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Experimental study of the cyclic behavior of concrete-filled double skin steel tube columns subjected to pure torsion
Thin-Walled Structures 122 (2018) 425–438
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Full length article
Experimental study of the cyclic behavior of concrete-filled double skin steel tube columns subjected to pure torsion
MARK
⁎
Yu-Hang Wanga,b, , Guo-Bing Luc, Xu-Hong Zhoua,b a b c
School of Civil Engineering, Chongqing University, Chongqing 400045, China Key Laboratory of New Technology for Construction of Cities in Mountain Area (Chongqing University), Ministry of Education, Chongqing 400045, China State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Concrete-filled double skin steel tube columns Quasi-static test Cyclic torsion Hysteretic performance Failure mode
Based on a quasi-static test on six concrete-filled double skin steel tube columns subject to cyclic pure torsion, the torsion behavior of concrete-filled double skin steel tube columns with various section types, hollow ratios and steel ratios was studied. The failure modes, torsion-rotation angle hysteretic curves and strain distribution law of concrete-filled double skin steel tube columns under reversed cyclic loading are obtained. The test results show that the hysteretic curves of concrete-filled double skin steel tube columns under pure torsion are plump. The unloading stiffness was close to the initial elastic stiffness. The good energy dissipation capacity of concretefilled double skin steel tube columns can be observed. Under a cyclic torsion moment, the torsion-resistance capacity of circular concrete-filled double skin steel tube columns was better than that of square and rectangular concrete-filled double skin steel tube columns. With the same thickness of the inner steel tube and the same section size and shape, the hollow ratio of concrete-filled double skin steel tube columns has little effect on the cyclic torsion behavior.
1. Introduction A concrete-filled double skin steel tube column (CFDST) is a composite member formed by pouring concrete between two concentric steel tubes. Compared with traditional solid concrete-filled steel tube columns (CFSTs), concrete-filled double skin steel tube columns have a wider section and larger bending stiffness using the same amount of materials. Concrete-filled double skin steel tube columns can be used in engineering areas such as piers, water-resistant casing pipes of offshore oil drilling platforms, and piles with large diameters in long-span electric power pylons and high-rise buildings. The major section types of concrete-filled double skin steel tubes are circular nested circular, circular nested square, square nested circular, square nested square, and rectangular nested rectangular [1]. Many studies have conducted experimental and theoretical analysis of the static behavior and seismic performance of concrete-filled double skin steel tube columns under bending moments and axial force (e.g., [2–8]), and the results have shown that concrete-filled double skin steel tube columns not only have large axial stiffness and flexural capacity but also possess satisfactory seismic performance. Taking the diameterto-thickness ratio, hollow ratio, slenderness ratio and eccentricity ratio of tubes as the main parameters, Han [9,10] proposed practical
⁎
calculation methods for the ultimate bearing capacity of concrete-filled double skin steel tube columns under axial loading and eccentric loading by conducting an axial compression and eccentric compression experiment on concrete-filled double skin steel tube columns. Taking the steel ratio and hollow ratio as the main parameters, Huang [11] carried out an experimental study and finite element analysis on the mechanical behavior of CFDSTs under monotonic pure torsion and proposed design formulas for the calculation of the torsional capacity of CFDSTs. In various practical engineering applications, CFDST members may be subjected to cyclic torsional loading, such as piers of a curved girder bridge and corner columns of a high-rise building under an earthquake or transmission towers that cross a river or sea under wind loading or an earthquake. Therefore, it is necessary to investigate the behavior of CFDST members under cyclic pure torsion. Compared with concretefilled steel tube columns, CFDST columns can make full use of the mechanical properties of materials. Reference [12] shows that concretefilled steel tube columns have perfect seismic performance. The torsion moment versus rotation angle hysteresis loops of CFST columns under cyclic torsion were plump. Torsion moment versus rotation angle skeleton curves have no obvious descending branch. Stiffness degradation and strength degradation of concrete-filled steel tube columns were not
Corresponding author at: School of Civil Engineering, Chongqing University, Chongqing 400045, China. E-mail address: [email protected] (Y.-H. Wang).
http://dx.doi.org/10.1016/j.tws.2017.10.034 Received 21 April 2017; Received in revised form 12 October 2017; Accepted 17 October 2017 0263-8231/ © 2017 Elsevier Ltd. All rights reserved.
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End plate
200
300
20
600
300
325
300
20
Shear key
End plate
770
300
(a) Elevation view
200
Inner steel tube
325
300
475
Outer steel tube
300
(b) Section form of specimens
Fig. 1. Geometric dimensions of the specimens.
variable parameters in the tests are the tube shape (circular, square or rectangular) and the hollow ratio ψ. The hollow ratio ψ is given by ψ = Ah/Asc. Ah is the hollow section area, which is given by Ah = π(d-ti)2/4 for a circular section, and Ah = (h-ti)(b-ti) for a square or rectangular section. Asc is the cross-sectional area of the CFDST (= Aso+Ac+Asi+Ah). Aso is the cross-sectional area of the outer steel tube. Ac is the cross-sectional area of the sandwiched concrete. Asi is the cross-sectional area of the inner steel tube. In references [11,12], welded steel tubes are used to create specimens, and the welding of steel tubes cracked in the experimentation. In this test, the seamless steel tubes are used for specimens to avoid the breakage of welding on steel tubes. The end plate and end region of the steel tubes are connected by a fillet weld. The surfaces of the upper and lower end plates between the double steel cylinders should be respectively welded with four shear connectors not only to ensure that the steel tubes and concrete can bear loading together but also to make sure that the torsion moment in the end region of the specimens can be transferred to steel tubes and concrete equably. The concrete between double skin steel tubes is poured through the holes reserved in the upper end plates.
Table 1 Details of the specimens. Section type
Specimen label
Dimensions of the outer steel tube D(H × B) × to (mm)
Dimensions of the inner steel tube d(h × b) × ti (mm)
ψ
CC-T1 CC-T2
ϕ325 × 8.15 ϕ325 × 8.15
ϕ159 × 4.34 ϕ219 × 6.30
0.21 0.40
RR-T1 RR-T2
300 × 200 × 4.60 300 × 200 × 4.60
160 × 80 × 3.80 200 × 100 × 3.88
0.18 0.29
SS-T1 SS-T2
300 × 300 × 5.34 300 × 300 × 5.34
100 × 100 × 3.54 200 × 200 × 3.54
0.09 0.41
obvious. However, there is still a lack of research on the mechanical properties of concrete-filled double skin tube columns under cyclic pure torsion loading. This paper focuses on the failure modes and hysteretic behavior of concrete-filled double skin steel tube columns under cyclic pure torsion by carrying out pseudo-static testing and analysis.
2.2. Material properties The strength grade of the concrete is C40. When the concrete is poured into the double skin steel tubes, the concrete test cubes, which are 150 mm on each edge, should be made for the material strength test, and both the specimens and concrete cubes should be naturally maintained under the same conditions. After 28 days, the compressive strength of those concrete test tubes was measured by standard testing methods, and the average value of the concrete compressive cube strength was 42.1 MPa. The property test data of 9 steel tubes is shown in Table 2 and Fig. 2, where fy is the yield strength of the steel tube, fu is the ultimate strength of the steel tube, and Es is the Young's modulus of the steel tube. From the material test, it can been seen that expect steel tubes numbered as 6, 8 and 9 shown in Fig. 2, the stress-strain curves of the coupons taken from other steel tubes have a visible yielding plateau. Thus, the stress corresponding to the plastic strain of 0.2% is adopted as the yield strength for steel tubes numbered as 6, 8 and 9 based on the method proposed by reference [13].
2. Experimental program 2.1. Design and manufacturing of specimens In this paper, six specimens of concrete-filled double skin tube columns were designed, including 2 CFDST members with circular hollow sections (CHSs) as the inner tube and outer tube, 2 CFDST members with square hollow sections (SHSs) as the inner tube and outer tube and 2 CFDST members with rectangular hollow sections (RHSs) as the inner tube and outer tube. The information of these specimens is shown in Fig. 1 and Table 1, where D (d) is the outside diameter of the outer (inner) circular steel tube, H (h) and B (b) are the outside diameters of the outer (inner) square and rectangular steel tube, and to (ti) is the wall thickness of the outer (inner) steel tube. The main Table 2 Steel material properties. No.
Dimensions of the steel tube (mm)
fy (MPa)
fu (MPa)
Es (× 105 MPa)
No.
