the outer tube and the core concrete;
Table 1 Measured geometric size of test beams. Specimen
L (mm)
Do (mm)
to (mm)
Di (mm)
ti (mm)
DCS300-3-180-3 DCS400-3-240-3 DCS400-3-280-3 DCS300-4-180-3 DCS300-4-180-3A DCS400-4-240-3 DCS400-4-280-3
2000 2000 2000 2000 2000 2000 2000
300.2 400.1 399.7 300.3 300.2 400.1 399.6
2.98 2.98 2.98 4.01 4.01 4.01 4.01
180.2 239.8 279.6 179.9 180.0 240.1 280.0
3.00 3.01 3.02 3.00 2.98 3.00 2.99
ti to Do/Di Do/to Di /ti Mu-U Mu-A Mu-H Mu-F Mue
thickness of inner tube thickness of outer tube outer diameter to inner diameter ratio diameter-to-thickness ratio of the outer tube diameter-to-thickness ratio of the inner tube ultimate bending moment calculated by the Uenaka's method ultimate bending moment calculated by the AISC method ultimate bending moment calculated by the Han's method ultimate bending moment calculated by the FEM method ultimate bending moment acquired from experiment
The tested specimens in this study were labeled such that the type of the specimens, outer diameter of outer steel tube, nominal thickness of outer steel tube, outer diameter of inner steel tube and nominal thickness of inner steel tube can be identified from the label. For example, the label “DCS400-4-280-3A” defines the specimen as follow:
The three letters indicate that the type of the specimen, where
the prefix letter “DCS” refers to dodecagonal section double skin concrete-filled steel tubes. The following three digits “400” indicate the outer diameter of the outer tube in mm. The following digit “4” is the nominal thickness of the outer steel tube in mm. The following three digits “280” indicate the outer diameter of the inner tube in mm. The following digit “3” is the nominal thickness of the inner steel tube in mm. The last character “A” refers to the repeated test specimen.
2.2. Test setup
Di
Do
Fig. 1. Size sketch diagram of a tested beam.
were brushed to remove any rust and loose debris present. Both the outer and inner steel tubes were placed centric. The selfcompacting concrete was cured without any vibration. During curing, a very small amount of longitudinal shrinkage occurred at the top of the specimens. High strength cement was used to fill this longitudinal gap before the welding of the top steel end plate. Two 20 mm thick steel plates were welded to both ends of the specimens to ensure full contact between specimens and end bearing. The measured cross-section dimensions and specimen length for each test specimen are shown in Table 1. The cross section of dodecagonal section specimen is shown Fig. 1.
The specimen was simply supported on rollers and the load was applied to the specimen by means of a spreader. The span of each beam was 2000 mm, with a 100 mm extent portion overhang at each edge support. The load was thus slowly applied and monotonically increased until failure after some unloading–reloading cycles in the elastic domain. Displacement control was used to drive the 10,000 kN hydraulic testing machine at a constant speed of 1.0 mm/min for all test specimens. The usage of displacement control allowed the tests to be continued to the post-ultimate stage. A data acquisition system was used to record the applied load and the readings of the transducers at regular intervals during the tests. When the mid-span deflection of the specimens reached about 3% of the length of the specimen, tests stopped. Fourteen strain gauges were attached around the specimen at the mid-span. Among these fourteen strain gauges, seven were attached on the corner of the dodecagonal section while the other seven were attached on the flat portion of the dodecagonal section as shown in Fig. 2. Fig. 3 gives a general view of the instrumentations. The deflection were measured by displacement transducer (LVDT) located underneath the bottom flange at midspan. Two dial indications were used to measure the settlements of the test frame during the test. 3. Material properties Tensile coupon tests were conducted to obtain the material
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intervals during the tests. The material properties of the angle were provided by the supplier. The values of Young's modulus (Es), yield stress (fy), ultimate tensile strength (fu) based on a gauge length of 50 mm are shown in Table 2. The compressive strength (fcu) and elastic modulus (Ec) obtained on 150-mm concrete cubes at 28 days were 35 MPa and 33,560 MPa, respectively. The tests were conducted from 28 days after the casting of concrete.
4. Test results 4.1. Load–deflection curve
Fig. 2. Arrangement of the strain gauges.
Loading plate
Specimen
Bearing
The tested specimens all failed in a very ductile manner. Typical failure mode of tested specimen DCS300-3-180-3 is shown in Fig. 4. No tensile fracture and welding failure were observed on the test specimens. Local deformation was observed at the two loading points on the outer tube. The measured load vs. mid-span deflection curves of six test specimens are given in Fig. 5. (The data of specimen DCS300-3-180-3 was not recorded due to computer error). It is shown that the load–deflection curves of specimens having less steel/concrete ratio of cross section are smoother. Based on the observation during the tests processor and load vs. mid-span deflection curves, the specimens are considered to experience three stages under loading until failure. In the first stage: load vs. mid-span deflection curves of specimens approximately remain straight line. In the second stage: the load vs. midspan deflection curves began to show nonlinear behavior. At the end of the second stage, the outer steel tubes in the tension zone reach yielding. In the third stage: the load remain constant and large deformation occurs until failure of the test specimens. For specimens having the inner tube diameter of 280 mm, the load– deflection curves drop more rapidly after the peak load compared with other specimens. This may due to the smaller concrete/steel cross section area ratio. Fig. 6 shows initial part of load vs. mid-span deflection curves of test specimens, which reflects the behavior of specimens at the elastic stage under bending. It is shown that for specimens having the same diameter of outer and inner steel tubes, initial stiffness increases with the increasing wall thickness of outer steel tube, such as specimen DCS400-4-280-3 and DCS400-3-280-3. For specimens having the same outer steel tube, initial stiffness decreases with the increasing diameter of the inner steel tube, such as specimen DCS400-4-280-3 and specimen DCS400-4-240-3. 4.2. Load–strain curve
Fig. 3. Test setup.
Typical load–strain curves and corresponding initial part of specimens DCS400-4-240-3, DCS400-3-240-3, DCS300-3-180-3, DCS300-4-180-3 are shown in Figs. 7–10, respectively. From the
Table 2 Measured material properties of steel. Nominal thickness (mm)
E (MPa)
fy (MPa)
fu (MPa)
3 4
201,000 199,500
366 452
530 542
properties of steel tube used in the test specimens. The coupons were taken from the steel tubes in the longitudinal direction belonging to the same batch as the column test specimens. The coupon dimensions conformed to the Australian Standard AS 1391 [15] for the tensile testing of metals using 12.5 mm wide coupons. The coupons were also tested in accordance with the AS 1391 [15] in a displacement controlled testing machine using friction grips. A calibrated extensometer of 50 mm gauge length was used to measure the longitudinal strain. A data acquisition system was used to record the load and the readings of strain at regular
Fig. 4. Failure mode of test specimen DCS300-3-180-3.
