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Bond-slip behaviour of concrete-filled stainless steel circular hollow section tubes
Journal of Constructional Steel Research 130 (2017) 248–263
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Journal of Constructional Steel Research
Bond-slip behaviour of concrete-filled stainless steel circular hollow section tubes Yu Chen a, Ran Feng b,⁎, Yongbo Shao c, Xiaotian Zhang d a
School of Urban Construction, Yangtze University, Jingzhou 434023, China School of Civil and Environmental Engineering, Harbin Institute of Technology, Shenzhen 518055, China School of Mechatronic Engineering, Southwest Petroleum University, Chengdu 610500, China d College of Civil Engineering, Huaqiao University, Xiamen 361021, China b c
a r t i c l e
i n f o
Article history: Received 24 May 2016 Received in revised form 15 November 2016 Accepted 10 December 2016 Available online 22 December 2016 Keywords: Bond-slip behaviour Circular hollow section (CHS) Concrete-filled Push-out test Shear resistance Stainless steel tube
a b s t r a c t This paper presents the repeated push-out tests on concrete-filled stainless steel circular hollow section (CHS) tubes with different values of height-to-diameter ratio, diameter-to-thickness ratio and concrete strengths. The bond-slip behaviour of all specimens and the strain distribution on the exterior of stainless steel tubes along the longitudinal height direction were carefully investigated. It was found that the shear failure loads of bonding slip decreased successively with more loading cycles of the repeated push-out test employed in the same direction. Hence, the mechanical interlock force and friction force of the interface elements gradually decreased. Furthermore, the bond-slip failure of the interface elements between the inner concrete and outer stainless steel tube of the specimens consists of the adhesive stage, the sliding stage and the friction resistant stage. It can be generally concluded that 70% of the shear resistance of the bonding strength is taken by the interface friction force, while the remaining 30% of the shear resistance of the bonding strength is sustained by the chemical adhesive force and the mechanical interlock force. On the other hand, it was demonstrated that the height-to-diameter ratio (H/D) and the diameter-to-thickness ratio (D/t) of the stainless steel tube as well as the concrete strength (C) have insignificant influence on the shear resistance of the bonding strength of the interface elements. It was also shown from the comparison that the current design rules of concrete-filled carbon steel CHS tubes are inapplicable to the shear resistance of the bonding strength of concrete-filled stainless steel CHS tubes. © 2016 Elsevier Ltd. All rights reserved.
1. Introduction The applications of concrete-filled stainless steel tubes could be traced back to last century, which are nowadays increasingly used in high-rise buildings and arch bridges [1–2] owing to their esthetical appearance, excellent corrosion resistance, superior load carrying capacity and seismic behaviour, good durability and low cost of maintenance. It is worth noting that concrete-filled stainless steel tubes possess both good mechanical properties of concrete-filled steel tubes (CFST) and excellent durability of stainless steel, which promote the potential employment of concrete-filled stainless steel tubes in onshore buildings, offshore platform, bridges, and many other practical applications with requirement for higher durability. Many researches including experimental investigations and theoretical analyses were conducted on the
⁎ Corresponding author. E-mail address: [email protected] (R. Feng).
http://dx.doi.org/10.1016/j.jcsr.2016.12.012 0143-974X/© 2016 Elsevier Ltd. All rights reserved.
mechanical behaviour of concrete-filled stainless steel columns under various loading conditions [3–12]. In addition, many studies were also performed to investigate the bond-slip behaviour of concrete-filled carbon steel tubular columns [13–16]. Up to the authors' knowledge, however, there is no research being carried out on the bond-slip behaviour of concrete-filled stainless steel tubes. For the design of concrete-filled stainless steel tubes, the bond strength between inner surface of stainless steel tube and outer surface of concrete infill as well as the constitutive relation of the bond-slip behaviour are the most critical concerns to guarantee that the outer stainless steel tube and inner concrete could sustain the applied loads simultaneously and reinforce with each other. In this study, the effects of the concrete strength (C), the height-to-diameter ratio (H/D) of stainless steel tube, the diameter-to-thickness ratio (D/t) of stainless steel tube, and the repeated action on the bond strength for shear resistance between interfaces were all investigated by using testing method. Furthermore, the failure process of bond surfaces under shear action together with the strain development on the outer surface of stainless steel tube were both discussed.
Y. Chen et al. / Journal of Constructional Steel Research 130 (2017) 248–263 Table 1 Geometric parameters of concrete-filled stainless steel CHS tubes.
Nomenclature Ac As C D d D0 Es f fc ft fu fy H k Le l0 Nu n P Pnu S Su t α γ θ τKang τTest τu
249
cross-section area of inner concrete cross-section area of outer steel tube concrete strength outer diameter of stainless steel CHS tube outer diameter of steel CHS tube inner diameter of stainless steel CHS tube elastic modulus of stainless steel tube friction resistance of bonding strength concrete cube strength tensile strength of concrete ultimate tensile stress of stainless steel tube 0.2% tensile proof stress of stainless steel tube overall height of stainless steel CHS tube influential factor for exterior of steel tube overall adhesive length overall length of interface shear failure load of bonding slip loading cycle of repeated push-out test axial load shear failure load or bond-slip load bond slip between inner concrete and outer stainless steel tube critical slippage at bond-slip failure overall thickness of stainless steel CHS tube steel ratio of concrete-filled steel CHS tube correction coefficient for uncertainty confinement factor for concrete-filled steel CHS tube shear resistance of bonding strength obtained from current design rules shear resistance of bonding strength obtained from tests shear resistance of bonding strength
2. Experimental investigation 2.1. Test specimens A total of 32 concrete-filled stainless steel circular hollow section (CHS) tubes with the identical outer diameter of 76 mm were designed and tested, as shown in Fig. 1, which included different values of heightto-diameter ratio (H/D) ranged from 4 to 10, diameter-to-thickness ratio (D/t) ranged from 69.1 to 152.0 and concrete strength (C) ranged
D (mm)
t (mm)
H (mm)
D/t
H/D
C (MPa)
H304-t0.5-C20 H304-t0.7-C20 H304-t0.9-C20 H304-t1.1-C20 H456-t0.5-C20 H456-t0.7-C20 H456-t0.9-C20 H456-t1.1-C20 H608-t0.5-C20 H608-t0.7-C20 H608-t0.9-C20 H608-t1.1-C20 H760-t0.5-C20 H760-t0.7-C20 H760-t0.9-C20 H760-t1.1-C20 H304-t0.5-C50 H304-t0.7-C50 H304-t0.9-C50 H304-t1.1-C50 H456-t0.5-C50 H456-t0.7-C50 H456-t0.9-C50 H456-t1.1-C50 H608-t0.5-C50 H608-t0.7-C50 H608-t0.9-C50 H608-t1.1-C50 H760-t0.5-C50 H760-t0.7-C50 H760-t0.9-C50 H760-t1.1-C50
76
0.5 0.7 0.9 1.1 0.5 0.7 0.9 1.1 0.5 0.7 0.9 1.1 0.5 0.7 0.9 1.1 0.5 0.7 0.9 1.1 0.5 0.7 0.9 1.1 0.5 0.7 0.9 1.1 0.5 0.7 0.9 1.1
304 304 304 304 456 456 456 456 608 608 608 608 760 760 760 760 304 304 304 304 456 456 456 456 608 608 608 608 760 760 760 760
152.0 108.6 84.4 69.1 152.0 108.6 84.4 69.1 152.0 108.6 84.4 69.1 152.0 108.6 84.4 69.1 152.0 108.6 84.4 69.1 152.0 108.6 84.4 69.1 152.0 108.6 84.4 69.1 152.0 108.6 84.4 69.1
4 4 4 4 6 6 6 6 8 8 8 8 10 10 10 10 4 4 4 4 6 6 6 6 8 8 8 8 10 10 10 10
32.3 32.3 32.3 32.3 32.3 32.3 32.3 32.3 32.3 32.3 32.3 32.3 32.3 32.3 32.3 32.3 51.7 51.7 51.7 51.7 51.7 51.7 51.7 51.7 51.7 51.7 51.7 51.7 51.7 51.7 51.7 51.7
from 20 MPa to 50 MPa. Dimensions of all specimens are detailed in Table 1, in which the label ‘H304-t0.5-C20’ defines a concrete-filled stainless steel CHS tube with height ‘H’ of 304 mm, thickness ‘t’ of 0.5 mm and nominal concrete cube strength ‘C’ of 20 MPa. In the fabrication of test specimens, a gap of 50 mm was deliberately remained at the top end of each specimen between inner concrete and outer stainless steel tube for the repeated push-out test. The material properties of stainless steel tubes were determined by uni-axial tensile coupon tests based on the recommendations of the Chinese Code of Metallic Materials (GB/T 228.1-2010) [17], which include the elastic modulus (Es) of 206 GPa, 0.2% tensile proof stress (fy) of 420 MPa and ultimate tensile stress (fu) of 630 MPa. The material properties of concrete were determined from compressive concrete cube tests. The concrete cubes with nominal side length of 150 mm were produced using commercially available materials with normal mixing and curing techniques [18–19]. The material properties of the concrete are summarized in Table 2 that include the measured concrete cube strengths and the mean values for three batches of concrete cubes for nominal concrete cube strengths of 20 MPa and 50 MPa, respectively.
t
Concrete
Specimen
H
Stainless steel tube
D Concrete
D Fig. 1. Concrete-filled stainless steel CHS tube.
Table 2 Measured concrete cube strengths. Nominal concrete strength (MPa)
Batch
Measured concrete cube strength (MPa)
Mean value (MPa)
20
1 2 3 4 5 6
31.4 31.1 34.4 48.7 50.8 55.5
32.3
50
51.7
250
Y. Chen et al. / Journal of Constructional Steel Research 130 (2017) 248–263
2.2. Test setup All specimens were installed vertically in the same loading machine with the self-balanced reaction frame, as shown in Fig. 2. A hydraulic jack was used to apply the axial compression to the test specimens and monitored by the load cell, which was positioned concentrically between the hydraulic jack and the reaction frame. A steel circular solid block with the cross-section area slightly smaller than that of the inner concrete was used to apply the axial compression to the test specimens, which was positioned concentrically to the inner concrete and outer stainless steel tube of the test specimens. Therefore, the compression force was applied to the inner concrete only by means of steel circular solid block, while an end plate was placed at the bottom to support the test specimens. The bond-slip failure between inner concrete and outer stainless steel tube was then occurred.
2.3. Arrangement of measuring system All specimens were initially subjected to the incremental monotonic static loading, which was first equally divided into comparatively large load levels (around 1/30 of the estimated peak load) within the elastic range, and then reduced to the comparatively small load levels after the occurrence of the nonlinear bond-slip failure between inner concrete and outer stainless steel tube. The specimens were subsequently unloaded to zero until the inner concrete at the bottom of the specimens being fully contacted with the end plate at the bottom supported the specimens. The maximum bond slippage is approximately 40–50 mm since an initial gap of 50 mm was deliberately remained at the end of each specimen between inner concrete and outer stainless steel tube. After that, the specimens were inverted and subjected to a reverse axial compression in the same loading way. This testing procedure was repeated four times in total for each specimen for a complete repeated push-out test. The applied loads and readings of displacement transducers and strain gauges were recorded automatically at regular intervals by using a data acquisition system. Two displacement transducers were positioned at the steel plates connected to the top end of steel circular solid block at the opposite sides to monitor the relative movement of the inner concrete with respect to the outer stainless steel tube, as shown in Fig. 2. The bond
Fig. 2. Test set-up.
slippage between inner concrete and outer stainless steel tube could be obtained from the average readings of these two displacement transducers. A total of four three-element rosettes strain gauges which enable strain values in three different directions at 45° interval to be measured simultaneously were positioned in line on the exterior of stainless steel tube along the longitudinal height direction, in which two strain gauges were positioned at the locations 10 mm away from both ends of the specimens, and two other strain gauges were positioned roughly at one third and two thirds of the total height of the specimens, respectively, as shown in Fig. 3. The use of displacement transducers enables the bond slippage between inner concrete and outer stainless steel tube of the specimens to be measured at each load level. Hence, the complete axial loadbond slippage curves of all specimens can be obtained. Furthermore, the use of strain gauges enables the strain distributions at the critical locations and strain development under different load levels to be determined for the specimens of H304-t0.5-C20, H304-t1.1-C20, H760-t0.5C20 and H760-t1.1-C20. On the other hand, the generation of the bonding shear force, the development of the bonding shear failure and the effects of other influential factors on the bonding shear force were all investigated.