Dimensions of the steel tube (mm)
fy (MPa)
fu (MPa)
Es (× 105 MPa)
1 2 3 4 5
ϕ325 × 8.15 ϕ219 × 6.30 ϕ159 × 4.34 300 × 300 × 5.34 200 × 200 × 3.54
317.07 361.27 329.02 352.00 283.00
506.41 481.87 475.46 508.57 403.67
2.10 2.08 2.33 1.97 2.17
6 7 8 9
100 300 200 160
310.67 232.71 406.33 353.33
371.67 388.78 479.33 430.33
1.91 2.05 2.39 1.87
426
× × × ×
100 × 3.54 200 × 4.60 100 × 3.88 80 × 3.80
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Fig. 2. Stress versus strain curves of the steel tubes.
Fig. 3. Test device.
high-strength bolts. One end of the rigid link connects with the middle of the top girder through an idealized hinge joint, and the other end also connects with the reaction wall using an idealized hinge joint. The rigid link can guarantee that there are no bending moments in specimens during the loading process. Cyclic torsional loading can be produced by applying compressive force and tensile force on the top beam through a hydraulic servo actuator. Nie [12] concluded that the rotation angle has a good linear relationship with the horizontal displacement of the concentrated loading point, and the displacement control method can be used for the torsion
2.3. Loading device and loading program To realize the pseudo-static cyclic loading of concrete-filled double skin steel tube columns under pure torsion loading, a loading device is designed, as shown in Fig. 3. The loading device is mainly composed of a top girder, a steel base, and a rigid link. The upper end plate and lower end plate of specimens should be connected with the top girder and steel base using high-strength bolts. The relative slip between specimens’ plates and top beams and bases cannot occur in the process of cyclic loading by the guarantee of exerting pre-tensile stress on the 427
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15
200
to 45°. During the entire loading process, the welding seam between the steel tube and end plates is undamaged, and neither the outer steel tube nor the inner steel tube undergoes buckling deformation. In a word, the specimens are not obviously broken.
10
150 100
5
50 0
0 -50
-5
-100
Rotation angle (°)
Displacement of load point (mm)
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3.1.2. Specimen CC-CT2 As the torsion angle of the specimen CC-T2 reaches 10.85°, the paint layer close to the end of the steel tube cracks along the circumferential direction, and the oil paint on the middle part of the steel tube begins peeling off and forms many waves in the direction of 45°. Finally, the outer steel tube close to the lower plate cracks along the circumferential direction. The length of the crack is close to 3/4 of the circumference. On the one end, the crack continues to develop obliquely along the column, and the angle between the crack and the horizontal line is approximately 45°. At the end of the test, peeling off the outer steel tube and concrete, the bottom of the inner steel tube was found to be cracked across the cross-section; the inner steel tube exhibited buckling deformation inward in the cracks, and there was no buckling deformation in the middle part of the inner steel pipe.
-10
-150 -200 0
5
10
15
20
25
30
35
40
-15 45
Number of loading cycles Fig. 4. Loading process.
loading with a constant incremental rotation angle. Test loading follows the displacement control, and the loading systems are shown in Fig. 4; the loading rate is controlled at 5 mm/min. The horizontal displacement Δ0 of the loading points can be calculated by the yield strength of the outer steel tubes. The first-stage loading follows a 0.5Δ0 displacement to perform cyclic loading once, the second-stage loading follows a Δ0 displacement to perform cyclic loading once, the third-stage loading follows a 5Δ0 displacement to perform cyclic loading twice, and the following stages of loading follow a 5Δ0 incremental displacement to perform cyclic loading twice until the damage of specimens occurs.
3.1.3. Specimen RR-CT1 As for specimen RR-T1, when the torsion angle reaches 3.99°, the middle part of the east and west surfaces of the outer steel tube begin buckling, an obvious outward wave occurs on the middle part of the west surface of the outer steel tube, and the included angle between the wave direction and the horizontal line is close to 49°. As soon as the torsion angle reaches 4.51°, the middle part of the south and north surfaces of the outer steel tube begin buckling outward. When the torsion angle reaches 5.8°, an oblique crack occurs on the middle part of the west surface of the outer steel tube, and the distance between the crack and top plate is 18 cm. With the increase of the reciprocating torque, the crack expands in the oblique direction, and the concrete of the cracked areas is crushed. As the torsion angle changes to 8.08°, Xshaped cracks occur on the buckling area of the south surface of the outer steel tube. When the torsion angle reaches 9.06°, X-shaped cracks occur on the middle part of the north surface of the outer steel tube, and the distance between the cracks and the top plate is 18 cm. With increasing reciprocating torque, two X-shaped cracks occur on the west surface of the outer steel tube, and the cracks gradually develop and connect. At the end of the test, peeling off the outer steel tube and concrete, the west surface of the inner steel tube was bent inwards.
2.4. Measuring point arrangement The tests aim to measure the horizontal concentrated force of the loading point, the horizontal displacement of the loading point, and the surface strain of the outer steel tube. The arrangement of the displacement meter is shown in Fig. 5. As the value of the torsion moment of each section of specimens under pure torsion loading is the same, the value of the rotation angle per unit length of each section of specimens under pure torsion loading is identical. The strain measuring points in this test are arranged at the middle section along the height of the specimen to avoid the influence of the weld heat-affected zone on the ends of the steel tube, as shown in Fig. 6.
3.1.4. Specimen RR-T2 As the torsion angle of the specimen RR-T2 approaches 3.82°, the middle part of the west surface of the outer steel tube begins buckling deformation outward, a wave was formed, and the included angle between the wave and the horizontal line is 46°. As soon as the torsion angle reaches 5.16°, a wave occurs on the middle part of the north surface and south surface of the outer steel tube. The included angle between the wave on the north surface and the horizontal line is 47°, and the included angle between the wave on the south surface and the horizontal line is 45°. When the torsion angle changes to 5.81°, the east
3. Test results and analysis 3.1. Test phenomenon and failure modes 3.1.1. Specimen CC-CT1 When the torsion angle of the specimen CC-T1 reaches 9.13°, the paint layer on the steel tube surface close to the end plate peels off, the oil paint on the middle part of the steel tube begins peeling off obliquely, and the angle between cracking and the horizontal line is close
Fig. 5. Measuring point arrangement of the displacement meters.
N W
E Displacement meter
800
S
Displacement meter
(a) vertical view
(b) side view
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Fig. 6. Arrangement of strain measuring points.
layer of the upper outer steel tube cracks in the circumferential direction, and the middle part of the east surface of the outer steel tube begins buckling outward and forms a wave. The included angle between the wave and the horizontal line is 46°. As the torsion angle approaches 5.13°, both the south surface and north surface of the outer steel tube begin buckling outward and form a wave on each surface, while the included angles between the wave on the south surface and north surface and the horizontal line are 49° and 45°, respectively. As soon as the torsion angle reaches 6.48°, an oblique crack occurs on the middle part of the east surface of the outer steel tube, and the crack's distance to the top plate is 18 cm. As the torsion angle approaches 8.34°, an X-type crack occurs on the south surface of the outer steel tube, and it is 15 cm from the top plate. When the torsion angle reaches 9.08°, an oblique crack occurs on the middle part of the east surface of the outer steel tube, and it is 10 cm in distance from the top plate. Then, this crack first develops obliquely to the top of the south surface and turns to expansion on the south surface along the horizontal line until the complete cracking of the south surface of the outer steel tube. An 11-cm vertical crack occurs on the top of the southwest corner of the outer steel tube. At the end of the test, peeling off the outer steel tube and concrete, the north surface, east surface and south surface are all buckling inward. In references [11,12], the behavior of CFDSTs under static pure torsion and CFST columns under cyclic torsion were investigated, respectively. The global failure modes of all specimens under cyclic pure torsion are shown in Fig. 7, and the failure modes of inner steel tubes are shown in Fig. 8. As we can see, concrete-filled double skin steel tube columns with circular sections possess a large ultimate torsional angle and excellent ductility under reciprocating torque loading, which is similar to the CFST columns with circular sections in reference [12]. However, the failure modes of CFDST columns with circular sections were different from those of CFST columns with circular sections in reference [12] and CFDST columns with circular sections in reference [11]. In this test, the failure of circular-section specimens occurred on the end of the steel tubes, and the failure modes of circular-section specimens were the low cyclic fatigue damage of the weld heat-affected zone. Steel tubes had no obvious damage. In reference [12], steel tubes of CFSTs with circular sections cracked, and the concrete near the crack was crushed. In reference [11], CFDSTs with circular sections had no
surface of the outer steel tube begins buckling outward. As the torsion angle reaches 7.86°, an oblique crack occurs on the middle part of the west surface of the outer steel tube, and the distance between the crack and top plate is 18 cm. Then, the crack expands obliquely. As soon as the torsion angle reaches 8.35°, a vertical crack occurs on the middle part of the south surface of the outer steel tube. In addition, an Xshaped crack occurs on the buckling area of the west surface and south surface of the outer steel tube, and the concrete in the cracked area is crushed. At the end of the test, peeling off the outer steel tube and concrete, the four surfaces of the inner steel tube are buckling inward, a crack occurs on the top southwest corner of the inner steel tube and this crack develops towards the upper south side of the inner steel tube with an oblique direction. 3.1.5. Specimen SS-T1 When the torsion angle of the specimen SS-T1 reaches 4.5°, the middle part of the west surface of the outer steel tube begins buckling deformation outward, and a wave occurs on the west surface of the outer steel tube. The included angle between the wave and horizontal line is 52°. As the torsion angle changes to 5.2°, the east surface and south surface of the outer steel tube begins buckling deformation outward. A wave occurs on the east surface and south surface of the outer steel tube, and the included angles between the waves and the horizontal line are both 49°. When the torsion angle reaches 8.23°, an oblique crack occurs on the middle part of the east surface and south surface of the outer steel tube, and the distances between the two cracks and the top plate are both 20.7 cm. However, two cracks develop obliquely. As soon as the torsion angle increases to 9.7°, two X-type cracks occur on the east surface and south surface of the outer steel tube, but the two cracks on the south surface of the outer steel tube are mutually connected; concrete in the cracked area is crushed. At the end of the test, peeling off the outer steel tube and concrete, the four sides of the inner steel tube are buckling inward. Additionally, the height of the buckling area of the inner steel tube to the lower end plate and the height of the buckling area of the outer steel tube to the lower plate are the same. 3.1.6. Specimen SS-T2 When the torsion angle of specimen SS-T2 reaches 3.9°, the paint 429
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Fig. 7. Global failure modes of specimens.