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DCS400-3-240-3 DCS400-4-240-3 DCS400-3-280-3 DCS400-4-280-3 DCS300-4-180-3 DCS300-4-180-3A
1500
Load(kN)
1200 900 600 300
bucking occurs at the flat portion the outer steel tube in compressive zone, as shown in the column tests [14]. Fig. 11 shows strain distribution along the height of the cross section of specimens at the initial part of specimens DCS400-3280-3 and DCS400-3-240-3. The strain curves of the two specimens are similar. The line x¼ 0 represents the mid-height of the cross-section of specimen, whereas the positive value represents the compressive zone, the negative value represents the tension zone. With the load increasing, the neutral axis move from the position at x¼ 0 to the compressive zone. It is obvious that the strain development in the compressive zone is less than those in the tension zone, which could be explained by the contribution from the concrete in compression.
0 0
15
30
45
60
75
90
5. Finite element analysis
Displacement(mm) Fig. 5. Load–deflection curves of test specimens.
Fig. 6. Initial load–deflection curves of test specimens.
complete load–strain curves, it could be seen that the strain gauges at the bottom of specimen (strain gauge 13 and 14) exhibit nonlinearity earlier than the strain gauges at the top of the specimen (strain gauge 1 and 2). The reason is that the concrete resist the compressive force so that the tensile strain develops faster that the compressive strain. From the initial part of the load–strain curves, it could be concluded that the compressive and tensile strain is linear at the initial stage, which means the plane-section assumption is applicable. It is also can be seen that both the strain of the corner portion and flat portion of the outer steel tube remain linear in the initial part, which may mean there is no local
5.1. Finite element model and verification Finite element method was used to further study the test specimen and provide more data in this study. According to the Han's study [16], the core concrete under the confined state of the double skin concrete-filled tubes are the same as the concretefilled steel tubes when the hollow section ratio smaller than 0.8. Therefore, the confined concrete material model proposed by Han [18] was used in this study. The measured material properties were used in the finite element model. The inner and outer steel tubes are modeled by reduced-integration shell elements (S4R), while the concrete and the end plates are modeled by 8-node brick elements (C3D8R) [19]. The two end plates were tied with the inner and outer steel tube and they were contacted with the core concrete. The interactions that the inner and outer steel tubes with the core concrete could be modeled by contact interaction as described in Huang et al. [19] and Han et al. [20]. The developed finite element model is shown in Fig. 12. Following the test procedure, the beam was four-points loaded. In the finite element model, the support plate was modeled as a rigid body, whose motion is governed by the reference point. The reference point of the support plate was restrained against x, y and z directions displacement as well as y- and z- axes rotation but free to rotate about the x-axis. The loading plate was also modeled as a rigid body. The reference point of the loading plate was restrained against x and z directions displacement as well as y- and z- axes rotation but free to move in y directions and rotate about the xaxis. The finite element analysis results were compared with the test results as shown in Table 3. It is shown that the ultimate strengths agree with the test results well. The mean value of Nu-F/Nue is 1.07,
Fig. 7. Load–strain curves of test specimen DCS400-4-240-3. (a) Complete curve and (b) initial part.
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Fig. 8. Load–strain curves of test specimen DCS400-3-240-3. (a) Complete curve and (b) initial part.
Fig. 9. Load–strain curves of test specimen DCS300-3-180-3. (a) Complete curve and (b) initial part.
Fig. 10. Load–strain curves of test specimen DCS300-4-180-3. (a) Complete curve and initial part.
Fig. 11. Strain distribution of test specimens. (a) DCS400-3-280-3 and (b) DCS400-3-240-3.
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Load
Load
Table 4 Geometric size of specimens for FEA parametric study. Specimens
Fig. 12. Developed finite element model.
Table 3 Comparison of ultimate strengths obtained from test results with FEA results. Specimens
Mue
Mu-FEA
Mu-FEA/Mue
DCS300-3-180-3 DCS300-4-180-3A DCS300-4-180-3B DCS400-3-240-3 DCS400-3-280-3 DCS400-4-240-3 DCS400-4-280-3
165.4 204.6 207.0 295.5 254.7 387.8 317.4
173.0 211.2 211.2 324.6 275.4 409.8 374.4
1.046 1.032 1.020 1.098 1.081 1.057 1.180
Mean COV
1.074 0.047
FEM DCS300-4-180-3 DCS300-4-180-3A
900
Load(kN)
600
L (mm)
DCS300-2-150-3 DCS300-3-150-3 DCS300-4-150-3 DCS300-2-180-3 DCS300-3-180-3 DCS300-4-180-3 DCS300-2-210-3 DCS300-3-210-3 DCS300-4-210-3 DCS400-2-240-2 DCS400-2-240-3 DCS400-2-240-4 DCS400-3-240-3 DCS400-4-240-3 DCS400-2-280-2 DCS400-2-280-3 DCS400-2-280-4 DCS400-3-280-3 DCS400-4-280-3 DCS400-2-200-2 DCS400-2-200-3 DCS400-2-200-4 DCS400-3-200-3 DCS400-4-200-3 DCS500-2-300-3 DCS500-3-300-3 DCS500-4-300-3 DCS500-2-350-3 DCS500-3-350-3 DCS500-4-350-3 DCS500-2-250-3 DCS500-3-250-3 DCS500-4-250-3
2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 3000 3000 3000 3000 3000 3000 3000 3000 3000
Do (mm)
to (mm)
Di (mm)
ti (mm)
300 300 300 300 300 300 300 300 300 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 500 500 500 500 500 500 500 500 500
2.0 3.0 4.0 2.0 3.0 4.0 2.0 3.0 4.0 2.0 2.0 2.0 3.0 4.0 2.0 2.0 2.0 3.0 4.0 2.0 2.0 2.0 3.0 4.0 2.0 3.0 4.0 2.0 3.0 4.0 2.0 3.0 4.0
150 150 150 180 180 180 210 210 210 240 240 240 240 240 280 280 280 280 280 200 200 200 200 200 300 300 300 350 350 350 250 250 250
3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 2.0 3.0 4.0 3.0 3.0 2.0 3.0 4.0 3.0 3.0 2.0 3.0 4.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0
cross section area of concrete tube.