3. Test results 3.1. Failure modes At the beginning of the tests, the axial compression force linearly increased up to the friction between inner concrete and outer stainless steel tube of the specimens within the elastic range of the materials. There is no any slippage observed during the tests. The bond-slip between inner concrete and outer stainless steel tube of the specimens occurred once the axial compression force reached the interface friction. Then the axial compression force nonlinearly increased with the increase of the interface slippage until a large value of slippage between inner concrete and outer stainless steel tube of the specimens was obtained with a sudden great sound. The movement of the inner concrete with respect to the outer stainless steel tube of the specimens monitored by the displacement transducers increased sharply. The axial compression force decreased a lot accordingly. After that, the slippage between inner concrete and outer stainless steel tube of the specimens gradually decreased with the reduction of the applied load levels in the
Fig. 3. Arrangement of strain gauges
Y. Chen et al. / Journal of Constructional Steel Research 130 (2017) 248–263
subsequent loading increments. Eventually the movement of the inner concrete with respect to the outer stainless steel tube of the specimens monitored by the displacement transducers was quite small that can be negligible. While the axial compression force increased substantially, which means the inner concrete at the bottom of the specimens being fully contacted with the end plate at the bottom supported the specimens. It was observed that the contact face of the inner concrete slightly was crushed by unloading the specimens to zero, as shown in Fig. 4a. Friction force of the interface is the main reason for slightly crushing inner concrete specially defective concrete. Whereas, the main parts of the inner concrete were still in a workable state and no yielding was found on the outer stainless steel tube, as shown in Fig. 4b. The specimens were then inverted to be loaded for the second loading cycle and subsequently followed by the third loading cycle and the fourth loading cycle. Starting from the third loading cycle, the bond-slip between inner concrete and outer stainless steel tube of the specimens occurred at a comparatively small load level, although the slipping rate is relatively low. 3.2. Axial load-bond slip curves The axial load versus bond slip curves of all specimens determined from the push-out tests are plotted in Fig. 5, in which the horizontal axis represents the bond slip (S) between inner concrete and outer stainless steel tube of the specimens obtained from the average readings of two displacement transducers positioned at the top end of steel circular solid block, the vertical axis represents the axial load (P) applied to the inner concrete only by means of steel circular solid block, and n is the loading cycle of the repeated push-out test. The loads at the peak point or the inflection point in the testing curves are defined as the shear failure load or the bond-slip load denoted by Pnu (n = 1, 2, 3 and 4) for different loading cycles of the repeated push-out test, while τu, f and Su are the shear resistance and friction resistance of the bonding strength as well as the critical slippage at the bond-slip failure, respectively, as summarized in Table 3. It is shown from the comparison that the shear failure loads of bonding slip decreased with more loading cycles of the repeated push-out test employed in the same direction for n = 1 and 3 or n = 2 and 4, which indicated that the mechanical interlock force was gradually weakened due to the cracking of the interface elements of the inner concrete. In addition, it is also shown that the axial load versus bond slip curves exhibited more nonlinearity with more loading cycles of the repeated push-out test employed, in which the shapes of the testing curves for the second and fourth loading cycles (n = 2 and 4) are quite similar, whereas the shapes of the testing curves
for the first and third loading cycles (n = 1 and 3) are quite different although their loading directions are identical. This may attribute to the introduction of the adhesive force and interlock force in the interface elements of the inner concrete in the first loading cycle and variation of these interface forces in the subsequent loading cycles, which significantly contributed to the shear resistance of the bonding strength. The axial load versus bond slip curves also exhibited the variation of the interface friction resistance. It is also shown from the comparison that the interface friction resistance gradually decreased with more loading cycles of the repeated push-out test employed in the same direction for n = 1 and 3 or n = 2 and 4. The friction resistance in the testing curves for the first and third loading cycles (n = 1 and 3) has an opposite tendency compared with that in the testing curves for the second and fourth loading cycles (n = 2 and 4), which means the interface friction decreased with the increase of the bond slip for loading cycles of the repeated push-out test employed in the opposite direction, whereas the interface friction increased with the increase of the bond slip for loading cycles of the repeated push-out test employed in the initial condition. This may attribute to the macro-offset of the inner diameter of stainless steel CHS tubes. If the variation of the inner diameters of stainless steel CHS tubes along the longitudinal height direction of the specimens are small (changing from large diameter to small diameter), the inner concrete slipped along the surface of a cone. In this case, the interface adhesive force between the inner concrete and outer stainless steel cone tube of the specimens increased with the increase of the bond slip, which indicates that the confinement provided by the outer stainless steel tube to the inner concrete gradually increased and the axial load versus bond slip curves have an increasing tendency. Conversely, if the loading cycles of the repeated push-out test were employed for the inner concrete in the opposite direction, the bond slip behaviour of the interface elements may cause the separation of the inner concrete and outer stainless steel tube of the specimens and weaken the interface forces. In this case, the confinement provided by the outer stainless steel tube to the inner concrete gradually decreased and the axial load versus bond slip curves have a decreasing tendency. There are two types of axial load versus bond slip curves as shown in Fig. 6a and b for testing curves of type I and type II, respectively. For testing curve of type I, there is a clear peak point in the curve. In the initial loading stage, the axial load linearly increased with a large slope until the bond-slip failure occurred, where the peak load was found. The axial loads dropped substantially in the post-ultimate stage with large bond slip. For testing curve of type II, the axial load keeps increasing and no clear peak point can be found in the curve. In the initial loading
Concrete slightly crushed
(a) Inner concrete
251
(b) Outer stainless steel tube
Fig. 4. Failure modes of specimens in the repeated push-out test.
252
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n=1
n=2
n=3
n=1
n=4
9000
16000
8000
14000
7000
12000
6000
n=2
n=3
n=4
10000
P/N
P/N
5000
8000
4000
6000
3000 2000
4000
1000
2000
0
0
0 2 4 6 8 10 12 14 16 18 20 S/mm
0 2 4 6 8 10 12 14 16 18 20 S/mm
(a1) H304-t0.5-C20
(a2) H456-t0.5-C20
n=1
n=2
n=3
n=1
n=4
n=2
n=3
n=4
16000
15000
14000 12000
12000 10000
P/N
P/N
9000 6000
8000 6000 4000
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2000 0
0
0 2 4 6 8 10 12 14 16 18 20 S/mm
0 2 4 6 8 10 12 14 16 18 20 S/mm
(a3) H608-t0.5-C20 n=1
n=2
n=3
(a4) H760-t0.5-C20 n=4
n=1
n=2
n=3
n=4
8000 12000
7000 10000
6000
8000
P/N
P/N
5000 4000
6000
3000
4000
2000 2000
1000
0
0 0 2 4 6 8 10 12 14 16 18 20 S/mm
(a5) H304-t0.7-C20
0 2 4 6 8 10 12 14 16 18 20 S/mm
(a6) H456-t0.7-C20
Fig. 5. Repeated push-out testing curves.
Y. Chen et al. / Journal of Constructional Steel Research 130 (2017) 248–263
n=1
n=2
n=3
n=1
n=4
n=2
253
n=3
n=4
18000
21000
16000
18000
14000 15000
12000
12000
P/N
P/N
10000
9000
8000 6000
6000
4000
3000
2000 0
0
0 2 4 6 8 10 12 14 16 18 20 S/mm
0 2 4 6 8 10 12 14 16 18 20 S/mm
(a7) H608-t0.7-C20 n=1
n=2
n=3
(a8) H760-t0.7-C20 n=4
n=1
6000
12000
5000
10500
n=2
n=3
n=4
9000
4000
P/N
7500
P/N
3000
6000 4500
2000
3000
1000 1500
0
0
0
2
4 6
8 10 12 14 16 18 20 S/mm
0 2 4 6 8 10 12 14 16 18 20 S/mm
(a9) H304-t0.9-C20 n=1
n=2
n=3
(a10) H456-t0.9-C20 n=4
n=1
n=2
n=3
n=4
18000
18000 15000
15000 12000
P/N
12000
P/N
9000
9000
6000
6000
3000
3000
0
0 0 2 4 6 8 10 12 14 16 18 20 S/mm
(a11) H608-t0.9-C20 Fig. 5 (continued)
0 2 4 6 8 10 12 14 16 18 20 S/mm
(a12) H760-t0.9-C20
254
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n=1
n=2
n=3
n=4
16000
n=1
n=2
n=3
n=4
14000
14000
12000
12000
10000 P/N
P/N
10000 8000
8000 6000
6000 4000
4000
2000
2000
0
0
0 2 4 6 8 10 12 14 16 18 20 S/mm
0 2 4 6 8 10 12 14 16 18 20 S/mm
(a13) H304-t1.1-C20 n=1
n=2
n=3
(a14) H456-t1.1-C20 n=4
n=1
27000
n=2
n=3
n=4
28000
24000 24000
21000
20000
15000
16000
P/N
P/N
18000
12000
12000
9000 8000
6000
4000
3000
0
0
0 2 4 6 8 10 12 14 16 18 20 S/mm
0 2 4 6 8 10 12 14 16 18 20 S/mm
(a15) H608-t1.1-C20 n=1
n=2
n=3
(a16) H760-t1.1-C20 n=4
n=1
n=2
n=3
n=4
12000
12000 10000
10000 8000
6000
P/N
P/N
8000
4000
6000 4000
2000
2000
0
0 0 2 4 6 8 10 12 14 16 18 20 S/mm
(b1) H304-t0.5-C50
0 2 4 6 8 10 12 14 16 18 20 S/mm
(b2) H456-t0.5-C50 Fig. 5 (continued)
Y. Chen et al. / Journal of Constructional Steel Research 130 (2017) 248–263
n=1
n=2
n=3
n=1
n=4
n=2
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n=3
n=4
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12000
16000 10000
14000 12000 10000
P/N
P/N
8000 6000 4000
8000 6000 4000
2000
2000 0
0 0 2 4 6 8 10 12 14 16 18 20 S/mm
0 2 4 6 8 10 12 14 16 18 20 S/mm
(b3) H608-t0.5-C50 n=1
n=2
(b4) H760-t0.5-C50
n=3
n=4
n=1
n=2
n=3
n=4
10000
10500 9000
8000
7500
6000
P/N
P/N
6000 4500
4000
3000
2000 1500 0
0 0 2 4 6 8 10 12 14 16 18 20 S/mm
0 2 4 6 8 10 12 14 16 18 20 S/mm
(b5) H304-t0.7-C50 n=1
n=2
(b6) H456-t0.7-C50
n=3
n=4
21000
n=2
n=3
n=4
21000
18000
18000
15000
15000
12000
12000
P/N
P/N
n=1
9000
9000
6000
6000
3000
3000
0
0 0 2 4 6 8 10 12 14 16 18 20 S/mm
(b7) H608-t0.7-C50 Fig. 5 (continued)
0 2 4 6 8 10 12 14 16 18 20 S/mm
(b8) H760-t0.7-C50
256
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n=1
n=2
n=3
n=4
12000
n=1
n=4
8000
8000
P/N
10000
6000
6000
4000
4000
2000
2000
0
0 0 2 4 6 8 10 12 14 16 18 20 S/mm
0 2 4 6 8 10 12 14 16 18 20 S/mm
(b9) H304-t0.9-C50 n=1
n=2
(b10) H456-t0.9-C50
n=3
n=1
n=4
21000
n=2
n=3
n=4
24000
18000
20000
15000
16000
12000
P/N
P/N
n=3
12000
10000
P/N
n=2
12000
9000
8000
6000
4000
3000
0
0
0 2 4 6 8 10 12 14 16 18 20 S/mm
0 2 4 6 8 10 12 14 16 18 20 S/mm
(b11) H608-t0.9-C50 n=1
n=2
n=3
(b12) H760-t0.9-C50 n=4
14000
n=1
n=2
n=3
n=4
12000
12000
10000
10000
P/N
P/N
8000 8000 6000
6000 4000
4000 2000
2000
0
0 0 2 4 6 8 10 12 14 16 18 20 S/mm
(b13) H304-t1.1-C50 Fig. 5 (continued)
0 2 4 6 8 10 12 14 16 18 20 S/mm
(b14) H456-t1.1-C50
Y. Chen et al. / Journal of Constructional Steel Research 130 (2017) 248–263
n=1
n=2
n=3
n=4
24000
n=1
n=2
257
n=3
n=4
25000
21000
20000
18000 15000
P/N
P/N
15000
12000 9000
10000
6000
5000
3000 0
0 0 2 4 6 8 10 12 14 16 18 20 S/mm
0 2 4 6 8 10 12 14 16 18 20 S/mm
(b15) H608-t1.1-C50
(b16) H760-t1.1-C50 Fig. 5 (continued)
stage, the axial load linearly increased with a large slope until a knee point formed. The testing curve converted from the linear stage to the nonlinear stage. After that, the axial load keeps increasing with a great reducing slope. The bond-slip failure of the interface elements between the inner concrete and outer stainless steel tube of the specimens can be divided into three distinctive stages based on the axial load versus bond slip
Table 3 Shear failure loads and bond-slip loads. Specimen
P1u (kN)
P2u (kN)
P3u (kN)
P4u (kN)
τu (MPa)
Su (mm)
f (kN)
f/P1u (%)
H304-t0.5-C20 H304-t0.7-C20 H304-t0.9-C20 H304-t1.1-C20 H456-t0.5-C20 H456-t0.7-C20 H456-t0.9-C20 H456-t1.1-C20 H608-t0.5-C20 H608-t0.7-C20 H608-t0.9-C20 H608-t1.1-C20 H760-t0.5-C20 H760-t0.7-C20 H760-t0.9-C20 H760-t1.1-C20 H304-t0.5-C50 H304-t0.7-C50 H304-t0.9-C50 H304-t1.1-C50 H456-t0.5-C50 H456-t0.7-C50 H456-t0.9-C50 H456-t1.1-C50 H608-t0.5-C50 H608-t0.7-C50 H608-t0.9-C50 H608-t1.1-C50 H760-t0.5-C50 H760-t0.7-C50 H760-t0.9-C50 H760-t1.1-C50
7.9 6.2 4.3 14.5 14.2 11.0 6.5 12.7 10.2 20.9 16.2 26.4 14.5 16.2 17.0 26.2 10.4 9.8 10.1 13.8 10.1 8.6 10.2 10.1 10.2 18.4 19.9 20.2 17.2 19.3 21.5 21.6
5.5 6.1 5.5 6.4 11.0 7.6 10.7 7.9 14.1 18.1 14.2 13.8 10.5 17.9 17.5 27.1 5.8 9.5 9.0 11.1 6.4 4.9 6.2 11.9 11.0 15.4 16.2 22.2 14.8 14.4 15.7 24.6
1.0 1.3 0.9 2.8 2.5 3.6 2.2 1.3 2.2 7.0 4.3 8.6 2.2 5.8 5.9 9.2 2.1 4.3 1.5 1.5 3.4 3.0 1.6 1.9 2.7 4.7 7.9 7.9 5.8 5.3 5.5 6.7
3.7 5.2 3.9 4.3 7.0 6.4 8.7 5.6 10.7 15.0 11.6 10.1 8.3 16.3 13.8 22.8 5.5 8.2 5.9 7.9 4.7 3.4 5.2 9.3 8.9 9.9 10.7 17.2 9.9 10.1 11.0 19.1