cracked. The failure modes of CFDST columns with square sections and rectangular sections are local buckling of steel tubes and cracking of steel tubes, and the sandwiched concrete was crushed. Compared with the experimental results in reference [12], the failure modes of CFST columns with rectangular sections were similar to those of CFDST columns with square sections and rectangular sections.
obvious damage, but the sandwiched concrete cracked. The ultimate torsional angle of square-section specimens and rectangular-section specimens is relatively small. For square-section specimens and rectangular-section specimens, the cross-diagonal waves appeared on the outer steel tubes, and cracks appeared on the tubes with lateral deformation finally. In reference [11], CFDSTs with square sections under static torsion were undamaged except the welding of one specimen 430
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Fig. 8. Buckling deformation of the internal steel tube of specimens.
lower, showing that concrete-filled double skin steel tube columns with circular sections have good energy dissipation capacity under the reciprocating torsion loading. Both concrete-filled double skin steel tube columns with square sections and concrete-filled double skin steel tube columns with rectangular sections showed a high degree of degradation of bearing capacity when the loading approached the peak of the bearing capacity. Compared with the concrete-filled double skin steel tube columns with circular sections, the energy dissipation capacity of these two types of concrete-filled double skin steel tube columns is lower.
3.2. Torsion moment versus rotation angle hysteresis loops The torsion moment versus rotation angle hysteresis curves of concretefilled double skin steel tube columns under the reciprocating torque loading are shown in Fig. 9. As Fig. 9 shows, the hysteresis loops of concrete-filled double skin tube columns are in plump shape and without a significant pinch phenomenon. The unloading stiffness is close to the initial elastic stiffness, and the degradation degree of the bearing capacity and stiffness of concrete-filled double skin steel tube columns with circular sections are
431
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Fig. 9. Torsion moment versus rotation angle hysteresis loops.
Table 3, we can see that, for the specimens with circular, square and rectangular sections, a similar conclusion could be drawn: (1) all torsion moment-rotation angle skeleton curves of specimens are S-shaped, which shows that all specimens under the low cyclic torsion loading experienced three loading phases (elastic state, plastic state and limit state); (2) for specimens with the same external overall dimensions of sections and loading methods (CC-T1, CC-T2; RR-T1, RR-T2; SS-T1, and SS-T2), increasing the section hollow ratio of specimens leads to a decrease of the sections and concrete areas, but due to the increase in the number of inner steel tubes, the ultimate torsional bearing capacity and elastic torsion stiffness of specimens are not reduced; (3) the descending branch of the skeleton curve of a concrete-filled double skin steel tube column with a circular section was not obvious, while the descending branches of a concrete-filled double skin steel tube column with a square section and a concrete-filled double skin steel tube column with
3.3. Torsion moment versus rotation angle skeleton curves The torsion moment versus rotation angle skeleton curves of concrete-filled double skin steel tube column specimens are shown in Fig. 10. According to the skeleton curves of specimens, the key mechanical characteristic data can be extracted, as shown in Table 3. The yield point of specimens can be defined according to the methods in reference [14]. The rotation ductility coefficient μθ is the ratio of the ultimate torsional angle θu to the yield rotation angle θy, which is an important index to measure the inelastic deformation capacity of members [15]. The larger μθ is in an effective range, the better the seismic performance of members is. Tp is the peak value of the Torsion moment. The ultimate torsional angle θu refers to the maximum torsion angle subjected to a load larger than 85% of the ultimate bearing capacity or the torsion angle at the end of the test. From Fig. 10 and
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Fig. 10. Torsion moment versus rotation angle skeleton curves.
Table 3 Mechanical characteristics of specimens. Specimen label
CC-T1 CC-T2 RR-T1 RR-T2 SS-T1 SS-T2
θy/(deg.)
Ty/(kN m)
θu/(deg.)
Tp/(kN m)
μθ
+
-
+
-
+
-
+
-
+
-
333.45 394.17 126.37 135.61 284.31 291.02
−343.29 −395.76 −113.70 −132.56 −338.39 −280.70
2.46 2.88 0.87 1.17 3.03 1.78
−2.70 −2.98 −1.22 −0.97 −2.76 −1.65
501.68 519.74 149.57 174.61 334.62 348.65
−489.19 −522.48 −148.47 −174.44 −364.98 −341.36
9.09 11.87 5.34 5.33 7.95 4.88
−9.08 −12.07 −5.45 −4.71 −7.82 −4.84
3.70 4.12 6.14 4.56 2.62 2.74
3.36 4.05 4.47 4.86 2.83 2.93
axial tensile strain exists on the outer steel tubes of concrete-filled double skin steel tube columns with circular, square and rectangular sections, and the axial strain value increases with the increase of the torsion moment. Fig. 12 shows the change rule of the circumferential strain of the outer steel tube of specimens. As we can see from Fig. 12, with increasing torsion moment, the circumferential strains of the outer steel tubes of all specimens are increasing at the same time, which shows that the outer steel tubes of concrete-filled double skin steel tube columns have a restraining effect on concrete under the pure torsion loading and that this effect is enhanced with the increase of the torsion moment. From Fig. 11 and Fig. 12, it can be concluded that the outer steel tubes of specimens under cyclic pure torsion loading are under the compound action of tension and torsion. According to the condition of deformation harmony, the inner steel tube is also under the compound action of tension, and torsion and the sandwiched concrete is under the compound action of compression and torsion. The strain of the outer steel tube can be used to calculate the bearing torsion moment of the outer tube.
a rectangular section are obvious, which means that the ductility of specimens with circular sections are significantly higher than specimens with square sections and rectangular sections. 3.4. Strain of outer steel tubes The strain of measured points on the outer steel tubes of all concrete-filled double skin steel tube column specimens are shown in Fig. 11 and Fig. 12, including the axial strain and circumferential strain. The strains of different measuring points on the same section of the outer steel tubes of concrete-filled double skin steel tube columns with circular sections are similar, so only a combination of statistics measured by one strain rosette from one point is selected for comparison. Meanwhile, the strains of different measuring points on the same section of the outer steel tubes of concrete-filled double skin steel tube columns with square sections or rectangular sections are obviously different, so the strain values of the long edge midpoint are selected for comparison. From Fig. 11, we can see that, under the pure torsion loading, the 433
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Fig. 11. Torsion moment versus axial strain curves.