300
6. Design methods
0 0
20
40
60
80
Displacement(mm) Fig. 13. Comparison of load vs. displacement curves obtained from test results with FEA results.
with the corresponding COV of 0.018. The load vs. mid-span deflection curve obtained from the finite element analysis also agrees with the test results well, as shown in Fig. 13. 5.2. Parametric study Since the established model was proven correct by the verification against the test results, it is used to carry out parametric study. The parameters considered include: the diameter-to-thickness ratio of outer steel tube, the ratio of outer diameter to inner diameter of steel tube and the thickness of the inner steel tube. The geometric size of the modeled specimens is presented in Table 4. The ultimate strengths obtained from the FEA results are shown in Table 5. It is shown that the diameter-to-thickness ratio has significant influence on the ultimate strength. The ultimate strength of specimens decreases when the diameter-to-thickness ratio of the outer steel tube increases. The ultimate strength of specimens also decreases with the increment of the inner and outer dodecagonal width ratios. This may due to the reduction of
Design methods proposed by Han [16] and Uenaka [4] were also used to predict the ultimate strength of dodecagonal section CFDST specimens. It should be noted that those design methods are for CFDST specimens with circular sections. Current AISC standard [17] does not have provisions for concrete-filled double skin steel tubes. Therefore, a new method was proposed based on the AISC standard design method for concrete-filled steel tubes and steel tubes. In this proposed method, the ultimate strength was considered as the summary strengths of outer steel tube þconcrete tube (Mo) and inner steel tube (Mi), as shown in Eq. (1). 6.1. Proposed method The ultimate strength of CFDST specimens under bending could be calculated as follows:
Mn = Mo + Mi
(1)
According to AISC specification [17], for circular solid concrete filled steel tube, if the diameter-to-thickness ratio is less than λ p ¼0.09E/fy, we call it compact section and do not need to consider the local stability; if the diameter-to-thickness ratio is between λ p ¼0.09E/fy and λ r ¼ 0.31E/fy, we call it non-compact section; otherwise we call it slender section. For compact section,
Mo = Mp For non-compact section,
(2)
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Table 5 Comparison of ultimate strengths obtained from design predictions with FEA results. Specimens
Mu-F
DCS300-2-150-3 DCS300-3-150-3 DCS300-4-150-3 DCS300-2-180-3 DCS300-3-180-3 DCS300-4-180-3 DCS300-2-210-3 DCS300-3-210-3 DCS300-4-210-3 DCS400-2-240-2 DCS400-2-240-3 DCS400-2-240-4 DCS400-3-240-3 DCS400-4-240-3 DCS400-2-280-2 DCS400-2-280-3 DCS400-2-280-4 DCS400-3-280-3 DCS400-4-280-3 DCS400-2-200-2 DCS400-2-200-3 DCS400-2-200-4 DCS400-3-200-3 DCS400-4-200-3 DCS500-2-300-3 DCS500-3-300-3 DCS500-4-300-3 DCS500-2-350-3 DCS500-3-350-3 DCS500-4-350-3 DCS500-2-250-3 DCS500-3-250-3 DCS500-4-250-3
125.5 163.5 235.7 123.5 173.0 211.2 133.6 167.4 226.1 208.7 234.3 278.1 324.6 409.8 200.8 226.4 263.3 275.4 374.4 204.5 233.2 280.7 298.5 420.6 389.1 491.2 675.3 393.3 487.7 658.6 365.5 491.3 622.6
Mu-H
Mu-U
Mu-Pro
Mu-H/Mu-F
Mu-U/Mu-F
Mu-Pro/Mu-F
118.5 146.0 199.7 130.0 156.9 210.4 139.5 165.7 218.6 227.1 252.0 300.0 300.3 401.6 221.8 248.4 302.1 317.3 409.8 208.5 228.6 267.3 278.4 373.5 424.5 501.3 648.5 420.6 530.5 674.0 382.9 462.7 612.4
95.0 123.5 182.5 98.1 127.7 190.9 106.7 137.2 204.4 169.5 183.0 197.5 233.7 342.7 168.7 192.2 217.6 245.3 343.6 177.6 184.7 190.0 234.0 334.9 302.9 379.8 544.7 307.3 388.0 568.2 313.4 391.3 544.9
63.2 90.2 137.9 71.5 98.4 146.1 81.1 108.1 150.2 114.1 119.8 152.2 165.6 242.5 113.2 136.6 180.2 182.4 250.4 104.6 117.4 142.2 151.2 228.1 207.7 252.3 358.1 212.4 278.3 384.2 182.8 256.4 335.9
0.944 0.893 0.847 1.053 0.907 0.996 1.044 0.990 0.967 1.088 1.076 1.079 0.925 0.980 1.105 1.097 1.147 1.152 1.095 1.020 0.980 0.952 0.933 0.888 1.091 1.021 0.960 1.069 1.088 1.023 1.048 0.942 0.984
0.757 0.755 0.774 0.794 0.738 0.904 0.799 0.820 0.904 0.812 0.781 0.710 0.720 0.836 0.840 0.849 0.826 0.891 0.918 0.868 0.792 0.677 0.784 0.796 0.778 0.773 0.807 0.781 0.796 0.863 0.857 0.796 0.875
0.504 0.552 0.585 0.579 0.569 0.692 0.607 0.646 0.664 0.547 0.511 0.547 0.510 0.592 0.564 0.603 0.684 0.662 0.669 0.511 0.503 0.507 0.507 0.542 0.534 0.514 0.530 0.540 0.571 0.583 0.500 0.522 0.540
1.01 0.076
0.81 0.070
0.57 0.101
Mean Cov
Mo = Mp − (Mp − My)⋅(
λ − λp λr − λp
)
For slender section
(3)
For slender section, more detailed method can be acquired from AISC specification [17]. where Mo is the combination ultimate bending moment of outer tube and the core concrete; Mi is the ultimate strength of the inner steel tube under bending; Mp is the moment corresponding to plastic stress distribution over the composite cross section; My is the capacity calculated by the elastic method; and λ is the diameter-to-thickness ratio of the steel tube. For Mi , different diameter-to-thickness ratio usually have different computing methods, according to the definition of AISC specification [17], if the diameter-to-thickness ratio λ ¼D/t of steel tube is less than λp ¼ 0.09E/fy, we call it compact section; however, if λ is between λp and λr ¼ 0.31E/fy, we call it non-compact section; whereas, we call it slender section. With the material properties of E ¼200,000 MPa, fy ¼345 MPa, thus 0.09E/fy ¼52.2, 0.31E/fy ¼179.7 could be obtained. However, the diameter-to-thickness ratio of the inner tubes of all the specimens were range from 60 to 93, so all of the inner tubes in this test were non-compact section. For compact section
Mi = f y ⋅Z
(4)
For non-compact section
Mi = {
0.021E + f y }S D /t
(5)
Mi = {
0.33E }⋅S D /t
(6)
where S is the elastic moment of inertia of the steel section and Z is the plastic bending modulus of steel section, for a circular steel D3 − (D − 2t )3
tube, Z = 6 Design strengths predicted by using the Han's method [16] are slightly unconservative compared with the test results (Table 6) and FEA results. The mean values of Mu-H/Mu-F and Mu-H/Mue are 1.01 and 1.08, respectively. The predictions obtained from equations proposed by Uenaka [4] are conservative for FEA results and generally conservative for test results. The mean values of Mu-U/ Mu-F and Mu-U/Mue are 0.81 and 0.91, respectively. Predictions of design equations proposed based on AISC standard [17] are very conservative for both FEA results and test results. The mean values of Mu-Pro/Mu-F and Mu-Pro/Mue are 0.57 and 0.67, respectively. However, the prediction from the proposed method are conservative for all specimens.