0.131 0.103 0.072 0.243 0.147 0.114 0.068 0.133 0.077 0.158 0.123 0.201 0.086 0.096 0.101 0.157 0.173 0.163 0.168 0.231 0.105 0.090 0.106 0.106 0.077 0.139 0.151 0.154 0.102 0.115 0.128 0.129
0.94 0.73 0.89 1.12 1.14 1.18 0.81 0.92 0.59 1.35 0.87 1.13 1.27 1.26 2.78 1.62 1.24 1.08 0.83 1.13 0.78 1.00 0.86 0.91 0.93 1.40 1.17 1.08 1.98 1.86 0.93 1.99
4.7 4.9 4.0 5.9 9.6 8.0 5.0 6.5 9.3 17.3 12.0 16.3 12.5 15.0 14.2 17.0 4.3 7.3 4.9 6.7 5.9 3.7 4.7 7.9 7.3 13.5 14.5 16.8 13.9 13.5 16.2 17.0
59% 79% 93% 41% 68% 73% 77% 51% 91% 83% 74% 62% 86% 93% 84% 65% 41% 74% 49% 49% 58% 43% 46% 78% 72% 73% 73% 83% 81% 70% 75% 79%
curves in the first loading cycle of the repeated push-out test, which included the adhesive stage (OA), the sliding stage (AB) and the friction resistant stage (post-ultimate stage), as shown in Fig. 7. In the initial loading stage where the adhesive stage occurs, there is no bond slip between the inner concrete and outer stainless steel tube except for the region at the ends of the specimens. The shear resistance of the bonding strength of the interface elements is sustained by the interface adhesive force, while the shear force is relatively small. The interface adhesive effect is gradually disappeared with the increase of the axial load, which cannot take into effect anymore. This adhesive stage in the axial load versus bond slip curve is relatively short, hence the interface adhesion may fail at a small axial load (corresponding to Point A in the testing curve as shown in Fig. 7). The interface adhesive force is replaced by the micro-interlock force developed at the uneven inner surface of the stainless steel tube to take the shear force of the interface elements. The bond slip gradually developed at the ends of the specimens with the further increase of the axial load. The shear resistance of the bonding strength of the sliding interface elements is sustained by the interlock force, while the shear resistance of the bonding strength of the non-sliding interface elements is sustained by the adhesive force. The failure load of the bonding strength will be reached (corresponding to Point B in the testing curve as shown in Fig. 7) once the maximum values of the resultant interlock force and adhesive force are obtained (corresponding to the peak point or the knee point in the testing curve). The interlock force at this stage is dominant in the shear resistance of the bonding strength. After that, the bond slip behaviour between the inner concrete and outer stainless steel tube of the specimens presents nonlinearity in the post-ultimate stage (after the peak point or the knee point in the testing curve). The interface adhesive force will be completely disappeared once the sliding of the interface elements between the inner concrete and outer stainless steel tube occurs along the whole height of the specimens. In the meanwhile, the interlock force of the interface elements with large bond slip remarkably reduced. Hence, the shear force of the bonding strength is mainly sustained by the interface friction force, which is proportional to the compression force in the normal direction of the interface elements and the interface friction coefficient. It is worth noting that the friction coefficient decreased with the increase of the bond slip and more loading cycles of the repeated push-out test. The compression force in the normal direction of the interface elements resulted from the confinement provided
258
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(a) Type I
(b) Type II Fig. 6. Typical axial load-bond slip curves.
by the outer stainless steel tube to the inner concrete in the transverse direction, which is determined by the variation of the inner diameter of the stainless steel tube. The inner concrete slipped along the surface of a cone with the variation of the inner diameter of the stainless steel tube. If the variation of the inner diameters of stainless steel CHS tubes along the longitudinal height direction of the specimens are changing from large diameter to small diameter, the inner concrete will be wedged into a cone. The stainless steel tube could provide a larger confinement to the inner concrete with the increase of the bond slip, which produces a larger friction force. However, if the variation of the inner diameters of stainless steel CHS tubes along the longitudinal height direction of the specimens are changing from small diameter to large diameter or the inner surface of stainless steel tube is frictionless, the outer stainless steel tube could not provide any confinement to the inner concrete. The interface friction force will then be remarkably reduced. If the resultant interlock force and adhesive force of the interface elements are larger than the initial interface friction force, the peak point will be found in the testing curve followed by the post-ultimate stage, as shown in Fig. 6a for testing curve of type I. The shear failure loads of bonding slip are equivalent to the resultant interlock force and adhesive force of the interface elements. This type of testing curve generally occurs for the specimens with the coarse inner surface of stainless steel tube. Conversely, if the resultant interlock force and adhesive force of the interface elements are smaller than the initial interface
friction force, no clear peak point can be found in the testing curve, in which a knee point is formed followed by the continuous increasing axial load, as shown in Fig. 6b for testing curve of type II. The shear failure loads of bonding slip are equivalent to the initial interface friction force. This type of testing curve generally occurs for the specimens with the smooth inner surface of stainless steel tube. It was found from the axial load versus bond slip curves that the post-ultimate stage (after the peak point or the knee point in the testing curve) is quite different for different specimens, which may attribute to the uneven degree of smoothness of the inner surface of stainless steel tube. If the degree of smoothness of the inner surface of stainless steel tube is significantly uneven, the interface friction force greatly increased with the increase of the bond slip, which resulted in the clear increasing post-ultimate stage, as shown in Fig. 8 for curve ‘a’. However, if the degree of smoothness of the inner surface of stainless steel tube is even, the interface friction force greatly decreased with the increase of the bond slip, which resulted in the substantial dropping post-ultimate stage, as shown in Fig. 8 for curve ‘c’. For specimens with the medium degree of smoothness of the inner surface of stainless steel tube, the post-ultimate stage of axial load versus bond slip curves is located between the curve ‘a’ and curve ‘c’, which somewhat dropped followed by a comparatively flat portion, as shown in Fig. 8 for curve ‘b’. It can be generally concluded from the previous analyses that the adhesive force, the interlock force and the friction force of the interface
Fig. 7. Bond-slip failure of the interface elements.
Fig. 8. Post-ultimate stage of the interface friction force.
Y. Chen et al. / Journal of Constructional Steel Research 130 (2017) 248–263
elements take effects sequentially in the bond-slip failure of the specimens, in which the adhesive force is dominant prior to the occurrence of the bond slip, the interlock force plays a primary role once the bond slip occurs until the shear failure load of bonding slip is reached, after that the friction force begins to take effect. In addition, the axial load versus bond slip curves present linearity in the initial loading stage, which developed gradually until the shear failure load of bonding slip is reached. After that, the testing curves converted from the linear stage to the nonlinear stage, which developed much faster. Furthermore, a comparatively large value of slippage between inner concrete and outer stainless steel tube of the specimens can be obtained before the shear failure load of bonding slip is reached. Therefore, only part of axial load versus bond slip curves prior to the attainment of the shear failure load of bonding slip needs to be considered in the practical applications.
3.3. Shear resistance of the bonding strength of the interface elements The shear resistance of the bonding strength of the interface elements consisted of three individual components including the chemical adhesive force between the cement gel and inner surface of stainless steel tube, the interlock force between the inner surface of stainless steel tube and inner concrete due to the uneven degree of smoothness of the interface, and the friction force of the interface elements between the inner surface of stainless steel tube and inner concrete. The adhesive force is a chemical absorption force between the cement and inner surface of stainless steel tube, which is significantly influenced by the properties of concrete including the concrete strength and water-to-cement ratio. Experimental investigation on the adhesion of the reinforced concrete structures indicates that the adhesive strength between the steel bar and concrete is minimal. The adhesion force will lose its function forever once the local bond slip occurs on the interface. The adhesion between the inner concrete and outer stainless steel tube of the specimens in the repeated push-out test in this study demonstrated the similar behaviour. The interlock force resulted from the uneven degree of smoothness of the inner surface of stainless steel tube and the interlock action of the wedged concrete, which depends on the uneven degree of smoothness of the interface and the shear strength of the inner concrete. It is the main component of the shear resistance of the bonding strength of the interface elements. It is worth noting that the uneven degree of smoothness of the inner surface of stainless steel tube is in difference of the order of 10− 2, which is the so-called micro-deviation. An enlarged view of the micro-interlock action is clearly shown in Fig. 9. The shear resistance of the bonding strength resulted from the microdeviation action is the so-called “micro-mechanical interlock force”.
Fig. 9. Micro-Interlocking action.
259
The interface friction force begins to take effect once the bond slip between the inner concrete and outer stainless steel tube occurs along the whole height of the specimens, which is proportional to the compression force in the normal direction of the interface elements and the interface friction coefficient. The friction coefficient between the inner concrete and outer stainless steel tube is dependent on the degree of smoothness of the inner surface of stainless steel tube, which is ranged from 0.3 to 0.5. It is worth noting that the friction coefficient decreased with the increase of the bond slip and more loading cycles of the repeated push-out test. Different from the friction force between the steel bar and concrete in the reinforced concrete structures, the friction force between the inner concrete and outer stainless steel tube in the concrete-filled steel tubes is mostly determined by the confinement from the outer stainless steel tube to the inner concrete in the transverse direction. It was found that the confinement in the transverse direction depends mainly on three influential factors. Firstly, the inner diameters of stainless steel CHS tubes along the longitudinal height direction of the specimens vary irregularly in the fabrication process, as shown in Fig. 10 for an enlarged view of variation of the inner diameters of stainless steel CHS tubes. The irregular variation of the inner diameters of stainless steel CHS tubes along the longitudinal height direction of the specimens are much larger than the uneven degree of smoothness of the inner surface of stainless steel tube, which is the so-called macro-deviation. The sliding concrete is wedged into a cone once the bond slip between the inner concrete and outer stainless steel tube occurs from top to bottom, as shown in Fig. 10. Hence, the wedge effect forms to make the confinement from the outer stainless steel tube to the inner concrete larger, which resulted in a large interface friction force. The shear resistance of the bonding strength resulted from the macro-deviation action is the so-called “macro-mechanical interlock force”. Secondly, the concrete-filled stainless steel tubular columns are usually subjected to eccentric compression force in practice, which produces a bending moment on the columns. The additional bending moment will produce a compression force on the interface in the radial direction, which could increase the interface friction force. Thirdly, the stress distribution at the beam-column connection is quite complicated. The so-called clamping effect and pinching effect at the interesting area could remarkably increase the compression force on the inner concrete in the radial direction. However, the clamping effect and pinching effect
Fig. 10. Variation of the inner diameters of stainless steel CHS tubes.