In this formula, +Fi and -Fi represent the i times of the loading value of the positive and negative peak points, respectively, and +Xi and -Xi represent the i times of the displacement value of the positive and negative peak points. The calculation results of the torsional stiffness degradation of all specimens are shown in Fig. 13. From Fig. 13, we can see that: (1) the stiffness degradation of concrete-filled double skin steel tube columns is extremely obvious at the initial stage of loading; with the gradual increase of the rotation angle, the stiffness decreases slowly, and the
3.5. Stiffness degradation The stiffness characteristics of specimens can be expressed by secant stiffness, and according to the specification for seismic test of building (JGJ/T101-2015), the secant stiffness Ki can be calculated by the following formula:
Ki =
+Fi + −Fi +Xi + −Xi
(1)
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Fig. 12. Torsion moment versus transverse strain curves.
stiffness shows a decreasing trend during the entire process; and (2) under the condition of the same section sizes and shapes, the torsional stiffness of specimens with a larger sectional hollow ratio is slightly higher than that of the specimens with a small hollow ratio in the later loading stage.
loading times under cyclic loading, which is shown via the strength degradation coefficient. According to the specification for seismic test of building (JGJ/T101-2015), the strength degradation coefficient λi can be calculated by the following formula:
λi =
3.6. Strength degradation
F ij F ij − 1
(2)
In this formula, F ij represents the loading value of the i times of the cyclic peak point with the j level loading, and F i-1 j represents the loading
Strength degradation refers to the phenomenon by which specimens’ bearing capacity gradually decreases with the increase of cyclic 435
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Fig. 13. Torsion stiffness degradation curves.
Fig. 16 shows the calculation results of the equivalent viscous damping coefficient of all specimens. From Fig. 16, we can see that: (1) during the initial loading period, a concrete-filled double skin steel tube column is still in the elastic stage, and the energy dissipation capacity of specimens is small; with the increase of the rotation angle, the energy dissipation capacity of specimens increases continuously; in the elasticplastic stage, the growth rate of the specimen energy dissipation capacity decreases; (2) local out-of-plane buckling had not occurred on the concrete-filled double skin steel tube columns with circular sections during the entire loading process, and the equivalent viscous damping coefficient of specimens such as CC-CT1 and CC-CT2 still increases with the increase of the torsion angle. At the beginning of loading, the equivalent viscous damping coefficients of concrete-filled double skin steel tube columns with square sections (SS-T1 and SS-T2) and concrete-filled double skin steel tube columns with rectangular sections (RR-T1 and RR-T2) always increase with the increase of the torsion angle. When the steel tubes of specimens are buckling (and the rotation angle is approximately 5°), the equivalent viscous damping coefficient of the specimens begins to decrease, and the equivalent viscous damping coefficient of the specimens with rectangular sections decreases faster. The following conclusion can be drawn: the seismic behavior decreases in the order of circular section, square section and rectangular section. A different section type can be applied to different architectures. (3) For the concrete-filled double skin steel tube columns with square sections and rectangular sections, the equivalent viscous damping coefficient of specimens is higher for higher steel quantity of the inner steel tubes; after local lateral buckling occurs on the outer steel tubes, concrete in the buckling area was crushed and lost bearing capacity. This means that the inner steel tube should bear more torsion loading after the outer steel tube undergoes buckling. As we know, the
value of the i-1 times of the cyclic peak point with the j level loading. The calculation results of the strength degradation coefficient of all specimens are shown in Fig. 14. From Fig. 14, we can see that: (1) the bearing capacity of concrete-filled double skin steel tube columns is strengthened in the initial loading stage; (2) with the gradual increase of the torsion angle, the strength degradation coefficient of a concretefilled double skin steel tube column with a circular section still remains above 0.9, and the strength degradation coefficients of a concrete-filled double skin steel tube column with a square section and one with a rectangular section remain above 0.8, which shows that the strength degradation phenomenon of concrete-filled double skin steel tube columns is not obvious under the cyclic reciprocating torsional loading. 3.7. Energy dissipation capacity The energy dissipation capacity of specimens is an important parameter reflecting the seismic performance of members. The energy dissipation capacity is usually measured by the included areas of loading-deformation hysteretic curves. A fuller hysteresis loop means it includes bigger areas, which represents the stronger energy dissipation capacity of specimens. The energy dissipation capacity, usually evaluated by the equivalent viscous damping coefficient ζeq and the calculating method, is given below:
ζ eq=
1 S(ABC + CDA) ∙ 2π S(OBE + ODF)
In this formula, S(ABC+CDA) represents the included areas of loadingdisplacement hysteretic curves, and S(OBE+ODF) represents the sum of the areas of the triangles ΔOBC and ΔODF, as Fig. 15 shows:
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Fig. 14. Strength degradation coefficient curves.
dissipation capacity of concrete-filled double skin steel tube columns is good. The torsional strength degradation and stiffness degradation of concrete-filled double skin steel tube columns with circular sections are relatively higher than those of concrete-filled double skin steel tube columns with square sections and rectangular sections. (2) During the entire loading process, the torsional bearing capacity of concrete-filled double skin steel tube columns with circular sections increases slowly, but the torsional bearing capacity of concretefilled double skin steel tube columns with square sections and rectangular sections begins to decrease when the local out-of-plane buckling occurs on the outer steel tube of specimens. Because of the lateral restraint of concrete, the failure modes of concrete-filled double skin steel tube columns with square sections and rectangular sections are the outer steel tubes buckling outward, the inner steel tubes buckling inward, and concrete in the buckling area becoming crushed. The positions of failure areas occur on the outer steel tubes and inner steel tubes at the same height. (3) Under the cyclic torsional loading, the torsional performance of concrete-filled double skin steel tube columns with circular sections is better than that of concrete-filled double skin steel tube columns with square sections and rectangular sections. Under the condition of the same section size and same thickness of the inner steel tube, the hollow ratio has little influence on the torsional behavior of concrete-filled double skin steel tube columns under cyclic torsional loading.
P B F
A
O
E C
Δ
D Fig. 15. Calculation of the equivalent viscous damping coefficient.
stress of material in the central region of the section of members under bending and torsion is less. Under the condition of the same amount of material, members with a hollow section can bear larger loading. 4. Conclusions In this paper, pseudo-static tests on six concrete-filled double skin steel tube columns under cyclic pure torsion loading have been carried out, and the failure modes, torsion moment-rotation angle hysteretic characteristics, strain state and its change rules of concrete-filled double skin steel tube columns under cyclic pure torsion loading are studied. (1) The torsion moment-rotation angle hysteresis curve of the concretefilled double skin steel tube columns under pure torsion loading is full and without any pinch phenomenon. This shows that the energy
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Fig. 16. Equivalent viscous damping coefficient curves. [6] M. Pagoulatou, T. Sheehan, X.H. Dai, D. Lam, Finite element analysis on the capacity of circular concrete-filled double-skin steel tubular (CFDST) stub columns, Eng. Struct. 72 (2014) 102–112. [7] L.H. Han, H. Huang, Z. Tao, X.L. Zhao, Concrete-filled double skin steel tubular (CFDST) beam-columns subjected to cyclic bending, Eng. Struct. 28 (2006) 1698–1714. [8] L.H. Han, H. Huang, Z. Tao, X.L. Zhao, Concrete-filled double skin steel tubular (CFDST) beam-columns subjected to cyclic bending, Eng. Struct. 28 (2006) 1698–1714. [9] 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 (2004) 1129–1158. [10] L.H. Han, Z. Tao, H. Huang, X.L. Zhao, Concrete-filled double skin (SHS outer and CHS inner) steel tubular beam-columns, Thin-Walled Struct. 42 (2004) 1329–1355. [11] H. Huang, L.H. Han, X.L. Zhao, Investigation on concrete filled double skin steel tubes (CFDSTs) under pure torsion, J. Constr. Steel Res. 90 (2013) 221–234. [12] J.G. Nie, Y.H. Wang, J.S. Fan, Experimental study on seismic behavior of concrete filled steel tube columns under pure torsion and compression-torsion cyclic load, J. Constr. Steel Res. 79 (2012) 115–126. [13] G. Shi, H.Y. Ban, S.K. Bijlaard, Tests and numerical study of ultra-high strength steel columns with end restraints, J. Constr. Steel Res. 70 (2012) 236–247. [14] X.H. Zhou, J.P. Liu, Performance and Design of Steel Tube Confined Concrete Column, Science Press, Beijing, 2010. [15] J.R. Tang, Seismic Resistance of Reinforced Concrete Frame Joints, Southeast University Press, Nanjing, 1989.