7. Conclusions The behavior of dodecagonal section double skin concrete-filled steel beam specimens under bending was studied in this paper. Both experimental investigation and finite element analysis were carried out. Load displacement curves and load strain curves were obtained. It is shown that all of these specimens experienced three
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Table 6 Comparison of ultimate strengths obtained from design predictions with test results. Specimens
Mu-H
Mu-U
Mu-Pro Mue
Mu-H/Mue Mu-U/Mue Mu-Pro/Mue
DCS300-3180-3 DCS300-4180-3A DCS300-4180-3B DCS400-3240-3 DCS400-3280-3 DCS400-4240-3 DCS400-4280-3
156.9
127.7
98.4
165.4
0.949
0.772
0.595
210.4
190.9
146.1
204.6 1.028
0.933
0.714
210.4
190.9
146.1
207.0
1.016
0.922
0.706
300.3 233.7 165.6
295.5 1.016
0.791
0.560
317.3
245.3 182.4
254.7 1.246
0.963
0.716
401.6
342.7 242.5
387.8
1.036
0.884
0.625
409.8 343.6 250.4
317.4
1.291
1.083
0.789
1.08 0.111
0.91 0.108
0.67 0.111
Mean COV
stages: elastic stage, elastic–plastic stage and plastic stage during load process. All tested specimens exhibited good ductility. There is no local bucking occurred at the flat portion of outer steel tube in the compression zone. The cross section at the mid-span remains plane at the initial stage. Design methods proposed by Han and Uenaka were used to predict the ultimate strength of test specimens and specimens in FEA parametric study. It is shown that the design predictions from the Han's method are slightly unconservative while the Uenaka's method are generally conservative. A new method was proposed based on current AISC standard. It is shown that the design predictions from the proposed method are very conservative for all specimens.
Acknowledgments The research work described in this paper was supported by National Key Technology R&D Program (2011BAJ09B03) and Public Projects of Zhejiang Province (2015C33005).
References [1] H. Huang, L.H. Han, Z. Tao, et al., Analytical behaviour of concrete-filled double skin steel tubular (CFDST) stub columns, J. Constr. Steel Res. 66 (4) (2010) 542–555. [2] L.H. Han, Y.J. Li, F.Y. Liao, Concrete-filled double skin steel tubular (CFDST) columns subjected to long-term sustained loading, Thin-Walled struct. 49 (12) (2011) 1534–1543. [3] X.L. Zhao, Grzebieta, Strength and ductility of concrete filled double skin (SHS inner and SHS outer) tubes, Thin-Walled Struct. 40 (02) (2002) 199–213. [4] K. Uenaka, H. Kitoh, Concrete filled double skin tubular members subjected to bending, Steel Compos. Struct. 4 (8) (2008) 297–312. [5] K. Uenaka, H. Kitoh, Mechanical behavior of concrete filled double skin tubular circular deep beams, Thin-Walled Struct. 49 (2) (2011) 256–263. [6] M. Shimizu, F. Tatsumi, Experimental study on ultimate strength of concrete filled double tubular steel with shear connector, Int. J. Steel Struct. 13 (1) (2013) 49–54. [7] L.H. Han, H. Huang, Z. Tao, et al., Concrete-filled double skin steel tubular (CFDST) beam-columns subjected to cyclic bending, Eng. Struct. 28 (12) (2006) 1698–1714. [8] J. Moon, C.W. Roeder, D.E. Lehman, et al., Analytical modeling of bending of circular concrete-filled steel tubes, Eng. Struct. 42 (2012) 349–361. [9] H. Lu, L.H. Han, X.L. Zhao, Analytical behavior of circular concrete-filled thinwalled steel tubes subjected to bending, Thin-Walled Struct. 47 (3) (2009) 346–358. [10] L.H. Han, Flexural behaviour of concrete-filled steel tubes, J. Constr. Steel Res. 60 (2) (2004) 313–337. [11] L.H. Han, H. Lu, G.H. Yao, et al., Further study on the flexural behaviour of concrete-filled steel tubes, J. Constr. Steel Res. 62 (6) (2006) 554–565. [12] A. Jiang, J. Chen, W. Jin, Experimental investigation and design of thin-walled concrete-filled steel tubes subject to bending, Thin-Walled Struct. 63 (2013) 44–50. [13] H. Lu, L.H. Han, X.L. Zhao, Analytical behavior of circular concrete-filled thinwalled steel tubes subjected to bending, Thin-Walled Struct. 47 (3) (2009) 346–358. [14] J. Chen, Y.Y. Ni, W.L. Jin, Column tests of dodecagonal section double skin concrete-filled steel tubes, Thin-Walled Struct. 88 (2015) 28–40. [15] AS, Australian Standard. Methods for tensile testing of metals. AS 1391, Standards Association of Australia, Sydney, Australia, 1991. [16] Z. Tao, L.H. Han, X.L. Zhao, Behaviour of concrete-filled double skin (CHS inner and CHS outer) steel tubular stub columns and beam columns, J. Constr. Steel Res. 60 (8) (2004) 1129–1158. [17] AISC, Specification for Structural Steel Buildings, ANSI/AISC 360-10, American Institute of Steel Construction, Chicago, IL, 2010. [18] L.H. Han, Theory and Practice of Concrete-filled Steel Tubular Structure, Science Press, Beijing, China, 2007. [19] H. Huang, L.H. Han, Z. Tao, et al., Analytical behaviour of concrete-filled double skin steel tubular (CFDST) stub columns, J. Constr. Steel Res. 66 (4) (2010) 542–555. [20] L.H. Han, G.H. Yao, Z. Tao, Performance of concrete-filled thin-walled steel tubes under pure torsion, Thin-Walled Struct. 45 (1) (2007) 24–36.