Y. Chen et al. / Journal of Constructional Steel Research 130 (2017) 248–263
900 800 700 600 500 400 300 200 100 0
8%Pu
1000
8%Pu 15%Pu
800
20%Pu 40%Pu
600
60%Pu 80%Pu
400
100%Pu
15%Pu 20%Pu 40%Pu 60%Pu
ε/µε
ε/µε
260
80%Pu 100%Pu
200 0
0
100
200
h/mm
300
0
400
(a) H304-t0.5-C20
400
h/mm
600
8%Pu 15%Pu 20%Pu 40%Pu 60%Pu 80%Pu 100%Pu
700
600
8%Pu
500
15%Pu
600
20%Pu
500
40%Pu
400
300
60%Pu
200
80%Pu 100%Pu
100 0
ε/µε
400
800
(b) H760-t0.5-C20
700
ε/µε
200
300 200 100 0
0
100
200
300
400
h/mm (c) H304-t1.1-C20
0
200
400
h/mm
600
800
(d) H760-t1.1-C20
Fig. 11. Strain distribution curve on outer surface of stainless steel tube.
do not exist in this study since the experimental work did not consider the effect of loading eccentricity. Hence, the interface friction force is mainly determined by the macro-deviation action of stainless steel CHS tubes. Based on the test results in this study, 70% of the shear resistance of the bonding strength is taken by the interface friction force, while the remaining 30% of the shear resistance of the bonding strength is sustained by the chemical adhesive force and the mechanical interlock force.
close to the free end increased much greater. The difference of the strains at the locations close to the free end and loading end of the specimens increased with the increase of the axial load, which indicates that the strain loses its continuity between the inner concrete and outer stainless steel tube and the bond slip occurs between them. In this loading stage, the axial load applied to the inner concrete is transferred to the outer stainless steel tube by means of the shear resistance of the bonding strength of the interface elements.
3.4. Strain distribution on outer surface of stainless steel tube
3.5. Influential factors on the shear resistance of the bonding strength of the interface elements
The strain distribution on outer surface of stainless steel tube was obtained from the measurements of three-element rosettes strain gauges as shown in Fig. 11, which were positioned in line on the exterior of stainless steel tube along the longitudinal height direction, as shown in Fig. 3. It is shown from the comparison that the strains on outer surface of stainless steel tube generally distributed linearly along the longitudinal height direction in the initial loading stage, in which the strains at the location close to the free end of the specimens are quite small. Furthermore, the strains at the locations close to the free end and loading end of the specimens increased with the increase of the axial load, in which the strains at the location
It is worth noting that the shear resistance of the bonding strength of the interface elements between the inner concrete and outer stainless steel tube is corresponding to the shear failure load of the bonding slip, which is the starting point of the occurrence of the bond slip and the critical point controlling the interaction between the inner concrete and outer stainless steel tube within the range of limit bond slip. Hence, it can be defined as the failure of the bond slip. However, the interface adhesive condition may vary irregularly along the longitudinal height direction and the circumferential direction of the specimens, which led to the unstable shear resistance of the bonding strength in certain
Y. Chen et al. / Journal of Constructional Steel Research 130 (2017) 248–263
0.3
0.25
0.25
D/t=152
0.15
D/t=69.1
D/t=108.6
τ/MPa
D/t=84.4
0.15
0.1 0.05
0.05
0 3
6 9 H/D
12
D/t=84.4 D/t=69.1
0.1
0
D/t=152
0.2
D/t=108.6
0.2 τ/MPa
261
0
15
0
3
6
9
12
15
H/D
(a) C20
(b) C50
Fig. 12. Effect of height-to-diameter ratio on the shear resistance of the bonding strength.
local area. Therefore, it is necessary to average the shear resistance of the bonding strength in a finite surface area to obtain the valid result, which can be defined as the design strength. Hence, the shear stress of the bonding strength is assumed to be uniformly distributed in the contact surface between the inner concrete and outer stainless steel tube of the specimens. The shear resistance of the bonding strength of the interface elements in the concrete-filled stainless steel CHS tubes can be calculated as follows: Nu πD0 l0
ð1Þ
τ/MPa
where τu is the shear resistance of the bonding strength, Nu is the shear failure load of the bonding slip, D0 is the inner diameter of the stainless steel CHS tube, and l0 is the overall length of the interface.
0.3
H/D=4
0.25
H/D=6
0.25
H/D=8
0.2
H/D=10
0.15 0.1
0.1
0
0
100 D/t (a) C20
150
200
H/D=8 H/D=10
0.05
50
H/D=6
0.15
0.05 0
H/D=4
0.2 τ/MPa
τu ¼
A parametric study was carried out in this study to investigate the effects of main influential factors including the height-to-diameter ratio (H/D) of the stainless steel tube, the diameter-to-thickness ratio (D/t) of the stainless steel tube, and the concrete strength (C) on the shear resistance of the bonding strength of the interface elements. It is shown from the comparison that the height-to-diameter ratio (H/D) and the diameter-to-thickness ratio (D/t) of the stainless steel tube have insignificant influence on the shear resistance of the bonding strength of the interface elements for both normal strength and high strength concrete with nominal concrete cube strengths of 20 MPa and 50 MPa, as shown in Figs. 12 and 13, respectively. Furthermore, it is also demonstrated from the comparison that the concrete strength (C) has minor influence on the shear resistance of the bonding strength of the interface elements, as shown in Table 4.
0
50
100 D/t (b) C50
Fig. 13. Effect of diameter-to-thickness ratio on the shear resistance of the bonding strength.
150
200
262
Y. Chen et al. / Journal of Constructional Steel Research 130 (2017) 248–263
4. Design rules There is no design rules currently used for the shear resistance of the bonding strength of concrete-filled stainless steel CHS tubes. However, the shear resistance of the bonding strength of concrete-filled carbon steel CHS tubes can be estimated by using the design equations proposed by Kang [20] as follows: 1 τu ¼ k γ
"
4Le d −0:00028 þ 29:09049α þ 0:11121 t d ! #
ð2Þ
þ0:03439θ−7:36037 f t where γ = 0.96 is the correction coefficient for the uncertainty, k is the influential factor for the exterior of steel tube, α = (D / D0)2 − 1 is the steel ratio of the concrete-filled steel CHS tube, θ = Asfy / (Acfc) is the confinement factor for the concrete-filled steel CHS tube, Le is the overall adhesive length, d is the diameter of the steel CHS tube, t is the thickness of the steel CHS tube, and ft is the tensile strength of the concrete, ft = 1/10fc is used for the concrete with nominal concrete cube strengths of 20 MPa, while ft = 1/13fc is used for the concrete with nominal concrete cube strengths of 50 MPa. Therefore, the shear resistance (τKang) of the bonding strength of concrete-filled stainless steel CHS tubes was calculated by substituting the measured tensile proof stress as the yield stress in Eq. (2), which was compared with the test results (τTest) as summarized in Table 5. It is demonstrated from the comparison that the current design rules of concrete-filled carbon steel CHS tubes are extremely unconservative for the shear resistance of the bonding strength of concrete-filled stainless steel CHS tubes with the mean value of the predict-to-test strength ratio (τKang/τTest) of 114.0 and the corresponding coefficient of variation (COV) of 0.845. This may attribute to the much smoother inner surface of stainless steel tube compared to carbon steel tube, which resulted in
Table 4 Effect of concrete strength on the shear resistance of the bonding strength. Specimen
τu (MPa)
τ20/τ50
H304-t0.5-C20 H304-t0.5-C50 H456-t0.5-C20 H456-t0.5-C50 H608-t0.5-C20 H608-t0.5-C50 H760-t0.5-C20 H760-t0.5-C50 H304-t0.7-C20 H304-t0.7-C50 H456-t0.7-C20 H456-t0.7-C50 H608-t0.7-C20 H608-t0.7-C50 H760-t0.7-C20 H760-t0.7-C50 H304-t0.9-C20 H304-t0.9-C50 H456-t0.9-C20 H456-t0.9-C50 H608-t0.9-C20 H608-t0.9-C50 H760-t0.9-C20 H760-t0.9-C50 H304-t1.1-C20 H304-t1.1-C50 H456-t1.1-C20 H456-t1.1-C50 H608-t1.1-C20 H608-t1.1-C50 H760-t1.1-C20 H760-t1.1-C50
0.131 0.173 0.147 0.105 0.077 0.077 0.086 0.102 0.103 0.163 0.114 0.090 0.158 0.139 0.096 0.115 0.072 0.168 0.068 0.106 0.123 0.151 0.101 0.128 0.243 0.231 0.133 0.106 0.201 0.154 0.157 0.129
0.757 1.400 1.000 0.843 0.632 1.267 1.137 0.835 0.429 0.642 0.815 0.789 1.052 1.255 1.305 1.217
the much smaller interlock force and friction force of the interface elements of stainless steel tube compared to carbon steel tube. Therefore, the current design rules of concrete-filled carbon steel CHS tubes are inapplicable to the shear resistance of the bonding strength of concretefilled stainless steel CHS tubes. Further research needs to be carried out to propose the accurate design formulae for the shear resistance of the bonding strength of concrete-filled stainless steel CHS tubes. Convergence studies will be carried out to obtain the optimum finite element mesh density by comparison between the small size test and finite element analysis results in the companion paper. An extensive parametric study will be carried out to investigate the effects of main geometric parameters on CFT columns with engineering size used in practice. Design equation of bond strength for CFT columns with engineering size will be proposed. 5. Conclusions Based on the repeated push-out tests on a total of 32 concrete-filled stainless steel CHS tubes with different values of height-to-diameter ratio, diameter-to-thickness ratio and concrete strength, the following conclusions can be drawn: (1) Contact face of the inner concrete slightly was crushed by unloading the specimens to zero. (2) 70% of the shear resistance of the bonding strength is taken by the interface friction force, while the remaining 30% of the shear resistance of the bonding strength is sustained by the chemical adhesive force and the mechanical interlock force. (3) Axial load versus bond slip curves with or without peak point were observed in test. (4) The current design rules of concrete-filled carbon steel CHS tubes are extremely unconservative for the shear resistance of the Table 5 Comparison of test strengths with design strengths for the shear resistance of the bonding strength of concrete-filled stainless steel CHS tubes. Specimen
τTest (MPa)
τKang (MPa)
τKang/τTest
H304-t0.5-C20 H304-t0.7-C20 H304-t0.9-C20 H304-t1.1-C20 H456-t0.5-C20 H456-t0.7-C20 H456-t0.9-C20 H456-t1.1-C20 H608-t0.5-C20 H608-t0.7-C20 H608-t0.9-C20 H608-t1.1-C20 H760-t0.5-C20 H760-t0.7-C20 H760-t0.9-C20 H760-t1.1-C20 H304-t0.5-C50 H304-t0.7-C50 H304-t0.9-C50 H304-t1.1-C50 H456-t0.5-C50 H456-t0.7-C50 H456-t0.9-C50 H456-t1.1-C50 H608-t0.5-C50 H608-t0.7-C50 H608-t0.9-C50 H608-t1.1-C50 H760-t0.5-C50 H760-t0.7-C50 H760-t0.9-C50 H760-t1.1-C50 Comparison
0.131 0.103 0.072 0.243 0.147 0.114 0.068 0.133 0.077 0.158 0.123 0.201 0.086 0.096 0.101 0.157 0.173 0.163 0.168 0.231 0.105 0.090 0.106 0.106 0.077 0.139 0.151 0.154 0.102 0.115 0.128 0.129 Mean COV
23.393 12.393 6.451 2.811 23.387 12.387 6.446 2.806 23.382 12.382 6.441 2.800 23.377 12.377 6.435 2.795 28.796 15.249 7.931 3.446 28.789 15.243 7.925 3.440 28.783 15.236 7.918 3.433 28.776 15.230 7.912 3.427
178.6 120.3 89.6 11.6 159.1 108.7 94.8 21.1 303.7 78.4 52.4 13.9 271.8 128.9 63.7 17.8 166.5 93.6 47.2 14.9 274.2 169.4 74.8 32.5 373.8 109.6 52.4 22.3 282.1 132.4 61.8 26.6 114.0 0.845
Y. Chen et al. / Journal of Constructional Steel Research 130 (2017) 248–263
bonding strength of concrete-filled stainless steel CHS tubes. Hence, the current design rules of concrete-filled carbon steel CHS tubes are inapplicable to the shear resistance of the bonding strength of concrete-filled stainless steel CHS tubes.
Acknowledgements This research work was supported by the National Natural Science Foundation of China (Nos. 51278209 and 51478047). The tests were conducted in Fujian Key Laboratory on Structural Engineering and Disaster Reduction at Huaqiao University. The support provided by the laboratory staff is gratefully acknowledged. References [1] E. Ellobody, B. Young, Design and behaviour of concrete-filled cold-formed stainless steel tube columns, Eng. Struct. 28 (2006) 716–728. [2] E. Ellobody, Nonlinear behavior of concrete-filled stainless steel stiffened slender tube columns, Thin-Walled Struct. 45 (2007) 259–273. [3] M.A. Dabaon, M.H. El-Boghdadi, M.F. Hassanein, Experimental investigation on concrete-filled stainless steel stiffened tubular stub columns, Eng. Struct. 31 (2009) 300–307. [4] M.F. Hassanein, Numerical modelling of concrete-filled lean duplex slender stainless steel tubular stub columns, J. Constr. Steel Res. 66 (2010) 1057–1068. [5] M.F. Hassanein, O.F. Kharoob, Q.Q. Liang, Behaviour of circular concrete-filled lean duplex stainless steel tubular short columns, Thin-Walled Struct. 68 (2013) 113–123. [6] E. Ellobody, Numerical modeling of fibre reinforced concrete-filled stainless steel tubular columns, Thin-Walled Struct. 63 (2013) 1–12.