Acknowledgements The writers gratefully acknowledge the financial support provided by the National Science Fund of China (#51508052), State Key Laboratory of Coastal and Offshore Engineering (LP1620) and Opening Funding of provided by key laboratory for structural engineering and disaster prevention of fujian province. References [1] L.H. Han, Y.F. Yang, Advanced Composite and Mixed Structures Testing-Theory and Design Approach, China Architecture & Building Press, Beijing, 2007. [2] S. Wei, S.T. Mau, C. Vipulanandan, et al., Performance of new sandwich tube under axial loading: analysis, J. Struct. Eng. ASCE 121 (12) (1995) 1815–1821. [3] F. Yagishita, H. Kitoh, M. Sugimoto, et al, Double-skin composite tubular columns subjected cyclic horizontal force and constant axial force, in: Proceedings of the 6th ASCCS Conference, Los Angeles, USA, 2000, pp. 497–503. [4] X.L. Zhao, R. Grzebieta, Strength and ductility of concrete filled double-skin (SHS inner and SHS outer) tubes, Thin-Walled Struct. 40 (2002) 199–213. [5] M. Elchalakani, X.L. Zhao, R. Grzebieta, Tests on concrete filled double-skin (CHS outer and SHS inner) composite short columns under axial compression, ThinWalled Struct. 40 (2002) 415–441.
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Full length article
Experimental study of the cyclic behavior of concrete-filled double skin steel tube columns subjected to pure torsion
MARK
⁎
Yu-Hang Wanga,b, , Guo-Bing Luc, Xu-Hong Zhoua,b a b c
School of Civil Engineering, Chongqing University, Chongqing 400045, China Key Laboratory of New Technology for Construction of Cities in Mountain Area (Chongqing University), Ministry of Education, Chongqing 400045, China State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Concrete-filled double skin steel tube columns Quasi-static test Cyclic torsion Hysteretic performance Failure mode
Based on a quasi-static test on six concrete-filled double skin steel tube columns subject to cyclic pure torsion, the torsion behavior of concrete-filled double skin steel tube columns with various section types, hollow ratios and steel ratios was studied. The failure modes, torsion-rotation angle hysteretic curves and strain distribution law of concrete-filled double skin steel tube columns under reversed cyclic loading are obtained. The test results show that the hysteretic curves of concrete-filled double skin steel tube columns under pure torsion are plump. The unloading stiffness was close to the initial elastic stiffness. The good energy dissipation capacity of concretefilled double skin steel tube columns can be observed. Under a cyclic torsion moment, the torsion-resistance capacity of circular concrete-filled double skin steel tube columns was better than that of square and rectangular concrete-filled double skin steel tube columns. With the same thickness of the inner steel tube and the same section size and shape, the hollow ratio of concrete-filled double skin steel tube columns has little effect on the cyclic torsion behavior.
1. Introduction A concrete-filled double skin steel tube column (CFDST) is a composite member formed by pouring concrete between two concentric steel tubes. Compared with traditional solid concrete-filled steel tube columns (CFSTs), concrete-filled double skin steel tube columns have a wider section and larger bending stiffness using the same amount of materials. Concrete-filled double skin steel tube columns can be used in engineering areas such as piers, water-resistant casing pipes of offshore oil drilling platforms, and piles with large diameters in long-span electric power pylons and high-rise buildings. The major section types of concrete-filled double skin steel tubes are circular nested circular, circular nested square, square nested circular, square nested square, and rectangular nested rectangular [1]. Many studies have conducted experimental and theoretical analysis of the static behavior and seismic performance of concrete-filled double skin steel tube columns under bending moments and axial force (e.g., [2–8]), and the results have shown that concrete-filled double skin steel tube columns not only have large axial stiffness and flexural capacity but also possess satisfactory seismic performance. Taking the diameterto-thickness ratio, hollow ratio, slenderness ratio and eccentricity ratio of tubes as the main parameters, Han [9,10] proposed practical
⁎
calculation methods for the ultimate bearing capacity of concrete-filled double skin steel tube columns under axial loading and eccentric loading by conducting an axial compression and eccentric compression experiment on concrete-filled double skin steel tube columns. Taking the steel ratio and hollow ratio as the main parameters, Huang [11] carried out an experimental study and finite element analysis on the mechanical behavior of CFDSTs under monotonic pure torsion and proposed design formulas for the calculation of the torsional capacity of CFDSTs. In various practical engineering applications, CFDST members may be subjected to cyclic torsional loading, such as piers of a curved girder bridge and corner columns of a high-rise building under an earthquake or transmission towers that cross a river or sea under wind loading or an earthquake. Therefore, it is necessary to investigate the behavior of CFDST members under cyclic pure torsion. Compared with concretefilled steel tube columns, CFDST columns can make full use of the mechanical properties of materials. Reference [12] shows that concretefilled steel tube columns have perfect seismic performance. The torsion moment versus rotation angle hysteresis loops of CFST columns under cyclic torsion were plump. Torsion moment versus rotation angle skeleton curves have no obvious descending branch. Stiffness degradation and strength degradation of concrete-filled steel tube columns were not
Corresponding author at: School of Civil Engineering, Chongqing University, Chongqing 400045, China. E-mail address: [email protected] (Y.-H. Wang).
http://dx.doi.org/10.1016/j.tws.2017.10.034 Received 21 April 2017; Received in revised form 12 October 2017; Accepted 17 October 2017 0263-8231/ © 2017 Elsevier Ltd. All rights reserved.
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End plate
200
300
20
600
300
325
300
20
Shear key
End plate
770
300
(a) Elevation view
200
Inner steel tube
325
300
475
Outer steel tube
300
(b) Section form of specimens
Fig. 1. Geometric dimensions of the specimens.
variable parameters in the tests are the tube shape (circular, square or rectangular) and the hollow ratio ψ. The hollow ratio ψ is given by ψ = Ah/Asc. Ah is the hollow section area, which is given by Ah = π(d-ti)2/4 for a circular section, and Ah = (h-ti)(b-ti) for a square or rectangular section. Asc is the cross-sectional area of the CFDST (= Aso+Ac+Asi+Ah). Aso is the cross-sectional area of the outer steel tube. Ac is the cross-sectional area of the sandwiched concrete. Asi is the cross-sectional area of the inner steel tube. In references [11,12], welded steel tubes are used to create specimens, and the welding of steel tubes cracked in the experimentation. In this test, the seamless steel tubes are used for specimens to avoid the breakage of welding on steel tubes. The end plate and end region of the steel tubes are connected by a fillet weld. The surfaces of the upper and lower end plates between the double steel cylinders should be respectively welded with four shear connectors not only to ensure that the steel tubes and concrete can bear loading together but also to make sure that the torsion moment in the end region of the specimens can be transferred to steel tubes and concrete equably. The concrete between double skin steel tubes is poured through the holes reserved in the upper end plates.
Table 1 Details of the specimens. Section type
Specimen label
Dimensions of the outer steel tube D(H × B) × to (mm)
Dimensions of the inner steel tube d(h × b) × ti (mm)
ψ
CC-T1 CC-T2
ϕ325 × 8.15 ϕ325 × 8.15
ϕ159 × 4.34 ϕ219 × 6.30
0.21 0.40
RR-T1 RR-T2
300 × 200 × 4.60 300 × 200 × 4.60
160 × 80 × 3.80 200 × 100 × 3.88
0.18 0.29
SS-T1 SS-T2
300 × 300 × 5.34 300 × 300 × 5.34
100 × 100 × 3.54 200 × 200 × 3.54
0.09 0.41
obvious. However, there is still a lack of research on the mechanical properties of concrete-filled double skin tube columns under cyclic pure torsion loading. This paper focuses on the failure modes and hysteretic behavior of concrete-filled double skin steel tube columns under cyclic pure torsion by carrying out pseudo-static testing and analysis.
2.2. Material properties The strength grade of the concrete is C40. When the concrete is poured into the double skin steel tubes, the concrete test cubes, which are 150 mm on each edge, should be made for the material strength test, and both the specimens and concrete cubes should be naturally maintained under the same conditions. After 28 days, the compressive strength of those concrete test tubes was measured by standard testing methods, and the average value of the concrete compressive cube strength was 42.1 MPa. The property test data of 9 steel tubes is shown in Table 2 and Fig. 2, where fy is the yield strength of the steel tube, fu is the ultimate strength of the steel tube, and Es is the Young's modulus of the steel tube. From the material test, it can been seen that expect steel tubes numbered as 6, 8 and 9 shown in Fig. 2, the stress-strain curves of the coupons taken from other steel tubes have a visible yielding plateau. Thus, the stress corresponding to the plastic strain of 0.2% is adopted as the yield strength for steel tubes numbered as 6, 8 and 9 based on the method proposed by reference [13].