Contents lists available at ScienceDirect
Thin-Walled Structures journal homepage: www.elsevier.com/locate/tws
Behavior of thin-walled dodecagonal section double skin concrete-filled steel tubes under bending Ju Chen a, Jun Wang a, Fang Xie b,n, Wei-liang Jin a a b
Department of Civil Engineering, Zhejiang University, China Yuanpei college, Shaoxing University, China
art ic l e i nf o
a b s t r a c t
Article history: Received 7 April 2015 Received in revised form 12 August 2015 Accepted 3 October 2015
The behavior of thin-walled dodecagonal section double skin concrete-filled steel tubes under bending was studied in this paper. Both experimental investigation and finite element analysis (FEA) were carried out. A total of 7 specimens were tested with the beam length of 2000 mm. The width to thickness ratio of the outer steel tube ranged from 75 to 133. The load–displacement curves, failure mode and ultimate capacity of test specimens were obtained. A finite element model was developed for the thin-walled dodecagonal section double skin concrete-filled steel tube subjected to bending. The FEA results were verified against the test results and parametric study was conducted using the verified model. In addition, the suitability of Han's method, Uenaka's method and proposed method for thin-walled circular section double skin concrete-filled steel tubes subjected to bending was also evaluated. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Bending Concrete-filled steel tube Dodecagonal section Double skin
1. Introduction Concrete Filled Double Skin Tubes (CFDST) are composite members which consist of an inner and outer steel tubes with the concrete filled between the steel tubes [1]. This kind of composite columns have been recognized to have a series of advantages, such as high strength and bending stiffness, good seismic and fire performance [2]. CFDST columns also holds the characteristics of Concrete-filled steel tubular (CFT), but have less self-weight. For the flexural properties of CFDST, some scholars have made a lot of research work in recent years, Zhao [3] studied the mechanical properties of square section CFDST subjected to pure bending; Uenaka et al. [4,5] reported the behavior of circular section CFDST under pure bending; Shimizu [6] carried out a fourpoint bending test on the circular section CFDST with shear connecters between the inner and outer tubes; Han et al. [7] studied the ductility and energy dissipation ability of CFDST beams with circular and square cross section. There were experimental and analytical studies have been conducted on the bending behavior of concrete-filled steel tubes (CFTs). Moon et al. [8] and Lu et al. [9] preformed finite element analysis (FEA) to study the flexural performance of circular section CFTs. Han et al. [10,11] studied the flexural behavior of rectangular and circular section CFTs and the design method was proposed; Jiang et al. [12] carried out a series of bending tests of thin-walled n
Corresponding author. Fax: þ 86 575 88319253. E-mail address: [email protected] (F. Xie).
http://dx.doi.org/10.1016/j.tws.2015.10.002 0263-8231/& 2015 Elsevier Ltd. All rights reserved.
concrete-filled steel tubes and developed an analytical model. Lu et al. [13] conducted analytical study on the flexural performance of circular section thin-walled CFTs. In retrospection of the former study about the CFDST specimens, investigation mainly focused on the circular and square section specimens. Chen et al. [14] reported the column tests of dodecagonal section double skin concrete-filled steel tubes. The dodecagonal section double skin concrete-filled steel tube is expected to have better local buckling resistance compared with square section specimens. It is also expected to have the advantage of easy fabrication and flat surface for connection compared with circular section specimens. There are practical applications of dodecagonal CFDST in electronic transmission poles in Zhejiang province, China. In this study, the behavior of dodecagonal section double skin concrete-filled steel tube under bending was studied. Both experimental investigation and finite element analysis were carried out. The suitability of current design method of circular section CFDST members were evaluated for dodecagonal section specimens.
2. Experimental investigation 2.1. Test specimens The tested specimens were fabricated by molding a flat steel plate into a dodecagonal shape, and then the ends of the steel tubes were cut to specified length of 2000 mm. The outside surface of inner steel tubes and insides surface of the outer steel tubes
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Nomenclature Ac Ace Asi Aso Di Do E L Mi Mo
cross-sectional area of concrete nominal cross section area of concrete, given by π(Do − 2tso)2 /4 cross-sectional area of inner tube cross-sectional area of outer tube outside diameter of inner tube outside diameter of outer tube elastic modulus of steel length of member ultimate bending capacity of the inner tube; composite ultimate bending capacity of the outer tube and the core concrete;
Table 1 Measured geometric size of test beams. Specimen
L (mm)
Do (mm)
to (mm)
Di (mm)
ti (mm)
DCS300-3-180-3 DCS400-3-240-3 DCS400-3-280-3 DCS300-4-180-3 DCS300-4-180-3A DCS400-4-240-3 DCS400-4-280-3
2000 2000 2000 2000 2000 2000 2000
300.2 400.1 399.7 300.3 300.2 400.1 399.6
2.98 2.98 2.98 4.01 4.01 4.01 4.01
180.2 239.8 279.6 179.9 180.0 240.1 280.0
3.00 3.01 3.02 3.00 2.98 3.00 2.99
ti to Do/Di Do/to Di /ti Mu-U Mu-A Mu-H Mu-F Mue
thickness of inner tube thickness of outer tube outer diameter to inner diameter ratio diameter-to-thickness ratio of the outer tube diameter-to-thickness ratio of the inner tube ultimate bending moment calculated by the Uenaka's method ultimate bending moment calculated by the AISC method ultimate bending moment calculated by the Han's method ultimate bending moment calculated by the FEM method ultimate bending moment acquired from experiment
The tested specimens in this study were labeled such that the type of the specimens, outer diameter of outer steel tube, nominal thickness of outer steel tube, outer diameter of inner steel tube and nominal thickness of inner steel tube can be identified from the label. For example, the label “DCS400-4-280-3A” defines the specimen as follow:
The three letters indicate that the type of the specimen, where
the prefix letter “DCS” refers to dodecagonal section double skin concrete-filled steel tubes. The following three digits “400” indicate the outer diameter of the outer tube in mm. The following digit “4” is the nominal thickness of the outer steel tube in mm. The following three digits “280” indicate the outer diameter of the inner tube in mm. The following digit “3” is the nominal thickness of the inner steel tube in mm. The last character “A” refers to the repeated test specimen.
2.2. Test setup
Di
Do
Fig. 1. Size sketch diagram of a tested beam.
were brushed to remove any rust and loose debris present. Both the outer and inner steel tubes were placed centric. The selfcompacting concrete was cured without any vibration. During curing, a very small amount of longitudinal shrinkage occurred at the top of the specimens. High strength cement was used to fill this longitudinal gap before the welding of the top steel end plate. Two 20 mm thick steel plates were welded to both ends of the specimens to ensure full contact between specimens and end bearing. The measured cross-section dimensions and specimen length for each test specimen are shown in Table 1. The cross section of dodecagonal section specimen is shown Fig. 1.