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Contents lists available at ScienceDirect
Journal of Constructional Steel Research
Bond-slip behaviour of concrete-filled stainless steel circular hollow section tubes Yu Chen a, Ran Feng b,⁎, Yongbo Shao c, Xiaotian Zhang d a
School of Urban Construction, Yangtze University, Jingzhou 434023, China School of Civil and Environmental Engineering, Harbin Institute of Technology, Shenzhen 518055, China School of Mechatronic Engineering, Southwest Petroleum University, Chengdu 610500, China d College of Civil Engineering, Huaqiao University, Xiamen 361021, China b c
a r t i c l e
i n f o
Article history: Received 24 May 2016 Received in revised form 15 November 2016 Accepted 10 December 2016 Available online 22 December 2016 Keywords: Bond-slip behaviour Circular hollow section (CHS) Concrete-filled Push-out test Shear resistance Stainless steel tube
a b s t r a c t This paper presents the repeated push-out tests on concrete-filled stainless steel circular hollow section (CHS) tubes with different values of height-to-diameter ratio, diameter-to-thickness ratio and concrete strengths. The bond-slip behaviour of all specimens and the strain distribution on the exterior of stainless steel tubes along the longitudinal height direction were carefully investigated. It was found that the shear failure loads of bonding slip decreased successively with more loading cycles of the repeated push-out test employed in the same direction. Hence, the mechanical interlock force and friction force of the interface elements gradually decreased. Furthermore, the bond-slip failure of the interface elements between the inner concrete and outer stainless steel tube of the specimens consists of the adhesive stage, the sliding stage and the friction resistant stage. It can be generally concluded that 70% of the shear resistance of the bonding strength is taken by the interface friction force, while the remaining 30% of the shear resistance of the bonding strength is sustained by the chemical adhesive force and the mechanical interlock force. On the other hand, it was demonstrated that the height-to-diameter ratio (H/D) and the diameter-to-thickness ratio (D/t) of the stainless steel tube as well as the concrete strength (C) have insignificant influence on the shear resistance of the bonding strength of the interface elements. It was also shown from the comparison that the current design rules of concrete-filled carbon steel CHS tubes are inapplicable to the shear resistance of the bonding strength of concrete-filled stainless steel CHS tubes. © 2016 Elsevier Ltd. All rights reserved.
1. Introduction The applications of concrete-filled stainless steel tubes could be traced back to last century, which are nowadays increasingly used in high-rise buildings and arch bridges [1–2] owing to their esthetical appearance, excellent corrosion resistance, superior load carrying capacity and seismic behaviour, good durability and low cost of maintenance. It is worth noting that concrete-filled stainless steel tubes possess both good mechanical properties of concrete-filled steel tubes (CFST) and excellent durability of stainless steel, which promote the potential employment of concrete-filled stainless steel tubes in onshore buildings, offshore platform, bridges, and many other practical applications with requirement for higher durability. Many researches including experimental investigations and theoretical analyses were conducted on the
⁎ Corresponding author. E-mail address: [email protected] (R. Feng).
http://dx.doi.org/10.1016/j.jcsr.2016.12.012 0143-974X/© 2016 Elsevier Ltd. All rights reserved.
mechanical behaviour of concrete-filled stainless steel columns under various loading conditions [3–12]. In addition, many studies were also performed to investigate the bond-slip behaviour of concrete-filled carbon steel tubular columns [13–16]. Up to the authors' knowledge, however, there is no research being carried out on the bond-slip behaviour of concrete-filled stainless steel tubes. For the design of concrete-filled stainless steel tubes, the bond strength between inner surface of stainless steel tube and outer surface of concrete infill as well as the constitutive relation of the bond-slip behaviour are the most critical concerns to guarantee that the outer stainless steel tube and inner concrete could sustain the applied loads simultaneously and reinforce with each other. In this study, the effects of the concrete strength (C), the height-to-diameter ratio (H/D) of stainless steel tube, the diameter-to-thickness ratio (D/t) of stainless steel tube, and the repeated action on the bond strength for shear resistance between interfaces were all investigated by using testing method. Furthermore, the failure process of bond surfaces under shear action together with the strain development on the outer surface of stainless steel tube were both discussed.
Y. Chen et al. / Journal of Constructional Steel Research 130 (2017) 248–263 Table 1 Geometric parameters of concrete-filled stainless steel CHS tubes.
Nomenclature Ac As C D d D0 Es f fc ft fu fy H k Le l0 Nu n P Pnu S Su t α γ θ τKang τTest τu
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cross-section area of inner concrete cross-section area of outer steel tube concrete strength outer diameter of stainless steel CHS tube outer diameter of steel CHS tube inner diameter of stainless steel CHS tube elastic modulus of stainless steel tube friction resistance of bonding strength concrete cube strength tensile strength of concrete ultimate tensile stress of stainless steel tube 0.2% tensile proof stress of stainless steel tube overall height of stainless steel CHS tube influential factor for exterior of steel tube overall adhesive length overall length of interface shear failure load of bonding slip loading cycle of repeated push-out test axial load shear failure load or bond-slip load bond slip between inner concrete and outer stainless steel tube critical slippage at bond-slip failure overall thickness of stainless steel CHS tube steel ratio of concrete-filled steel CHS tube correction coefficient for uncertainty confinement factor for concrete-filled steel CHS tube shear resistance of bonding strength obtained from current design rules shear resistance of bonding strength obtained from tests shear resistance of bonding strength
2. Experimental investigation 2.1. Test specimens A total of 32 concrete-filled stainless steel circular hollow section (CHS) tubes with the identical outer diameter of 76 mm were designed and tested, as shown in Fig. 1, which included different values of heightto-diameter ratio (H/D) ranged from 4 to 10, diameter-to-thickness ratio (D/t) ranged from 69.1 to 152.0 and concrete strength (C) ranged
D (mm)
t (mm)
H (mm)
D/t
H/D
C (MPa)
H304-t0.5-C20 H304-t0.7-C20 H304-t0.9-C20 H304-t1.1-C20 H456-t0.5-C20 H456-t0.7-C20 H456-t0.9-C20 H456-t1.1-C20 H608-t0.5-C20 H608-t0.7-C20 H608-t0.9-C20 H608-t1.1-C20 H760-t0.5-C20 H760-t0.7-C20 H760-t0.9-C20 H760-t1.1-C20 H304-t0.5-C50 H304-t0.7-C50 H304-t0.9-C50 H304-t1.1-C50 H456-t0.5-C50 H456-t0.7-C50 H456-t0.9-C50 H456-t1.1-C50 H608-t0.5-C50 H608-t0.7-C50 H608-t0.9-C50 H608-t1.1-C50 H760-t0.5-C50 H760-t0.7-C50 H760-t0.9-C50 H760-t1.1-C50
76
0.5 0.7 0.9 1.1 0.5 0.7 0.9 1.1 0.5 0.7 0.9 1.1 0.5 0.7 0.9 1.1 0.5 0.7 0.9 1.1 0.5 0.7 0.9 1.1 0.5 0.7 0.9 1.1 0.5 0.7 0.9 1.1
304 304 304 304 456 456 456 456 608 608 608 608 760 760 760 760 304 304 304 304 456 456 456 456 608 608 608 608 760 760 760 760
152.0 108.6 84.4 69.1 152.0 108.6 84.4 69.1 152.0 108.6 84.4 69.1 152.0 108.6 84.4 69.1 152.0 108.6 84.4 69.1 152.0 108.6 84.4 69.1 152.0 108.6 84.4 69.1 152.0 108.6 84.4 69.1
4 4 4 4 6 6 6 6 8 8 8 8 10 10 10 10 4 4 4 4 6 6 6 6 8 8 8 8 10 10 10 10
32.3 32.3 32.3 32.3 32.3 32.3 32.3 32.3 32.3 32.3 32.3 32.3 32.3 32.3 32.3 32.3 51.7 51.7 51.7 51.7 51.7 51.7 51.7 51.7 51.7 51.7 51.7 51.7 51.7 51.7 51.7 51.7
from 20 MPa to 50 MPa. Dimensions of all specimens are detailed in Table 1, in which the label ‘H304-t0.5-C20’ defines a concrete-filled stainless steel CHS tube with height ‘H’ of 304 mm, thickness ‘t’ of 0.5 mm and nominal concrete cube strength ‘C’ of 20 MPa. In the fabrication of test specimens, a gap of 50 mm was deliberately remained at the top end of each specimen between inner concrete and outer stainless steel tube for the repeated push-out test. The material properties of stainless steel tubes were determined by uni-axial tensile coupon tests based on the recommendations of the Chinese Code of Metallic Materials (GB/T 228.1-2010) [17], which include the elastic modulus (Es) of 206 GPa, 0.2% tensile proof stress (fy) of 420 MPa and ultimate tensile stress (fu) of 630 MPa. The material properties of concrete were determined from compressive concrete cube tests. The concrete cubes with nominal side length of 150 mm were produced using commercially available materials with normal mixing and curing techniques [18–19]. The material properties of the concrete are summarized in Table 2 that include the measured concrete cube strengths and the mean values for three batches of concrete cubes for nominal concrete cube strengths of 20 MPa and 50 MPa, respectively.
t
Concrete
Specimen
H
Stainless steel tube
D Concrete
D Fig. 1. Concrete-filled stainless steel CHS tube.
Table 2 Measured concrete cube strengths. Nominal concrete strength (MPa)
Batch
Measured concrete cube strength (MPa)
Mean value (MPa)
20
1 2 3 4 5 6
31.4 31.1 34.4 48.7 50.8 55.5
32.3
50
51.7
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2.2. Test setup All specimens were installed vertically in the same loading machine with the self-balanced reaction frame, as shown in Fig. 2. A hydraulic jack was used to apply the axial compression to the test specimens and monitored by the load cell, which was positioned concentrically between the hydraulic jack and the reaction frame. A steel circular solid block with the cross-section area slightly smaller than that of the inner concrete was used to apply the axial compression to the test specimens, which was positioned concentrically to the inner concrete and outer stainless steel tube of the test specimens. Therefore, the compression force was applied to the inner concrete only by means of steel circular solid block, while an end plate was placed at the bottom to support the test specimens. The bond-slip failure between inner concrete and outer stainless steel tube was then occurred.
2.3. Arrangement of measuring system All specimens were initially subjected to the incremental monotonic static loading, which was first equally divided into comparatively large load levels (around 1/30 of the estimated peak load) within the elastic range, and then reduced to the comparatively small load levels after the occurrence of the nonlinear bond-slip failure between inner concrete and outer stainless steel tube. The specimens were subsequently unloaded to zero until the inner concrete at the bottom of the specimens being fully contacted with the end plate at the bottom supported the specimens. The maximum bond slippage is approximately 40–50 mm since an initial gap of 50 mm was deliberately remained at the end of each specimen between inner concrete and outer stainless steel tube. After that, the specimens were inverted and subjected to a reverse axial compression in the same loading way. This testing procedure was repeated four times in total for each specimen for a complete repeated push-out test. The applied loads and readings of displacement transducers and strain gauges were recorded automatically at regular intervals by using a data acquisition system. Two displacement transducers were positioned at the steel plates connected to the top end of steel circular solid block at the opposite sides to monitor the relative movement of the inner concrete with respect to the outer stainless steel tube, as shown in Fig. 2. The bond
Fig. 2. Test set-up.
slippage between inner concrete and outer stainless steel tube could be obtained from the average readings of these two displacement transducers. A total of four three-element rosettes strain gauges which enable strain values in three different directions at 45° interval to be measured simultaneously were positioned in line on the exterior of stainless steel tube along the longitudinal height direction, in which two strain gauges were positioned at the locations 10 mm away from both ends of the specimens, and two other strain gauges were positioned roughly at one third and two thirds of the total height of the specimens, respectively, as shown in Fig. 3. The use of displacement transducers enables the bond slippage between inner concrete and outer stainless steel tube of the specimens to be measured at each load level. Hence, the complete axial loadbond slippage curves of all specimens can be obtained. Furthermore, the use of strain gauges enables the strain distributions at the critical locations and strain development under different load levels to be determined for the specimens of H304-t0.5-C20, H304-t1.1-C20, H760-t0.5C20 and H760-t1.1-C20. On the other hand, the generation of the bonding shear force, the development of the bonding shear failure and the effects of other influential factors on the bonding shear force were all investigated.