2. Experimental program 2.1. Design and manufacturing of specimens In this paper, six specimens of concrete-filled double skin tube columns were designed, including 2 CFDST members with circular hollow sections (CHSs) as the inner tube and outer tube, 2 CFDST members with square hollow sections (SHSs) as the inner tube and outer tube and 2 CFDST members with rectangular hollow sections (RHSs) as the inner tube and outer tube. The information of these specimens is shown in Fig. 1 and Table 1, where D (d) is the outside diameter of the outer (inner) circular steel tube, H (h) and B (b) are the outside diameters of the outer (inner) square and rectangular steel tube, and to (ti) is the wall thickness of the outer (inner) steel tube. The main Table 2 Steel material properties. No.
Dimensions of the steel tube (mm)
fy (MPa)
fu (MPa)
Es (× 105 MPa)
No.
Dimensions of the steel tube (mm)
fy (MPa)
fu (MPa)
Es (× 105 MPa)
1 2 3 4 5
ϕ325 × 8.15 ϕ219 × 6.30 ϕ159 × 4.34 300 × 300 × 5.34 200 × 200 × 3.54
317.07 361.27 329.02 352.00 283.00
506.41 481.87 475.46 508.57 403.67
2.10 2.08 2.33 1.97 2.17
6 7 8 9
100 300 200 160
310.67 232.71 406.33 353.33
371.67 388.78 479.33 430.33
1.91 2.05 2.39 1.87
426
× × × ×
100 × 3.54 200 × 4.60 100 × 3.88 80 × 3.80
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Fig. 2. Stress versus strain curves of the steel tubes.
Fig. 3. Test device.
high-strength bolts. One end of the rigid link connects with the middle of the top girder through an idealized hinge joint, and the other end also connects with the reaction wall using an idealized hinge joint. The rigid link can guarantee that there are no bending moments in specimens during the loading process. Cyclic torsional loading can be produced by applying compressive force and tensile force on the top beam through a hydraulic servo actuator. Nie [12] concluded that the rotation angle has a good linear relationship with the horizontal displacement of the concentrated loading point, and the displacement control method can be used for the torsion
2.3. Loading device and loading program To realize the pseudo-static cyclic loading of concrete-filled double skin steel tube columns under pure torsion loading, a loading device is designed, as shown in Fig. 3. The loading device is mainly composed of a top girder, a steel base, and a rigid link. The upper end plate and lower end plate of specimens should be connected with the top girder and steel base using high-strength bolts. The relative slip between specimens’ plates and top beams and bases cannot occur in the process of cyclic loading by the guarantee of exerting pre-tensile stress on the 427
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15
200
to 45°. During the entire loading process, the welding seam between the steel tube and end plates is undamaged, and neither the outer steel tube nor the inner steel tube undergoes buckling deformation. In a word, the specimens are not obviously broken.
10
150 100
5
50 0
0 -50
-5
-100
Rotation angle (°)
Displacement of load point (mm)
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3.1.2. Specimen CC-CT2 As the torsion angle of the specimen CC-T2 reaches 10.85°, the paint layer close to the end of the steel tube cracks along the circumferential direction, and the oil paint on the middle part of the steel tube begins peeling off and forms many waves in the direction of 45°. Finally, the outer steel tube close to the lower plate cracks along the circumferential direction. The length of the crack is close to 3/4 of the circumference. On the one end, the crack continues to develop obliquely along the column, and the angle between the crack and the horizontal line is approximately 45°. At the end of the test, peeling off the outer steel tube and concrete, the bottom of the inner steel tube was found to be cracked across the cross-section; the inner steel tube exhibited buckling deformation inward in the cracks, and there was no buckling deformation in the middle part of the inner steel pipe.
-10
-150 -200 0
5
10
15
20
25
30
35
40
-15 45
Number of loading cycles Fig. 4. Loading process.
loading with a constant incremental rotation angle. Test loading follows the displacement control, and the loading systems are shown in Fig. 4; the loading rate is controlled at 5 mm/min. The horizontal displacement Δ0 of the loading points can be calculated by the yield strength of the outer steel tubes. The first-stage loading follows a 0.5Δ0 displacement to perform cyclic loading once, the second-stage loading follows a Δ0 displacement to perform cyclic loading once, the third-stage loading follows a 5Δ0 displacement to perform cyclic loading twice, and the following stages of loading follow a 5Δ0 incremental displacement to perform cyclic loading twice until the damage of specimens occurs.
3.1.3. Specimen RR-CT1 As for specimen RR-T1, when the torsion angle reaches 3.99°, the middle part of the east and west surfaces of the outer steel tube begin buckling, an obvious outward wave occurs on the middle part of the west surface of the outer steel tube, and the included angle between the wave direction and the horizontal line is close to 49°. As soon as the torsion angle reaches 4.51°, the middle part of the south and north surfaces of the outer steel tube begin buckling outward. When the torsion angle reaches 5.8°, an oblique crack occurs on the middle part of the west surface of the outer steel tube, and the distance between the crack and top plate is 18 cm. With the increase of the reciprocating torque, the crack expands in the oblique direction, and the concrete of the cracked areas is crushed. As the torsion angle changes to 8.08°, Xshaped cracks occur on the buckling area of the south surface of the outer steel tube. When the torsion angle reaches 9.06°, X-shaped cracks occur on the middle part of the north surface of the outer steel tube, and the distance between the cracks and the top plate is 18 cm. With increasing reciprocating torque, two X-shaped cracks occur on the west surface of the outer steel tube, and the cracks gradually develop and connect. At the end of the test, peeling off the outer steel tube and concrete, the west surface of the inner steel tube was bent inwards.
2.4. Measuring point arrangement The tests aim to measure the horizontal concentrated force of the loading point, the horizontal displacement of the loading point, and the surface strain of the outer steel tube. The arrangement of the displacement meter is shown in Fig. 5. As the value of the torsion moment of each section of specimens under pure torsion loading is the same, the value of the rotation angle per unit length of each section of specimens under pure torsion loading is identical. The strain measuring points in this test are arranged at the middle section along the height of the specimen to avoid the influence of the weld heat-affected zone on the ends of the steel tube, as shown in Fig. 6.
3.1.4. Specimen RR-T2 As the torsion angle of the specimen RR-T2 approaches 3.82°, the middle part of the west surface of the outer steel tube begins buckling deformation outward, a wave was formed, and the included angle between the wave and the horizontal line is 46°. As soon as the torsion angle reaches 5.16°, a wave occurs on the middle part of the north surface and south surface of the outer steel tube. The included angle between the wave on the north surface and the horizontal line is 47°, and the included angle between the wave on the south surface and the horizontal line is 45°. When the torsion angle changes to 5.81°, the east
3. Test results and analysis 3.1. Test phenomenon and failure modes 3.1.1. Specimen CC-CT1 When the torsion angle of the specimen CC-T1 reaches 9.13°, the paint layer on the steel tube surface close to the end plate peels off, the oil paint on the middle part of the steel tube begins peeling off obliquely, and the angle between cracking and the horizontal line is close
Fig. 5. Measuring point arrangement of the displacement meters.
N W
E Displacement meter
800
S
Displacement meter
(a) vertical view
(b) side view
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Fig. 6. Arrangement of strain measuring points.