The specimen was simply supported on rollers and the load was applied to the specimen by means of a spreader. The span of each beam was 2000 mm, with a 100 mm extent portion overhang at each edge support. The load was thus slowly applied and monotonically increased until failure after some unloading–reloading cycles in the elastic domain. Displacement control was used to drive the 10,000 kN hydraulic testing machine at a constant speed of 1.0 mm/min for all test specimens. The usage of displacement control allowed the tests to be continued to the post-ultimate stage. A data acquisition system was used to record the applied load and the readings of the transducers at regular intervals during the tests. When the mid-span deflection of the specimens reached about 3% of the length of the specimen, tests stopped. Fourteen strain gauges were attached around the specimen at the mid-span. Among these fourteen strain gauges, seven were attached on the corner of the dodecagonal section while the other seven were attached on the flat portion of the dodecagonal section as shown in Fig. 2. Fig. 3 gives a general view of the instrumentations. The deflection were measured by displacement transducer (LVDT) located underneath the bottom flange at midspan. Two dial indications were used to measure the settlements of the test frame during the test. 3. Material properties Tensile coupon tests were conducted to obtain the material
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intervals during the tests. The material properties of the angle were provided by the supplier. The values of Young's modulus (Es), yield stress (fy), ultimate tensile strength (fu) based on a gauge length of 50 mm are shown in Table 2. The compressive strength (fcu) and elastic modulus (Ec) obtained on 150-mm concrete cubes at 28 days were 35 MPa and 33,560 MPa, respectively. The tests were conducted from 28 days after the casting of concrete.
4. Test results 4.1. Load–deflection curve
Fig. 2. Arrangement of the strain gauges.
Loading plate
Specimen
Bearing
The tested specimens all failed in a very ductile manner. Typical failure mode of tested specimen DCS300-3-180-3 is shown in Fig. 4. No tensile fracture and welding failure were observed on the test specimens. Local deformation was observed at the two loading points on the outer tube. The measured load vs. mid-span deflection curves of six test specimens are given in Fig. 5. (The data of specimen DCS300-3-180-3 was not recorded due to computer error). It is shown that the load–deflection curves of specimens having less steel/concrete ratio of cross section are smoother. Based on the observation during the tests processor and load vs. mid-span deflection curves, the specimens are considered to experience three stages under loading until failure. In the first stage: load vs. mid-span deflection curves of specimens approximately remain straight line. In the second stage: the load vs. midspan deflection curves began to show nonlinear behavior. At the end of the second stage, the outer steel tubes in the tension zone reach yielding. In the third stage: the load remain constant and large deformation occurs until failure of the test specimens. For specimens having the inner tube diameter of 280 mm, the load– deflection curves drop more rapidly after the peak load compared with other specimens. This may due to the smaller concrete/steel cross section area ratio. Fig. 6 shows initial part of load vs. mid-span deflection curves of test specimens, which reflects the behavior of specimens at the elastic stage under bending. It is shown that for specimens having the same diameter of outer and inner steel tubes, initial stiffness increases with the increasing wall thickness of outer steel tube, such as specimen DCS400-4-280-3 and DCS400-3-280-3. For specimens having the same outer steel tube, initial stiffness decreases with the increasing diameter of the inner steel tube, such as specimen DCS400-4-280-3 and specimen DCS400-4-240-3. 4.2. Load–strain curve
Fig. 3. Test setup.
Typical load–strain curves and corresponding initial part of specimens DCS400-4-240-3, DCS400-3-240-3, DCS300-3-180-3, DCS300-4-180-3 are shown in Figs. 7–10, respectively. From the
Table 2 Measured material properties of steel. Nominal thickness (mm)
E (MPa)
fy (MPa)
fu (MPa)
3 4
201,000 199,500
366 452
530 542
properties of steel tube used in the test specimens. The coupons were taken from the steel tubes in the longitudinal direction belonging to the same batch as the column test specimens. The coupon dimensions conformed to the Australian Standard AS 1391 [15] for the tensile testing of metals using 12.5 mm wide coupons. The coupons were also tested in accordance with the AS 1391 [15] in a displacement controlled testing machine using friction grips. A calibrated extensometer of 50 mm gauge length was used to measure the longitudinal strain. A data acquisition system was used to record the load and the readings of strain at regular
Fig. 4. Failure mode of test specimen DCS300-3-180-3.
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DCS400-3-240-3 DCS400-4-240-3 DCS400-3-280-3 DCS400-4-280-3 DCS300-4-180-3 DCS300-4-180-3A
1500
Load(kN)
1200 900 600 300
bucking occurs at the flat portion the outer steel tube in compressive zone, as shown in the column tests [14]. Fig. 11 shows strain distribution along the height of the cross section of specimens at the initial part of specimens DCS400-3280-3 and DCS400-3-240-3. The strain curves of the two specimens are similar. The line x¼ 0 represents the mid-height of the cross-section of specimen, whereas the positive value represents the compressive zone, the negative value represents the tension zone. With the load increasing, the neutral axis move from the position at x¼ 0 to the compressive zone. It is obvious that the strain development in the compressive zone is less than those in the tension zone, which could be explained by the contribution from the concrete in compression.
0 0
15
30
45
60
75
90
5. Finite element analysis
Displacement(mm) Fig. 5. Load–deflection curves of test specimens.
Fig. 6. Initial load–deflection curves of test specimens.
complete load–strain curves, it could be seen that the strain gauges at the bottom of specimen (strain gauge 13 and 14) exhibit nonlinearity earlier than the strain gauges at the top of the specimen (strain gauge 1 and 2). The reason is that the concrete resist the compressive force so that the tensile strain develops faster that the compressive strain. From the initial part of the load–strain curves, it could be concluded that the compressive and tensile strain is linear at the initial stage, which means the plane-section assumption is applicable. It is also can be seen that both the strain of the corner portion and flat portion of the outer steel tube remain linear in the initial part, which may mean there is no local
5.1. Finite element model and verification Finite element method was used to further study the test specimen and provide more data in this study. According to the Han's study [16], the core concrete under the confined state of the double skin concrete-filled tubes are the same as the concretefilled steel tubes when the hollow section ratio smaller than 0.8. Therefore, the confined concrete material model proposed by Han [18] was used in this study. The measured material properties were used in the finite element model. The inner and outer steel tubes are modeled by reduced-integration shell elements (S4R), while the concrete and the end plates are modeled by 8-node brick elements (C3D8R) [19]. The two end plates were tied with the inner and outer steel tube and they were contacted with the core concrete. The interactions that the inner and outer steel tubes with the core concrete could be modeled by contact interaction as described in Huang et al. [19] and Han et al. [20]. The developed finite element model is shown in Fig. 12. Following the test procedure, the beam was four-points loaded. In the finite element model, the support plate was modeled as a rigid body, whose motion is governed by the reference point. The reference point of the support plate was restrained against x, y and z directions displacement as well as y- and z- axes rotation but free to rotate about the x-axis. The loading plate was also modeled as a rigid body. The reference point of the loading plate was restrained against x and z directions displacement as well as y- and z- axes rotation but free to move in y directions and rotate about the xaxis. The finite element analysis results were compared with the test results as shown in Table 3. It is shown that the ultimate strengths agree with the test results well. The mean value of Nu-F/Nue is 1.07,
Fig. 7. Load–strain curves of test specimen DCS400-4-240-3. (a) Complete curve and (b) initial part.