3. Test results 3.1. Failure modes At the beginning of the tests, the axial compression force linearly increased up to the friction between inner concrete and outer stainless steel tube of the specimens within the elastic range of the materials. There is no any slippage observed during the tests. The bond-slip between inner concrete and outer stainless steel tube of the specimens occurred once the axial compression force reached the interface friction. Then the axial compression force nonlinearly increased with the increase of the interface slippage until a large value of slippage between inner concrete and outer stainless steel tube of the specimens was obtained with a sudden great sound. The movement of the inner concrete with respect to the outer stainless steel tube of the specimens monitored by the displacement transducers increased sharply. The axial compression force decreased a lot accordingly. After that, the slippage between inner concrete and outer stainless steel tube of the specimens gradually decreased with the reduction of the applied load levels in the
Fig. 3. Arrangement of strain gauges
Y. Chen et al. / Journal of Constructional Steel Research 130 (2017) 248–263
subsequent loading increments. Eventually the movement of the inner concrete with respect to the outer stainless steel tube of the specimens monitored by the displacement transducers was quite small that can be negligible. While the axial compression force increased substantially, which means the inner concrete at the bottom of the specimens being fully contacted with the end plate at the bottom supported the specimens. It was observed that the contact face of the inner concrete slightly was crushed by unloading the specimens to zero, as shown in Fig. 4a. Friction force of the interface is the main reason for slightly crushing inner concrete specially defective concrete. Whereas, the main parts of the inner concrete were still in a workable state and no yielding was found on the outer stainless steel tube, as shown in Fig. 4b. The specimens were then inverted to be loaded for the second loading cycle and subsequently followed by the third loading cycle and the fourth loading cycle. Starting from the third loading cycle, the bond-slip between inner concrete and outer stainless steel tube of the specimens occurred at a comparatively small load level, although the slipping rate is relatively low. 3.2. Axial load-bond slip curves The axial load versus bond slip curves of all specimens determined from the push-out tests are plotted in Fig. 5, in which the horizontal axis represents the bond slip (S) between inner concrete and outer stainless steel tube of the specimens obtained from the average readings of two displacement transducers positioned at the top end of steel circular solid block, the vertical axis represents the axial load (P) applied to the inner concrete only by means of steel circular solid block, and n is the loading cycle of the repeated push-out test. The loads at the peak point or the inflection point in the testing curves are defined as the shear failure load or the bond-slip load denoted by Pnu (n = 1, 2, 3 and 4) for different loading cycles of the repeated push-out test, while τu, f and Su are the shear resistance and friction resistance of the bonding strength as well as the critical slippage at the bond-slip failure, respectively, as summarized in Table 3. It is shown from the comparison that the shear failure loads of bonding slip decreased with more loading cycles of the repeated push-out test employed in the same direction for n = 1 and 3 or n = 2 and 4, which indicated that the mechanical interlock force was gradually weakened due to the cracking of the interface elements of the inner concrete. In addition, it is also shown that the axial load versus bond slip curves exhibited more nonlinearity with more loading cycles of the repeated push-out test employed, in which the shapes of the testing curves for the second and fourth loading cycles (n = 2 and 4) are quite similar, whereas the shapes of the testing curves
for the first and third loading cycles (n = 1 and 3) are quite different although their loading directions are identical. This may attribute to the introduction of the adhesive force and interlock force in the interface elements of the inner concrete in the first loading cycle and variation of these interface forces in the subsequent loading cycles, which significantly contributed to the shear resistance of the bonding strength. The axial load versus bond slip curves also exhibited the variation of the interface friction resistance. It is also shown from the comparison that the interface friction resistance gradually decreased with more loading cycles of the repeated push-out test employed in the same direction for n = 1 and 3 or n = 2 and 4. The friction resistance in the testing curves for the first and third loading cycles (n = 1 and 3) has an opposite tendency compared with that in the testing curves for the second and fourth loading cycles (n = 2 and 4), which means the interface friction decreased with the increase of the bond slip for loading cycles of the repeated push-out test employed in the opposite direction, whereas the interface friction increased with the increase of the bond slip for loading cycles of the repeated push-out test employed in the initial condition. This may attribute to the macro-offset of the inner diameter of stainless steel CHS tubes. If the variation of the inner diameters of stainless steel CHS tubes along the longitudinal height direction of the specimens are small (changing from large diameter to small diameter), the inner concrete slipped along the surface of a cone. In this case, the interface adhesive force between the inner concrete and outer stainless steel cone tube of the specimens increased with the increase of the bond slip, which indicates that the confinement provided by the outer stainless steel tube to the inner concrete gradually increased and the axial load versus bond slip curves have an increasing tendency. Conversely, if the loading cycles of the repeated push-out test were employed for the inner concrete in the opposite direction, the bond slip behaviour of the interface elements may cause the separation of the inner concrete and outer stainless steel tube of the specimens and weaken the interface forces. In this case, the confinement provided by the outer stainless steel tube to the inner concrete gradually decreased and the axial load versus bond slip curves have a decreasing tendency. There are two types of axial load versus bond slip curves as shown in Fig. 6a and b for testing curves of type I and type II, respectively. For testing curve of type I, there is a clear peak point in the curve. In the initial loading stage, the axial load linearly increased with a large slope until the bond-slip failure occurred, where the peak load was found. The axial loads dropped substantially in the post-ultimate stage with large bond slip. For testing curve of type II, the axial load keeps increasing and no clear peak point can be found in the curve. In the initial loading
Concrete slightly crushed
(a) Inner concrete
251
(b) Outer stainless steel tube
Fig. 4. Failure modes of specimens in the repeated push-out test.
252
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n=1
n=2
n=3
n=1
n=4
9000
16000
8000
14000
7000
12000
6000
n=2
n=3
n=4
10000
P/N
P/N
5000
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0
0
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0 2 4 6 8 10 12 14 16 18 20 S/mm
(a1) H304-t0.5-C20
(a2) H456-t0.5-C20
n=1
n=2
n=3
n=1
n=4
n=2
n=3
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P/N
9000 6000
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0
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0 2 4 6 8 10 12 14 16 18 20 S/mm
(a3) H608-t0.5-C20 n=1
n=2
n=3
(a4) H760-t0.5-C20 n=4
n=1
n=2
n=3
n=4
8000 12000
7000 10000
6000
8000
P/N
P/N
5000 4000
6000
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0
0 0 2 4 6 8 10 12 14 16 18 20 S/mm
(a5) H304-t0.7-C20
0 2 4 6 8 10 12 14 16 18 20 S/mm
(a6) H456-t0.7-C20
Fig. 5. Repeated push-out testing curves.
Y. Chen et al. / Journal of Constructional Steel Research 130 (2017) 248–263
n=1
n=2
n=3
n=1
n=4
n=2
253
n=3
n=4
18000
21000
16000
18000
14000 15000
12000
12000
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P/N
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9000
8000 6000
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0
0 2 4 6 8 10 12 14 16 18 20 S/mm
0 2 4 6 8 10 12 14 16 18 20 S/mm
(a7) H608-t0.7-C20 n=1
n=2
n=3
(a8) H760-t0.7-C20 n=4
n=1
6000
12000
5000
10500
n=2
n=3
n=4
9000
4000
P/N
7500
P/N
3000
6000 4500
2000
3000
1000 1500
0
0
0
2
4 6
8 10 12 14 16 18 20 S/mm
0 2 4 6 8 10 12 14 16 18 20 S/mm
(a9) H304-t0.9-C20 n=1
n=2
n=3
(a10) H456-t0.9-C20 n=4
n=1
n=2
n=3
n=4
18000
18000 15000
15000 12000
P/N
12000
P/N
9000
9000
6000
6000
3000
3000
0
0 0 2 4 6 8 10 12 14 16 18 20 S/mm
(a11) H608-t0.9-C20 Fig. 5 (continued)
0 2 4 6 8 10 12 14 16 18 20 S/mm
(a12) H760-t0.9-C20
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n=1
n=2
n=3
n=4
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n=1
n=2
n=3
n=4
14000
14000
12000
12000
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P/N
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8000 6000
6000 4000
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2000
0
0
0 2 4 6 8 10 12 14 16 18 20 S/mm
0 2 4 6 8 10 12 14 16 18 20 S/mm
(a13) H304-t1.1-C20 n=1
n=2
n=3
(a14) H456-t1.1-C20 n=4
n=1
27000
n=2
n=3
n=4
28000
24000 24000
21000
20000
15000
16000
P/N
P/N
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12000
9000 8000
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3000
0
0
0 2 4 6 8 10 12 14 16 18 20 S/mm
0 2 4 6 8 10 12 14 16 18 20 S/mm
(a15) H608-t1.1-C20 n=1
n=2
n=3
(a16) H760-t1.1-C20 n=4
n=1
n=2
n=3
n=4
12000
12000 10000
10000 8000
6000
P/N
P/N
8000
4000
6000 4000
2000
2000
0
0 0 2 4 6 8 10 12 14 16 18 20 S/mm
(b1) H304-t0.5-C50
0 2 4 6 8 10 12 14 16 18 20 S/mm
(b2) H456-t0.5-C50 Fig. 5 (continued)
Y. Chen et al. / Journal of Constructional Steel Research 130 (2017) 248–263
n=1
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n=4
n=2
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n=3
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14000 12000 10000
P/N
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8000 6000 4000
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0 2 4 6 8 10 12 14 16 18 20 S/mm
(b3) H608-t0.5-C50 n=1
n=2
(b4) H760-t0.5-C50
n=3
n=4
n=1
n=2
n=3
n=4
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10500 9000
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P/N
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4000
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0 0 2 4 6 8 10 12 14 16 18 20 S/mm
0 2 4 6 8 10 12 14 16 18 20 S/mm
(b5) H304-t0.7-C50 n=1
n=2
(b6) H456-t0.7-C50
n=3
n=4
21000
n=2
n=3
n=4
21000
18000
18000
15000
15000
12000
12000
P/N
P/N
n=1
9000
9000
6000
6000
3000
3000
0
0 0 2 4 6 8 10 12 14 16 18 20 S/mm
(b7) H608-t0.7-C50 Fig. 5 (continued)
0 2 4 6 8 10 12 14 16 18 20 S/mm
(b8) H760-t0.7-C50
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n=2
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n=1
n=4
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6000
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0
0 0 2 4 6 8 10 12 14 16 18 20 S/mm
0 2 4 6 8 10 12 14 16 18 20 S/mm
(b9) H304-t0.9-C50 n=1
n=2
(b10) H456-t0.9-C50
n=3
n=1
n=4
21000
n=2
n=3
n=4
24000
18000
20000
15000
16000
12000
P/N
P/N
n=3
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P/N
n=2
12000
9000
8000
6000
4000
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0
0
0 2 4 6 8 10 12 14 16 18 20 S/mm
0 2 4 6 8 10 12 14 16 18 20 S/mm
(b11) H608-t0.9-C50 n=1
n=2
n=3
(b12) H760-t0.9-C50 n=4
14000
n=1
n=2
n=3
n=4
12000
12000
10000
10000
P/N
P/N
8000 8000 6000
6000 4000
4000 2000
2000
0
0 0 2 4 6 8 10 12 14 16 18 20 S/mm
(b13) H304-t1.1-C50 Fig. 5 (continued)
0 2 4 6 8 10 12 14 16 18 20 S/mm
(b14) H456-t1.1-C50
Y. Chen et al. / Journal of Constructional Steel Research 130 (2017) 248–263
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n=2
n=3
n=4
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n=1
n=2
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n=3
n=4
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21000
20000
18000 15000
P/N
P/N
15000
12000 9000
10000
6000
5000
3000 0
0 0 2 4 6 8 10 12 14 16 18 20 S/mm
0 2 4 6 8 10 12 14 16 18 20 S/mm
(b15) H608-t1.1-C50
(b16) H760-t1.1-C50 Fig. 5 (continued)
stage, the axial load linearly increased with a large slope until a knee point formed. The testing curve converted from the linear stage to the nonlinear stage. After that, the axial load keeps increasing with a great reducing slope. The bond-slip failure of the interface elements between the inner concrete and outer stainless steel tube of the specimens can be divided into three distinctive stages based on the axial load versus bond slip
Table 3 Shear failure loads and bond-slip loads. Specimen
P1u (kN)
P2u (kN)
P3u (kN)
P4u (kN)
τu (MPa)
Su (mm)
f (kN)
f/P1u (%)
H304-t0.5-C20 H304-t0.7-C20 H304-t0.9-C20 H304-t1.1-C20 H456-t0.5-C20 H456-t0.7-C20 H456-t0.9-C20 H456-t1.1-C20 H608-t0.5-C20 H608-t0.7-C20 H608-t0.9-C20 H608-t1.1-C20 H760-t0.5-C20 H760-t0.7-C20 H760-t0.9-C20 H760-t1.1-C20 H304-t0.5-C50 H304-t0.7-C50 H304-t0.9-C50 H304-t1.1-C50 H456-t0.5-C50 H456-t0.7-C50 H456-t0.9-C50 H456-t1.1-C50 H608-t0.5-C50 H608-t0.7-C50 H608-t0.9-C50 H608-t1.1-C50 H760-t0.5-C50 H760-t0.7-C50 H760-t0.9-C50 H760-t1.1-C50