layer of the upper outer steel tube cracks in the circumferential direction, and the middle part of the east surface of the outer steel tube begins buckling outward and forms a wave. The included angle between the wave and the horizontal line is 46°. As the torsion angle approaches 5.13°, both the south surface and north surface of the outer steel tube begin buckling outward and form a wave on each surface, while the included angles between the wave on the south surface and north surface and the horizontal line are 49° and 45°, respectively. As soon as the torsion angle reaches 6.48°, an oblique crack occurs on the middle part of the east surface of the outer steel tube, and the crack's distance to the top plate is 18 cm. As the torsion angle approaches 8.34°, an X-type crack occurs on the south surface of the outer steel tube, and it is 15 cm from the top plate. When the torsion angle reaches 9.08°, an oblique crack occurs on the middle part of the east surface of the outer steel tube, and it is 10 cm in distance from the top plate. Then, this crack first develops obliquely to the top of the south surface and turns to expansion on the south surface along the horizontal line until the complete cracking of the south surface of the outer steel tube. An 11-cm vertical crack occurs on the top of the southwest corner of the outer steel tube. At the end of the test, peeling off the outer steel tube and concrete, the north surface, east surface and south surface are all buckling inward. In references [11,12], the behavior of CFDSTs under static pure torsion and CFST columns under cyclic torsion were investigated, respectively. The global failure modes of all specimens under cyclic pure torsion are shown in Fig. 7, and the failure modes of inner steel tubes are shown in Fig. 8. As we can see, concrete-filled double skin steel tube columns with circular sections possess a large ultimate torsional angle and excellent ductility under reciprocating torque loading, which is similar to the CFST columns with circular sections in reference [12]. However, the failure modes of CFDST columns with circular sections were different from those of CFST columns with circular sections in reference [12] and CFDST columns with circular sections in reference [11]. In this test, the failure of circular-section specimens occurred on the end of the steel tubes, and the failure modes of circular-section specimens were the low cyclic fatigue damage of the weld heat-affected zone. Steel tubes had no obvious damage. In reference [12], steel tubes of CFSTs with circular sections cracked, and the concrete near the crack was crushed. In reference [11], CFDSTs with circular sections had no
surface of the outer steel tube begins buckling outward. As the torsion angle reaches 7.86°, an oblique crack occurs on the middle part of the west surface of the outer steel tube, and the distance between the crack and top plate is 18 cm. Then, the crack expands obliquely. As soon as the torsion angle reaches 8.35°, a vertical crack occurs on the middle part of the south surface of the outer steel tube. In addition, an Xshaped crack occurs on the buckling area of the west surface and south surface of the outer steel tube, and the concrete in the cracked area is crushed. At the end of the test, peeling off the outer steel tube and concrete, the four surfaces of the inner steel tube are buckling inward, a crack occurs on the top southwest corner of the inner steel tube and this crack develops towards the upper south side of the inner steel tube with an oblique direction. 3.1.5. Specimen SS-T1 When the torsion angle of the specimen SS-T1 reaches 4.5°, the middle part of the west surface of the outer steel tube begins buckling deformation outward, and a wave occurs on the west surface of the outer steel tube. The included angle between the wave and horizontal line is 52°. As the torsion angle changes to 5.2°, the east surface and south surface of the outer steel tube begins buckling deformation outward. A wave occurs on the east surface and south surface of the outer steel tube, and the included angles between the waves and the horizontal line are both 49°. When the torsion angle reaches 8.23°, an oblique crack occurs on the middle part of the east surface and south surface of the outer steel tube, and the distances between the two cracks and the top plate are both 20.7 cm. However, two cracks develop obliquely. As soon as the torsion angle increases to 9.7°, two X-type cracks occur on the east surface and south surface of the outer steel tube, but the two cracks on the south surface of the outer steel tube are mutually connected; concrete in the cracked area is crushed. At the end of the test, peeling off the outer steel tube and concrete, the four sides of the inner steel tube are buckling inward. Additionally, the height of the buckling area of the inner steel tube to the lower end plate and the height of the buckling area of the outer steel tube to the lower plate are the same. 3.1.6. Specimen SS-T2 When the torsion angle of specimen SS-T2 reaches 3.9°, the paint 429
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Fig. 7. Global failure modes of specimens.
cracked. The failure modes of CFDST columns with square sections and rectangular sections are local buckling of steel tubes and cracking of steel tubes, and the sandwiched concrete was crushed. Compared with the experimental results in reference [12], the failure modes of CFST columns with rectangular sections were similar to those of CFDST columns with square sections and rectangular sections.
obvious damage, but the sandwiched concrete cracked. The ultimate torsional angle of square-section specimens and rectangular-section specimens is relatively small. For square-section specimens and rectangular-section specimens, the cross-diagonal waves appeared on the outer steel tubes, and cracks appeared on the tubes with lateral deformation finally. In reference [11], CFDSTs with square sections under static torsion were undamaged except the welding of one specimen 430
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Fig. 8. Buckling deformation of the internal steel tube of specimens.
lower, showing that concrete-filled double skin steel tube columns with circular sections have good energy dissipation capacity under the reciprocating torsion loading. Both concrete-filled double skin steel tube columns with square sections and concrete-filled double skin steel tube columns with rectangular sections showed a high degree of degradation of bearing capacity when the loading approached the peak of the bearing capacity. Compared with the concrete-filled double skin steel tube columns with circular sections, the energy dissipation capacity of these two types of concrete-filled double skin steel tube columns is lower.
3.2. Torsion moment versus rotation angle hysteresis loops The torsion moment versus rotation angle hysteresis curves of concretefilled double skin steel tube columns under the reciprocating torque loading are shown in Fig. 9. As Fig. 9 shows, the hysteresis loops of concrete-filled double skin tube columns are in plump shape and without a significant pinch phenomenon. The unloading stiffness is close to the initial elastic stiffness, and the degradation degree of the bearing capacity and stiffness of concrete-filled double skin steel tube columns with circular sections are
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Fig. 9. Torsion moment versus rotation angle hysteresis loops.
Table 3, we can see that, for the specimens with circular, square and rectangular sections, a similar conclusion could be drawn: (1) all torsion moment-rotation angle skeleton curves of specimens are S-shaped, which shows that all specimens under the low cyclic torsion loading experienced three loading phases (elastic state, plastic state and limit state); (2) for specimens with the same external overall dimensions of sections and loading methods (CC-T1, CC-T2; RR-T1, RR-T2; SS-T1, and SS-T2), increasing the section hollow ratio of specimens leads to a decrease of the sections and concrete areas, but due to the increase in the number of inner steel tubes, the ultimate torsional bearing capacity and elastic torsion stiffness of specimens are not reduced; (3) the descending branch of the skeleton curve of a concrete-filled double skin steel tube column with a circular section was not obvious, while the descending branches of a concrete-filled double skin steel tube column with a square section and a concrete-filled double skin steel tube column with
3.3. Torsion moment versus rotation angle skeleton curves The torsion moment versus rotation angle skeleton curves of concrete-filled double skin steel tube column specimens are shown in Fig. 10. According to the skeleton curves of specimens, the key mechanical characteristic data can be extracted, as shown in Table 3. The yield point of specimens can be defined according to the methods in reference [14]. The rotation ductility coefficient μθ is the ratio of the ultimate torsional angle θu to the yield rotation angle θy, which is an important index to measure the inelastic deformation capacity of members [15]. The larger μθ is in an effective range, the better the seismic performance of members is. Tp is the peak value of the Torsion moment. The ultimate torsional angle θu refers to the maximum torsion angle subjected to a load larger than 85% of the ultimate bearing capacity or the torsion angle at the end of the test. From Fig. 10 and
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Fig. 10. Torsion moment versus rotation angle skeleton curves.
Table 3 Mechanical characteristics of specimens. Specimen label
CC-T1 CC-T2 RR-T1 RR-T2 SS-T1 SS-T2
θy/(deg.)
Ty/(kN m)
θu/(deg.)
Tp/(kN m)
μθ
+
-
+
-
+
-
+
-
+
-
333.45 394.17 126.37 135.61 284.31 291.02
−343.29 −395.76 −113.70 −132.56 −338.39 −280.70
2.46 2.88 0.87 1.17 3.03 1.78
−2.70 −2.98 −1.22 −0.97 −2.76 −1.65
501.68 519.74 149.57 174.61 334.62 348.65
−489.19 −522.48 −148.47 −174.44 −364.98 −341.36
9.09 11.87 5.34 5.33 7.95 4.88
−9.08 −12.07 −5.45 −4.71 −7.82 −4.84
3.70 4.12 6.14 4.56 2.62 2.74
3.36 4.05 4.47 4.86 2.83 2.93
axial tensile strain exists on the outer steel tubes of concrete-filled double skin steel tube columns with circular, square and rectangular sections, and the axial strain value increases with the increase of the torsion moment. Fig. 12 shows the change rule of the circumferential strain of the outer steel tube of specimens. As we can see from Fig. 12, with increasing torsion moment, the circumferential strains of the outer steel tubes of all specimens are increasing at the same time, which shows that the outer steel tubes of concrete-filled double skin steel tube columns have a restraining effect on concrete under the pure torsion loading and that this effect is enhanced with the increase of the torsion moment. From Fig. 11 and Fig. 12, it can be concluded that the outer steel tubes of specimens under cyclic pure torsion loading are under the compound action of tension and torsion. According to the condition of deformation harmony, the inner steel tube is also under the compound action of tension, and torsion and the sandwiched concrete is under the compound action of compression and torsion. The strain of the outer steel tube can be used to calculate the bearing torsion moment of the outer tube.
a rectangular section are obvious, which means that the ductility of specimens with circular sections are significantly higher than specimens with square sections and rectangular sections. 3.4. Strain of outer steel tubes The strain of measured points on the outer steel tubes of all concrete-filled double skin steel tube column specimens are shown in Fig. 11 and Fig. 12, including the axial strain and circumferential strain. The strains of different measuring points on the same section of the outer steel tubes of concrete-filled double skin steel tube columns with circular sections are similar, so only a combination of statistics measured by one strain rosette from one point is selected for comparison. Meanwhile, the strains of different measuring points on the same section of the outer steel tubes of concrete-filled double skin steel tube columns with square sections or rectangular sections are obviously different, so the strain values of the long edge midpoint are selected for comparison. From Fig. 11, we can see that, under the pure torsion loading, the 433
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Fig. 11. Torsion moment versus axial strain curves.