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Fig. 8. Load–strain curves of test specimen DCS400-3-240-3. (a) Complete curve and (b) initial part.
Fig. 9. Load–strain curves of test specimen DCS300-3-180-3. (a) Complete curve and (b) initial part.
Fig. 10. Load–strain curves of test specimen DCS300-4-180-3. (a) Complete curve and initial part.
Fig. 11. Strain distribution of test specimens. (a) DCS400-3-280-3 and (b) DCS400-3-240-3.
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Load
Load
Table 4 Geometric size of specimens for FEA parametric study. Specimens
Fig. 12. Developed finite element model.
Table 3 Comparison of ultimate strengths obtained from test results with FEA results. Specimens
Mue
Mu-FEA
Mu-FEA/Mue
DCS300-3-180-3 DCS300-4-180-3A DCS300-4-180-3B DCS400-3-240-3 DCS400-3-280-3 DCS400-4-240-3 DCS400-4-280-3
165.4 204.6 207.0 295.5 254.7 387.8 317.4
173.0 211.2 211.2 324.6 275.4 409.8 374.4
1.046 1.032 1.020 1.098 1.081 1.057 1.180
Mean COV
1.074 0.047
FEM DCS300-4-180-3 DCS300-4-180-3A
900
Load(kN)
600
L (mm)
DCS300-2-150-3 DCS300-3-150-3 DCS300-4-150-3 DCS300-2-180-3 DCS300-3-180-3 DCS300-4-180-3 DCS300-2-210-3 DCS300-3-210-3 DCS300-4-210-3 DCS400-2-240-2 DCS400-2-240-3 DCS400-2-240-4 DCS400-3-240-3 DCS400-4-240-3 DCS400-2-280-2 DCS400-2-280-3 DCS400-2-280-4 DCS400-3-280-3 DCS400-4-280-3 DCS400-2-200-2 DCS400-2-200-3 DCS400-2-200-4 DCS400-3-200-3 DCS400-4-200-3 DCS500-2-300-3 DCS500-3-300-3 DCS500-4-300-3 DCS500-2-350-3 DCS500-3-350-3 DCS500-4-350-3 DCS500-2-250-3 DCS500-3-250-3 DCS500-4-250-3
2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 3000 3000 3000 3000 3000 3000 3000 3000 3000
Do (mm)
to (mm)
Di (mm)
ti (mm)
300 300 300 300 300 300 300 300 300 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 500 500 500 500 500 500 500 500 500
2.0 3.0 4.0 2.0 3.0 4.0 2.0 3.0 4.0 2.0 2.0 2.0 3.0 4.0 2.0 2.0 2.0 3.0 4.0 2.0 2.0 2.0 3.0 4.0 2.0 3.0 4.0 2.0 3.0 4.0 2.0 3.0 4.0
150 150 150 180 180 180 210 210 210 240 240 240 240 240 280 280 280 280 280 200 200 200 200 200 300 300 300 350 350 350 250 250 250
3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 2.0 3.0 4.0 3.0 3.0 2.0 3.0 4.0 3.0 3.0 2.0 3.0 4.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0
cross section area of concrete tube.
300
6. Design methods
0 0
20
40
60
80
Displacement(mm) Fig. 13. Comparison of load vs. displacement curves obtained from test results with FEA results.
with the corresponding COV of 0.018. The load vs. mid-span deflection curve obtained from the finite element analysis also agrees with the test results well, as shown in Fig. 13. 5.2. Parametric study Since the established model was proven correct by the verification against the test results, it is used to carry out parametric study. The parameters considered include: the diameter-to-thickness ratio of outer steel tube, the ratio of outer diameter to inner diameter of steel tube and the thickness of the inner steel tube. The geometric size of the modeled specimens is presented in Table 4. The ultimate strengths obtained from the FEA results are shown in Table 5. It is shown that the diameter-to-thickness ratio has significant influence on the ultimate strength. The ultimate strength of specimens decreases when the diameter-to-thickness ratio of the outer steel tube increases. The ultimate strength of specimens also decreases with the increment of the inner and outer dodecagonal width ratios. This may due to the reduction of
Design methods proposed by Han [16] and Uenaka [4] were also used to predict the ultimate strength of dodecagonal section CFDST specimens. It should be noted that those design methods are for CFDST specimens with circular sections. Current AISC standard [17] does not have provisions for concrete-filled double skin steel tubes. Therefore, a new method was proposed based on the AISC standard design method for concrete-filled steel tubes and steel tubes. In this proposed method, the ultimate strength was considered as the summary strengths of outer steel tube þconcrete tube (Mo) and inner steel tube (Mi), as shown in Eq. (1). 6.1. Proposed method The ultimate strength of CFDST specimens under bending could be calculated as follows:
Mn = Mo + Mi
(1)
According to AISC specification [17], for circular solid concrete filled steel tube, if the diameter-to-thickness ratio is less than λ p ¼0.09E/fy, we call it compact section and do not need to consider the local stability; if the diameter-to-thickness ratio is between λ p ¼0.09E/fy and λ r ¼ 0.31E/fy, we call it non-compact section; otherwise we call it slender section. For compact section,
Mo = Mp For non-compact section,
(2)
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Table 5 Comparison of ultimate strengths obtained from design predictions with FEA results. Specimens
Mu-F
DCS300-2-150-3 DCS300-3-150-3 DCS300-4-150-3 DCS300-2-180-3 DCS300-3-180-3 DCS300-4-180-3 DCS300-2-210-3 DCS300-3-210-3 DCS300-4-210-3 DCS400-2-240-2 DCS400-2-240-3 DCS400-2-240-4 DCS400-3-240-3 DCS400-4-240-3 DCS400-2-280-2 DCS400-2-280-3 DCS400-2-280-4 DCS400-3-280-3 DCS400-4-280-3 DCS400-2-200-2 DCS400-2-200-3 DCS400-2-200-4 DCS400-3-200-3 DCS400-4-200-3 DCS500-2-300-3 DCS500-3-300-3 DCS500-4-300-3 DCS500-2-350-3 DCS500-3-350-3 DCS500-4-350-3 DCS500-2-250-3 DCS500-3-250-3 DCS500-4-250-3
125.5 163.5 235.7 123.5 173.0 211.2 133.6 167.4 226.1 208.7 234.3 278.1 324.6 409.8 200.8 226.4 263.3 275.4 374.4 204.5 233.2 280.7 298.5 420.6 389.1 491.2 675.3 393.3 487.7 658.6 365.5 491.3 622.6