7.9 6.2 4.3 14.5 14.2 11.0 6.5 12.7 10.2 20.9 16.2 26.4 14.5 16.2 17.0 26.2 10.4 9.8 10.1 13.8 10.1 8.6 10.2 10.1 10.2 18.4 19.9 20.2 17.2 19.3 21.5 21.6
5.5 6.1 5.5 6.4 11.0 7.6 10.7 7.9 14.1 18.1 14.2 13.8 10.5 17.9 17.5 27.1 5.8 9.5 9.0 11.1 6.4 4.9 6.2 11.9 11.0 15.4 16.2 22.2 14.8 14.4 15.7 24.6
1.0 1.3 0.9 2.8 2.5 3.6 2.2 1.3 2.2 7.0 4.3 8.6 2.2 5.8 5.9 9.2 2.1 4.3 1.5 1.5 3.4 3.0 1.6 1.9 2.7 4.7 7.9 7.9 5.8 5.3 5.5 6.7
3.7 5.2 3.9 4.3 7.0 6.4 8.7 5.6 10.7 15.0 11.6 10.1 8.3 16.3 13.8 22.8 5.5 8.2 5.9 7.9 4.7 3.4 5.2 9.3 8.9 9.9 10.7 17.2 9.9 10.1 11.0 19.1
0.131 0.103 0.072 0.243 0.147 0.114 0.068 0.133 0.077 0.158 0.123 0.201 0.086 0.096 0.101 0.157 0.173 0.163 0.168 0.231 0.105 0.090 0.106 0.106 0.077 0.139 0.151 0.154 0.102 0.115 0.128 0.129
0.94 0.73 0.89 1.12 1.14 1.18 0.81 0.92 0.59 1.35 0.87 1.13 1.27 1.26 2.78 1.62 1.24 1.08 0.83 1.13 0.78 1.00 0.86 0.91 0.93 1.40 1.17 1.08 1.98 1.86 0.93 1.99
4.7 4.9 4.0 5.9 9.6 8.0 5.0 6.5 9.3 17.3 12.0 16.3 12.5 15.0 14.2 17.0 4.3 7.3 4.9 6.7 5.9 3.7 4.7 7.9 7.3 13.5 14.5 16.8 13.9 13.5 16.2 17.0
59% 79% 93% 41% 68% 73% 77% 51% 91% 83% 74% 62% 86% 93% 84% 65% 41% 74% 49% 49% 58% 43% 46% 78% 72% 73% 73% 83% 81% 70% 75% 79%
curves in the first loading cycle of the repeated push-out test, which included the adhesive stage (OA), the sliding stage (AB) and the friction resistant stage (post-ultimate stage), as shown in Fig. 7. In the initial loading stage where the adhesive stage occurs, there is no bond slip between the inner concrete and outer stainless steel tube except for the region at the ends of the specimens. The shear resistance of the bonding strength of the interface elements is sustained by the interface adhesive force, while the shear force is relatively small. The interface adhesive effect is gradually disappeared with the increase of the axial load, which cannot take into effect anymore. This adhesive stage in the axial load versus bond slip curve is relatively short, hence the interface adhesion may fail at a small axial load (corresponding to Point A in the testing curve as shown in Fig. 7). The interface adhesive force is replaced by the micro-interlock force developed at the uneven inner surface of the stainless steel tube to take the shear force of the interface elements. The bond slip gradually developed at the ends of the specimens with the further increase of the axial load. The shear resistance of the bonding strength of the sliding interface elements is sustained by the interlock force, while the shear resistance of the bonding strength of the non-sliding interface elements is sustained by the adhesive force. The failure load of the bonding strength will be reached (corresponding to Point B in the testing curve as shown in Fig. 7) once the maximum values of the resultant interlock force and adhesive force are obtained (corresponding to the peak point or the knee point in the testing curve). The interlock force at this stage is dominant in the shear resistance of the bonding strength. After that, the bond slip behaviour between the inner concrete and outer stainless steel tube of the specimens presents nonlinearity in the post-ultimate stage (after the peak point or the knee point in the testing curve). The interface adhesive force will be completely disappeared once the sliding of the interface elements between the inner concrete and outer stainless steel tube occurs along the whole height of the specimens. In the meanwhile, the interlock force of the interface elements with large bond slip remarkably reduced. Hence, the shear force of the bonding strength is mainly sustained by the interface friction force, which is proportional to the compression force in the normal direction of the interface elements and the interface friction coefficient. It is worth noting that the friction coefficient decreased with the increase of the bond slip and more loading cycles of the repeated push-out test. The compression force in the normal direction of the interface elements resulted from the confinement provided
258
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(a) Type I
(b) Type II Fig. 6. Typical axial load-bond slip curves.
by the outer stainless steel tube to the inner concrete in the transverse direction, which is determined by the variation of the inner diameter of the stainless steel tube. The inner concrete slipped along the surface of a cone with the variation of the inner diameter of the stainless steel tube. If the variation of the inner diameters of stainless steel CHS tubes along the longitudinal height direction of the specimens are changing from large diameter to small diameter, the inner concrete will be wedged into a cone. The stainless steel tube could provide a larger confinement to the inner concrete with the increase of the bond slip, which produces a larger friction force. However, if the variation of the inner diameters of stainless steel CHS tubes along the longitudinal height direction of the specimens are changing from small diameter to large diameter or the inner surface of stainless steel tube is frictionless, the outer stainless steel tube could not provide any confinement to the inner concrete. The interface friction force will then be remarkably reduced. If the resultant interlock force and adhesive force of the interface elements are larger than the initial interface friction force, the peak point will be found in the testing curve followed by the post-ultimate stage, as shown in Fig. 6a for testing curve of type I. The shear failure loads of bonding slip are equivalent to the resultant interlock force and adhesive force of the interface elements. This type of testing curve generally occurs for the specimens with the coarse inner surface of stainless steel tube. Conversely, if the resultant interlock force and adhesive force of the interface elements are smaller than the initial interface
friction force, no clear peak point can be found in the testing curve, in which a knee point is formed followed by the continuous increasing axial load, as shown in Fig. 6b for testing curve of type II. The shear failure loads of bonding slip are equivalent to the initial interface friction force. This type of testing curve generally occurs for the specimens with the smooth inner surface of stainless steel tube. It was found from the axial load versus bond slip curves that the post-ultimate stage (after the peak point or the knee point in the testing curve) is quite different for different specimens, which may attribute to the uneven degree of smoothness of the inner surface of stainless steel tube. If the degree of smoothness of the inner surface of stainless steel tube is significantly uneven, the interface friction force greatly increased with the increase of the bond slip, which resulted in the clear increasing post-ultimate stage, as shown in Fig. 8 for curve ‘a’. However, if the degree of smoothness of the inner surface of stainless steel tube is even, the interface friction force greatly decreased with the increase of the bond slip, which resulted in the substantial dropping post-ultimate stage, as shown in Fig. 8 for curve ‘c’. For specimens with the medium degree of smoothness of the inner surface of stainless steel tube, the post-ultimate stage of axial load versus bond slip curves is located between the curve ‘a’ and curve ‘c’, which somewhat dropped followed by a comparatively flat portion, as shown in Fig. 8 for curve ‘b’. It can be generally concluded from the previous analyses that the adhesive force, the interlock force and the friction force of the interface
Fig. 7. Bond-slip failure of the interface elements.
Fig. 8. Post-ultimate stage of the interface friction force.
Y. Chen et al. / Journal of Constructional Steel Research 130 (2017) 248–263
elements take effects sequentially in the bond-slip failure of the specimens, in which the adhesive force is dominant prior to the occurrence of the bond slip, the interlock force plays a primary role once the bond slip occurs until the shear failure load of bonding slip is reached, after that the friction force begins to take effect. In addition, the axial load versus bond slip curves present linearity in the initial loading stage, which developed gradually until the shear failure load of bonding slip is reached. After that, the testing curves converted from the linear stage to the nonlinear stage, which developed much faster. Furthermore, a comparatively large value of slippage between inner concrete and outer stainless steel tube of the specimens can be obtained before the shear failure load of bonding slip is reached. Therefore, only part of axial load versus bond slip curves prior to the attainment of the shear failure load of bonding slip needs to be considered in the practical applications.
3.3. Shear resistance of the bonding strength of the interface elements The shear resistance of the bonding strength of the interface elements consisted of three individual components including the chemical adhesive force between the cement gel and inner surface of stainless steel tube, the interlock force between the inner surface of stainless steel tube and inner concrete due to the uneven degree of smoothness of the interface, and the friction force of the interface elements between the inner surface of stainless steel tube and inner concrete. The adhesive force is a chemical absorption force between the cement and inner surface of stainless steel tube, which is significantly influenced by the properties of concrete including the concrete strength and water-to-cement ratio. Experimental investigation on the adhesion of the reinforced concrete structures indicates that the adhesive strength between the steel bar and concrete is minimal. The adhesion force will lose its function forever once the local bond slip occurs on the interface. The adhesion between the inner concrete and outer stainless steel tube of the specimens in the repeated push-out test in this study demonstrated the similar behaviour. The interlock force resulted from the uneven degree of smoothness of the inner surface of stainless steel tube and the interlock action of the wedged concrete, which depends on the uneven degree of smoothness of the interface and the shear strength of the inner concrete. It is the main component of the shear resistance of the bonding strength of the interface elements. It is worth noting that the uneven degree of smoothness of the inner surface of stainless steel tube is in difference of the order of 10− 2, which is the so-called micro-deviation. An enlarged view of the micro-interlock action is clearly shown in Fig. 9. The shear resistance of the bonding strength resulted from the microdeviation action is the so-called “micro-mechanical interlock force”.
Fig. 9. Micro-Interlocking action.
259
The interface friction force begins to take effect once the bond slip between the inner concrete and outer stainless steel tube occurs along the whole height of the specimens, which is proportional to the compression force in the normal direction of the interface elements and the interface friction coefficient. The friction coefficient between the inner concrete and outer stainless steel tube is dependent on the degree of smoothness of the inner surface of stainless steel tube, which is ranged from 0.3 to 0.5. It is worth noting that the friction coefficient decreased with the increase of the bond slip and more loading cycles of the repeated push-out test. Different from the friction force between the steel bar and concrete in the reinforced concrete structures, the friction force between the inner concrete and outer stainless steel tube in the concrete-filled steel tubes is mostly determined by the confinement from the outer stainless steel tube to the inner concrete in the transverse direction. It was found that the confinement in the transverse direction depends mainly on three influential factors. Firstly, the inner diameters of stainless steel CHS tubes along the longitudinal height direction of the specimens vary irregularly in the fabrication process, as shown in Fig. 10 for an enlarged view of variation of the inner diameters of stainless steel CHS tubes. The irregular variation of the inner diameters of stainless steel CHS tubes along the longitudinal height direction of the specimens are much larger than the uneven degree of smoothness of the inner surface of stainless steel tube, which is the so-called macro-deviation. The sliding concrete is wedged into a cone once the bond slip between the inner concrete and outer stainless steel tube occurs from top to bottom, as shown in Fig. 10. Hence, the wedge effect forms to make the confinement from the outer stainless steel tube to the inner concrete larger, which resulted in a large interface friction force. The shear resistance of the bonding strength resulted from the macro-deviation action is the so-called “macro-mechanical interlock force”. Secondly, the concrete-filled stainless steel tubular columns are usually subjected to eccentric compression force in practice, which produces a bending moment on the columns. The additional bending moment will produce a compression force on the interface in the radial direction, which could increase the interface friction force. Thirdly, the stress distribution at the beam-column connection is quite complicated. The so-called clamping effect and pinching effect at the interesting area could remarkably increase the compression force on the inner concrete in the radial direction. However, the clamping effect and pinching effect
Fig. 10. Variation of the inner diameters of stainless steel CHS tubes.