In this formula, +Fi and -Fi represent the i times of the loading value of the positive and negative peak points, respectively, and +Xi and -Xi represent the i times of the displacement value of the positive and negative peak points. The calculation results of the torsional stiffness degradation of all specimens are shown in Fig. 13. From Fig. 13, we can see that: (1) the stiffness degradation of concrete-filled double skin steel tube columns is extremely obvious at the initial stage of loading; with the gradual increase of the rotation angle, the stiffness decreases slowly, and the
3.5. Stiffness degradation The stiffness characteristics of specimens can be expressed by secant stiffness, and according to the specification for seismic test of building (JGJ/T101-2015), the secant stiffness Ki can be calculated by the following formula:
Ki =
+Fi + −Fi +Xi + −Xi
(1)
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Fig. 12. Torsion moment versus transverse strain curves.
stiffness shows a decreasing trend during the entire process; and (2) under the condition of the same section sizes and shapes, the torsional stiffness of specimens with a larger sectional hollow ratio is slightly higher than that of the specimens with a small hollow ratio in the later loading stage.
loading times under cyclic loading, which is shown via the strength degradation coefficient. According to the specification for seismic test of building (JGJ/T101-2015), the strength degradation coefficient λi can be calculated by the following formula:
λi =
3.6. Strength degradation
F ij F ij − 1
(2)
In this formula, F ij represents the loading value of the i times of the cyclic peak point with the j level loading, and F i-1 j represents the loading
Strength degradation refers to the phenomenon by which specimens’ bearing capacity gradually decreases with the increase of cyclic 435
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Fig. 13. Torsion stiffness degradation curves.
Fig. 16 shows the calculation results of the equivalent viscous damping coefficient of all specimens. From Fig. 16, we can see that: (1) during the initial loading period, a concrete-filled double skin steel tube column is still in the elastic stage, and the energy dissipation capacity of specimens is small; with the increase of the rotation angle, the energy dissipation capacity of specimens increases continuously; in the elasticplastic stage, the growth rate of the specimen energy dissipation capacity decreases; (2) local out-of-plane buckling had not occurred on the concrete-filled double skin steel tube columns with circular sections during the entire loading process, and the equivalent viscous damping coefficient of specimens such as CC-CT1 and CC-CT2 still increases with the increase of the torsion angle. At the beginning of loading, the equivalent viscous damping coefficients of concrete-filled double skin steel tube columns with square sections (SS-T1 and SS-T2) and concrete-filled double skin steel tube columns with rectangular sections (RR-T1 and RR-T2) always increase with the increase of the torsion angle. When the steel tubes of specimens are buckling (and the rotation angle is approximately 5°), the equivalent viscous damping coefficient of the specimens begins to decrease, and the equivalent viscous damping coefficient of the specimens with rectangular sections decreases faster. The following conclusion can be drawn: the seismic behavior decreases in the order of circular section, square section and rectangular section. A different section type can be applied to different architectures. (3) For the concrete-filled double skin steel tube columns with square sections and rectangular sections, the equivalent viscous damping coefficient of specimens is higher for higher steel quantity of the inner steel tubes; after local lateral buckling occurs on the outer steel tubes, concrete in the buckling area was crushed and lost bearing capacity. This means that the inner steel tube should bear more torsion loading after the outer steel tube undergoes buckling. As we know, the
value of the i-1 times of the cyclic peak point with the j level loading. The calculation results of the strength degradation coefficient of all specimens are shown in Fig. 14. From Fig. 14, we can see that: (1) the bearing capacity of concrete-filled double skin steel tube columns is strengthened in the initial loading stage; (2) with the gradual increase of the torsion angle, the strength degradation coefficient of a concretefilled double skin steel tube column with a circular section still remains above 0.9, and the strength degradation coefficients of a concrete-filled double skin steel tube column with a square section and one with a rectangular section remain above 0.8, which shows that the strength degradation phenomenon of concrete-filled double skin steel tube columns is not obvious under the cyclic reciprocating torsional loading. 3.7. Energy dissipation capacity The energy dissipation capacity of specimens is an important parameter reflecting the seismic performance of members. The energy dissipation capacity is usually measured by the included areas of loading-deformation hysteretic curves. A fuller hysteresis loop means it includes bigger areas, which represents the stronger energy dissipation capacity of specimens. The energy dissipation capacity, usually evaluated by the equivalent viscous damping coefficient ζeq and the calculating method, is given below:
ζ eq=
1 S(ABC + CDA) ∙ 2π S(OBE + ODF)
In this formula, S(ABC+CDA) represents the included areas of loadingdisplacement hysteretic curves, and S(OBE+ODF) represents the sum of the areas of the triangles ΔOBC and ΔODF, as Fig. 15 shows:
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Fig. 14. Strength degradation coefficient curves.
dissipation capacity of concrete-filled double skin steel tube columns is good. The torsional strength degradation and stiffness degradation of concrete-filled double skin steel tube columns with circular sections are relatively higher than those of concrete-filled double skin steel tube columns with square sections and rectangular sections. (2) During the entire loading process, the torsional bearing capacity of concrete-filled double skin steel tube columns with circular sections increases slowly, but the torsional bearing capacity of concretefilled double skin steel tube columns with square sections and rectangular sections begins to decrease when the local out-of-plane buckling occurs on the outer steel tube of specimens. Because of the lateral restraint of concrete, the failure modes of concrete-filled double skin steel tube columns with square sections and rectangular sections are the outer steel tubes buckling outward, the inner steel tubes buckling inward, and concrete in the buckling area becoming crushed. The positions of failure areas occur on the outer steel tubes and inner steel tubes at the same height. (3) Under the cyclic torsional loading, the torsional performance of concrete-filled double skin steel tube columns with circular sections is better than that of concrete-filled double skin steel tube columns with square sections and rectangular sections. Under the condition of the same section size and same thickness of the inner steel tube, the hollow ratio has little influence on the torsional behavior of concrete-filled double skin steel tube columns under cyclic torsional loading.
P B F
A
O
E C
Δ
D Fig. 15. Calculation of the equivalent viscous damping coefficient.
stress of material in the central region of the section of members under bending and torsion is less. Under the condition of the same amount of material, members with a hollow section can bear larger loading. 4. Conclusions In this paper, pseudo-static tests on six concrete-filled double skin steel tube columns under cyclic pure torsion loading have been carried out, and the failure modes, torsion moment-rotation angle hysteretic characteristics, strain state and its change rules of concrete-filled double skin steel tube columns under cyclic pure torsion loading are studied. (1) The torsion moment-rotation angle hysteresis curve of the concretefilled double skin steel tube columns under pure torsion loading is full and without any pinch phenomenon. This shows that the energy
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Acknowledgements The writers gratefully acknowledge the financial support provided by the National Science Fund of China (#51508052), State Key Laboratory of Coastal and Offshore Engineering (LP1620) and Opening Funding of provided by key laboratory for structural engineering and disaster prevention of fujian province. References [1] L.H. Han, Y.F. Yang, Advanced Composite and Mixed Structures Testing-Theory and Design Approach, China Architecture & Building Press, Beijing, 2007. [2] S. Wei, S.T. Mau, C. Vipulanandan, et al., Performance of new sandwich tube under axial loading: analysis, J. Struct. Eng. ASCE 121 (12) (1995) 1815–1821. [3] F. Yagishita, H. Kitoh, M. Sugimoto, et al, Double-skin composite tubular columns subjected cyclic horizontal force and constant axial force, in: Proceedings of the 6th ASCCS Conference, Los Angeles, USA, 2000, pp. 497–503. [4] X.L. Zhao, R. Grzebieta, Strength and ductility of concrete filled double-skin (SHS inner and SHS outer) tubes, Thin-Walled Struct. 40 (2002) 199–213. [5] M. Elchalakani, X.L. Zhao, R. Grzebieta, Tests on concrete filled double-skin (CHS outer and SHS inner) composite short columns under axial compression, ThinWalled Struct. 40 (2002) 415–441.
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