Mu-H
Mu-U
Mu-Pro
Mu-H/Mu-F
Mu-U/Mu-F
Mu-Pro/Mu-F
118.5 146.0 199.7 130.0 156.9 210.4 139.5 165.7 218.6 227.1 252.0 300.0 300.3 401.6 221.8 248.4 302.1 317.3 409.8 208.5 228.6 267.3 278.4 373.5 424.5 501.3 648.5 420.6 530.5 674.0 382.9 462.7 612.4
95.0 123.5 182.5 98.1 127.7 190.9 106.7 137.2 204.4 169.5 183.0 197.5 233.7 342.7 168.7 192.2 217.6 245.3 343.6 177.6 184.7 190.0 234.0 334.9 302.9 379.8 544.7 307.3 388.0 568.2 313.4 391.3 544.9
63.2 90.2 137.9 71.5 98.4 146.1 81.1 108.1 150.2 114.1 119.8 152.2 165.6 242.5 113.2 136.6 180.2 182.4 250.4 104.6 117.4 142.2 151.2 228.1 207.7 252.3 358.1 212.4 278.3 384.2 182.8 256.4 335.9
0.944 0.893 0.847 1.053 0.907 0.996 1.044 0.990 0.967 1.088 1.076 1.079 0.925 0.980 1.105 1.097 1.147 1.152 1.095 1.020 0.980 0.952 0.933 0.888 1.091 1.021 0.960 1.069 1.088 1.023 1.048 0.942 0.984
0.757 0.755 0.774 0.794 0.738 0.904 0.799 0.820 0.904 0.812 0.781 0.710 0.720 0.836 0.840 0.849 0.826 0.891 0.918 0.868 0.792 0.677 0.784 0.796 0.778 0.773 0.807 0.781 0.796 0.863 0.857 0.796 0.875
0.504 0.552 0.585 0.579 0.569 0.692 0.607 0.646 0.664 0.547 0.511 0.547 0.510 0.592 0.564 0.603 0.684 0.662 0.669 0.511 0.503 0.507 0.507 0.542 0.534 0.514 0.530 0.540 0.571 0.583 0.500 0.522 0.540
1.01 0.076
0.81 0.070
0.57 0.101
Mean Cov
Mo = Mp − (Mp − My)⋅(
λ − λp λr − λp
)
For slender section
(3)
For slender section, more detailed method can be acquired from AISC specification [17]. where Mo is the combination ultimate bending moment of outer tube and the core concrete; Mi is the ultimate strength of the inner steel tube under bending; Mp is the moment corresponding to plastic stress distribution over the composite cross section; My is the capacity calculated by the elastic method; and λ is the diameter-to-thickness ratio of the steel tube. For Mi , different diameter-to-thickness ratio usually have different computing methods, according to the definition of AISC specification [17], if the diameter-to-thickness ratio λ ¼D/t of steel tube is less than λp ¼ 0.09E/fy, we call it compact section; however, if λ is between λp and λr ¼ 0.31E/fy, we call it non-compact section; whereas, we call it slender section. With the material properties of E ¼200,000 MPa, fy ¼345 MPa, thus 0.09E/fy ¼52.2, 0.31E/fy ¼179.7 could be obtained. However, the diameter-to-thickness ratio of the inner tubes of all the specimens were range from 60 to 93, so all of the inner tubes in this test were non-compact section. For compact section
Mi = f y ⋅Z
(4)
For non-compact section
Mi = {
0.021E + f y }S D /t
(5)
Mi = {
0.33E }⋅S D /t
(6)
where S is the elastic moment of inertia of the steel section and Z is the plastic bending modulus of steel section, for a circular steel D3 − (D − 2t )3
tube, Z = 6 Design strengths predicted by using the Han's method [16] are slightly unconservative compared with the test results (Table 6) and FEA results. The mean values of Mu-H/Mu-F and Mu-H/Mue are 1.01 and 1.08, respectively. The predictions obtained from equations proposed by Uenaka [4] are conservative for FEA results and generally conservative for test results. The mean values of Mu-U/ Mu-F and Mu-U/Mue are 0.81 and 0.91, respectively. Predictions of design equations proposed based on AISC standard [17] are very conservative for both FEA results and test results. The mean values of Mu-Pro/Mu-F and Mu-Pro/Mue are 0.57 and 0.67, respectively. However, the prediction from the proposed method are conservative for all specimens.
7. Conclusions The behavior of dodecagonal section double skin concrete-filled steel beam specimens under bending was studied in this paper. Both experimental investigation and finite element analysis were carried out. Load displacement curves and load strain curves were obtained. It is shown that all of these specimens experienced three
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J. Chen et al. / Thin-Walled Structures 98 (2016) 293–300
Table 6 Comparison of ultimate strengths obtained from design predictions with test results. Specimens
Mu-H
Mu-U
Mu-Pro Mue
Mu-H/Mue Mu-U/Mue Mu-Pro/Mue
DCS300-3180-3 DCS300-4180-3A DCS300-4180-3B DCS400-3240-3 DCS400-3280-3 DCS400-4240-3 DCS400-4280-3
156.9
127.7
98.4
165.4
0.949
0.772
0.595
210.4
190.9
146.1
204.6 1.028
0.933
0.714
210.4
190.9
146.1
207.0
1.016
0.922
0.706
300.3 233.7 165.6
295.5 1.016
0.791
0.560
317.3
245.3 182.4
254.7 1.246
0.963
0.716
401.6
342.7 242.5
387.8
1.036
0.884
0.625
409.8 343.6 250.4
317.4
1.291
1.083
0.789
1.08 0.111
0.91 0.108
0.67 0.111
Mean COV
stages: elastic stage, elastic–plastic stage and plastic stage during load process. All tested specimens exhibited good ductility. There is no local bucking occurred at the flat portion of outer steel tube in the compression zone. The cross section at the mid-span remains plane at the initial stage. Design methods proposed by Han and Uenaka were used to predict the ultimate strength of test specimens and specimens in FEA parametric study. It is shown that the design predictions from the Han's method are slightly unconservative while the Uenaka's method are generally conservative. A new method was proposed based on current AISC standard. It is shown that the design predictions from the proposed method are very conservative for all specimens.
Acknowledgments The research work described in this paper was supported by National Key Technology R&D Program (2011BAJ09B03) and Public Projects of Zhejiang Province (2015C33005).
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