Y. Chen et al. / Journal of Constructional Steel Research 130 (2017) 248–263
900 800 700 600 500 400 300 200 100 0
8%Pu
1000
8%Pu 15%Pu
800
20%Pu 40%Pu
600
60%Pu 80%Pu
400
100%Pu
15%Pu 20%Pu 40%Pu 60%Pu
ε/µε
ε/µε
260
80%Pu 100%Pu
200 0
0
100
200
h/mm
300
0
400
(a) H304-t0.5-C20
400
h/mm
600
8%Pu 15%Pu 20%Pu 40%Pu 60%Pu 80%Pu 100%Pu
700
600
8%Pu
500
15%Pu
600
20%Pu
500
40%Pu
400
300
60%Pu
200
80%Pu 100%Pu
100 0
ε/µε
400
800
(b) H760-t0.5-C20
700
ε/µε
200
300 200 100 0
0
100
200
300
400
h/mm (c) H304-t1.1-C20
0
200
400
h/mm
600
800
(d) H760-t1.1-C20
Fig. 11. Strain distribution curve on outer surface of stainless steel tube.
do not exist in this study since the experimental work did not consider the effect of loading eccentricity. Hence, the interface friction force is mainly determined by the macro-deviation action of stainless steel CHS tubes. Based on the test results in this study, 70% of the shear resistance of the bonding strength is taken by the interface friction force, while the remaining 30% of the shear resistance of the bonding strength is sustained by the chemical adhesive force and the mechanical interlock force.
close to the free end increased much greater. The difference of the strains at the locations close to the free end and loading end of the specimens increased with the increase of the axial load, which indicates that the strain loses its continuity between the inner concrete and outer stainless steel tube and the bond slip occurs between them. In this loading stage, the axial load applied to the inner concrete is transferred to the outer stainless steel tube by means of the shear resistance of the bonding strength of the interface elements.
3.4. Strain distribution on outer surface of stainless steel tube
3.5. Influential factors on the shear resistance of the bonding strength of the interface elements
The strain distribution on outer surface of stainless steel tube was obtained from the measurements of three-element rosettes strain gauges as shown in Fig. 11, which were positioned in line on the exterior of stainless steel tube along the longitudinal height direction, as shown in Fig. 3. It is shown from the comparison that the strains on outer surface of stainless steel tube generally distributed linearly along the longitudinal height direction in the initial loading stage, in which the strains at the location close to the free end of the specimens are quite small. Furthermore, the strains at the locations close to the free end and loading end of the specimens increased with the increase of the axial load, in which the strains at the location
It is worth noting that the shear resistance of the bonding strength of the interface elements between the inner concrete and outer stainless steel tube is corresponding to the shear failure load of the bonding slip, which is the starting point of the occurrence of the bond slip and the critical point controlling the interaction between the inner concrete and outer stainless steel tube within the range of limit bond slip. Hence, it can be defined as the failure of the bond slip. However, the interface adhesive condition may vary irregularly along the longitudinal height direction and the circumferential direction of the specimens, which led to the unstable shear resistance of the bonding strength in certain
Y. Chen et al. / Journal of Constructional Steel Research 130 (2017) 248–263
0.3
0.25
0.25
D/t=152
0.15
D/t=69.1
D/t=108.6
τ/MPa
D/t=84.4
0.15
0.1 0.05
0.05
0 3
6 9 H/D
12
D/t=84.4 D/t=69.1
0.1
0
D/t=152
0.2
D/t=108.6
0.2 τ/MPa
261
0
15
0
3
6
9
12
15
H/D
(a) C20
(b) C50
Fig. 12. Effect of height-to-diameter ratio on the shear resistance of the bonding strength.
local area. Therefore, it is necessary to average the shear resistance of the bonding strength in a finite surface area to obtain the valid result, which can be defined as the design strength. Hence, the shear stress of the bonding strength is assumed to be uniformly distributed in the contact surface between the inner concrete and outer stainless steel tube of the specimens. The shear resistance of the bonding strength of the interface elements in the concrete-filled stainless steel CHS tubes can be calculated as follows: Nu πD0 l0
ð1Þ
τ/MPa
where τu is the shear resistance of the bonding strength, Nu is the shear failure load of the bonding slip, D0 is the inner diameter of the stainless steel CHS tube, and l0 is the overall length of the interface.
0.3
H/D=4
0.25
H/D=6
0.25
H/D=8
0.2
H/D=10
0.15 0.1
0.1
0
0
100 D/t (a) C20
150
200
H/D=8 H/D=10
0.05
50
H/D=6
0.15
0.05 0
H/D=4
0.2 τ/MPa
τu ¼
A parametric study was carried out in this study to investigate the effects of main influential factors including the height-to-diameter ratio (H/D) of the stainless steel tube, the diameter-to-thickness ratio (D/t) of the stainless steel tube, and the concrete strength (C) on the shear resistance of the bonding strength of the interface elements. It is shown from the comparison that the height-to-diameter ratio (H/D) and the diameter-to-thickness ratio (D/t) of the stainless steel tube have insignificant influence on the shear resistance of the bonding strength of the interface elements for both normal strength and high strength concrete with nominal concrete cube strengths of 20 MPa and 50 MPa, as shown in Figs. 12 and 13, respectively. Furthermore, it is also demonstrated from the comparison that the concrete strength (C) has minor influence on the shear resistance of the bonding strength of the interface elements, as shown in Table 4.
0
50
100 D/t (b) C50
Fig. 13. Effect of diameter-to-thickness ratio on the shear resistance of the bonding strength.
150
200
262
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4. Design rules There is no design rules currently used for the shear resistance of the bonding strength of concrete-filled stainless steel CHS tubes. However, the shear resistance of the bonding strength of concrete-filled carbon steel CHS tubes can be estimated by using the design equations proposed by Kang [20] as follows: 1 τu ¼ k γ
"
4Le d −0:00028 þ 29:09049α þ 0:11121 t d ! #
ð2Þ
þ0:03439θ−7:36037 f t where γ = 0.96 is the correction coefficient for the uncertainty, k is the influential factor for the exterior of steel tube, α = (D / D0)2 − 1 is the steel ratio of the concrete-filled steel CHS tube, θ = Asfy / (Acfc) is the confinement factor for the concrete-filled steel CHS tube, Le is the overall adhesive length, d is the diameter of the steel CHS tube, t is the thickness of the steel CHS tube, and ft is the tensile strength of the concrete, ft = 1/10fc is used for the concrete with nominal concrete cube strengths of 20 MPa, while ft = 1/13fc is used for the concrete with nominal concrete cube strengths of 50 MPa. Therefore, the shear resistance (τKang) of the bonding strength of concrete-filled stainless steel CHS tubes was calculated by substituting the measured tensile proof stress as the yield stress in Eq. (2), which was compared with the test results (τTest) as summarized in Table 5. It is demonstrated from the comparison that the current design rules of concrete-filled carbon steel CHS tubes are extremely unconservative for the shear resistance of the bonding strength of concrete-filled stainless steel CHS tubes with the mean value of the predict-to-test strength ratio (τKang/τTest) of 114.0 and the corresponding coefficient of variation (COV) of 0.845. This may attribute to the much smoother inner surface of stainless steel tube compared to carbon steel tube, which resulted in
Table 4 Effect of concrete strength on the shear resistance of the bonding strength. Specimen
τu (MPa)
τ20/τ50
H304-t0.5-C20 H304-t0.5-C50 H456-t0.5-C20 H456-t0.5-C50 H608-t0.5-C20 H608-t0.5-C50 H760-t0.5-C20 H760-t0.5-C50 H304-t0.7-C20 H304-t0.7-C50 H456-t0.7-C20 H456-t0.7-C50 H608-t0.7-C20 H608-t0.7-C50 H760-t0.7-C20 H760-t0.7-C50 H304-t0.9-C20 H304-t0.9-C50 H456-t0.9-C20 H456-t0.9-C50 H608-t0.9-C20 H608-t0.9-C50 H760-t0.9-C20 H760-t0.9-C50 H304-t1.1-C20 H304-t1.1-C50 H456-t1.1-C20 H456-t1.1-C50 H608-t1.1-C20 H608-t1.1-C50 H760-t1.1-C20 H760-t1.1-C50
0.131 0.173 0.147 0.105 0.077 0.077 0.086 0.102 0.103 0.163 0.114 0.090 0.158 0.139 0.096 0.115 0.072 0.168 0.068 0.106 0.123 0.151 0.101 0.128 0.243 0.231 0.133 0.106 0.201 0.154 0.157 0.129
0.757 1.400 1.000 0.843 0.632 1.267 1.137 0.835 0.429 0.642 0.815 0.789 1.052 1.255 1.305 1.217
the much smaller interlock force and friction force of the interface elements of stainless steel tube compared to carbon steel tube. Therefore, the current design rules of concrete-filled carbon steel CHS tubes are inapplicable to the shear resistance of the bonding strength of concretefilled stainless steel CHS tubes. Further research needs to be carried out to propose the accurate design formulae for the shear resistance of the bonding strength of concrete-filled stainless steel CHS tubes. Convergence studies will be carried out to obtain the optimum finite element mesh density by comparison between the small size test and finite element analysis results in the companion paper. An extensive parametric study will be carried out to investigate the effects of main geometric parameters on CFT columns with engineering size used in practice. Design equation of bond strength for CFT columns with engineering size will be proposed. 5. Conclusions Based on the repeated push-out tests on a total of 32 concrete-filled stainless steel CHS tubes with different values of height-to-diameter ratio, diameter-to-thickness ratio and concrete strength, the following conclusions can be drawn: (1) Contact face of the inner concrete slightly was crushed by unloading the specimens to zero. (2) 70% of the shear resistance of the bonding strength is taken by the interface friction force, while the remaining 30% of the shear resistance of the bonding strength is sustained by the chemical adhesive force and the mechanical interlock force. (3) Axial load versus bond slip curves with or without peak point were observed in test. (4) The current design rules of concrete-filled carbon steel CHS tubes are extremely unconservative for the shear resistance of the Table 5 Comparison of test strengths with design strengths for the shear resistance of the bonding strength of concrete-filled stainless steel CHS tubes. Specimen
τTest (MPa)
τKang (MPa)
τKang/τTest
H304-t0.5-C20 H304-t0.7-C20 H304-t0.9-C20 H304-t1.1-C20 H456-t0.5-C20 H456-t0.7-C20 H456-t0.9-C20 H456-t1.1-C20 H608-t0.5-C20 H608-t0.7-C20 H608-t0.9-C20 H608-t1.1-C20 H760-t0.5-C20 H760-t0.7-C20 H760-t0.9-C20 H760-t1.1-C20 H304-t0.5-C50 H304-t0.7-C50 H304-t0.9-C50 H304-t1.1-C50 H456-t0.5-C50 H456-t0.7-C50 H456-t0.9-C50 H456-t1.1-C50 H608-t0.5-C50 H608-t0.7-C50 H608-t0.9-C50 H608-t1.1-C50 H760-t0.5-C50 H760-t0.7-C50 H760-t0.9-C50 H760-t1.1-C50 Comparison
0.131 0.103 0.072 0.243 0.147 0.114 0.068 0.133 0.077 0.158 0.123 0.201 0.086 0.096 0.101 0.157 0.173 0.163 0.168 0.231 0.105 0.090 0.106 0.106 0.077 0.139 0.151 0.154 0.102 0.115 0.128 0.129 Mean COV
23.393 12.393 6.451 2.811 23.387 12.387 6.446 2.806 23.382 12.382 6.441 2.800 23.377 12.377 6.435 2.795 28.796 15.249 7.931 3.446 28.789 15.243 7.925 3.440 28.783 15.236 7.918 3.433 28.776 15.230 7.912 3.427
178.6 120.3 89.6 11.6 159.1 108.7 94.8 21.1 303.7 78.4 52.4 13.9 271.8 128.9 63.7 17.8 166.5 93.6 47.2 14.9 274.2 169.4 74.8 32.5 373.8 109.6 52.4 22.3 282.1 132.4 61.8 26.6 114.0 0.845
Y. Chen et al. / Journal of Constructional Steel Research 130 (2017) 248–263
bonding strength of concrete-filled stainless steel CHS tubes. Hence, the current design rules of concrete-filled carbon steel CHS tubes are inapplicable to the shear resistance of the bonding strength of concrete-filled stainless steel CHS tubes.
Acknowledgements This research work was supported by the National Natural Science Foundation of China (Nos. 51278209 and 51478047). The tests were conducted in Fujian Key Laboratory on Structural Engineering and Disaster Reduction at Huaqiao University. The support provided by the laboratory staff is gratefully acknowledged. References [1] E. Ellobody, B. Young, Design and behaviour of concrete-filled cold-formed stainless steel tube columns, Eng. Struct. 28 (2006) 716–728. [2] E. Ellobody, Nonlinear behavior of concrete-filled stainless steel stiffened slender tube columns, Thin-Walled Struct. 45 (2007) 259–273. [3] M.A. Dabaon, M.H. El-Boghdadi, M.F. Hassanein, Experimental investigation on concrete-filled stainless steel stiffened tubular stub columns, Eng. Struct. 31 (2009) 300–307. [4] M.F. Hassanein, Numerical modelling of concrete-filled lean duplex slender stainless steel tubular stub columns, J. Constr. Steel Res. 66 (2010) 1057–1068. [5] M.F. Hassanein, O.F. Kharoob, Q.Q. Liang, Behaviour of circular concrete-filled lean duplex stainless steel tubular short columns, Thin-Walled Struct. 68 (2013) 113–123. [6] E. Ellobody, Numerical modeling of fibre reinforced concrete-filled stainless steel tubular columns, Thin-Walled Struct. 63 (2013) 1–12.
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