Performance and design of partially CFRP-jacketed circular CFT column under eccentric compression

Journal of Constructional Steel Research 166 (2020) 105925

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Journal of Constructional Steel Research

Performance and design of partially CFRP-jacketed circular CFT column under eccentric compression Qihan Shen a,b, Jingfeng Wang a,c,⁎, Qiuyu Xu a, Yubo Cui a a b c

School of Civil Engineering, Hefei University of Technology, Anhui Province 230009, China Department of Civil & Environmental Engineering, National University of Singapore, 119077, Singapore Anhui Civil Engineering Structures and Materials Laboratory, Anhui Province 230009, China

a r t i c l e

i n f o

Article history: Received 12 September 2019 Received in revised form 16 December 2019 Accepted 23 December 2019 Available online xxxx Keywords: Carbon fibre reinforced polymer (CFRP) Circular concrete-filled steel tubular (CFT) column Eccentric compressive behaviour Partial wrapping scheme Design formula

a b s t r a c t Nowadays, the carbon fibre reinforced polymer (CFRP) strengthening technology that uses the partial wrapping scheme is commonly applied in reinforcement engineering. Nevertheless, related investigations on partially CFRP jacketed concrete-filled steel tubular (CFT) columns under eccentric bearing forces are rarely reported. Herein, a series of experimental and analytical works on the eccentric behaviour of the partially CFRP jacketed circular CFT short and slender columns are presented. The influence of various parameters, in terms of steel yield stress, load eccentricity, number of CFRP layers, CFRP spacing, and column slenderness, on the eccentric compressive response of the specimens were analysed. Mechanical properties were evaluated by discussing the laws of the eccentric pressure (N)-vertical displacement (δ) curves, typical failure modes, strain responses, strength and ductility indexes, etc. Following these, a modified finite element model of the partially CFRP jacketed circular CFT column subjected to an eccentric bearing force was developed and validated against the existing experimental results. The contact stress and the effective jacketing scheme of the composite column were also discussed. Finally, based on an analysis of the confining stress transferring mechanism of the partial wrapping scheme, design formulae were proposed to assess the axial and eccentric load bearing capacity of the partially CFRP jacketed circular CFT column. The observations drawn from this study might provide a good basis for the future applications of CFRP strengthening CFT structures. © 2020 Elsevier Ltd. All rights reserved.

1. Introduction In a rapidly developing society, the numerous existing building structures need to be repaired or strengthened, owing to different degrading conditions such as increased loads, usage changes, construction errors, faulty design, structural damages, and corrosion [1]. To guarantee safety of personal life and property, a series of strengthening technologies have been proposed and been gradually used for the structures, including enlarging cross-sections, wrapping structural steel, inserting steel plates, and planting reinforcement bars [2]. Among these, the carbon fibre reinforced polymer (CFRP) materials are more favoured by engineers and scholars due to their superior qualities, such as high tensile strength, low weight, excellent corrosion resistance, and construction convenience [3–5]. The CFRP composites were used for the first time in the 1990s, to repair the reinforced concrete (RC) members and therefore, plenty of studies concentrating on the strengthening property of the CFRP confined RC members have been conducted over the past two decades ⁎ Corresponding author at: School of Civil Engineering, Hefei University of Technology, Anhui Province 230009, China. E-mail address: [email protected] (J. Wang).

https://doi.org/10.1016/j.jcsr.2019.105925 0143-974X/© 2020 Elsevier Ltd. All rights reserved.

[6–8]. The aforementioned prominent properties of the CFRP make it quite appropriate for strengthening the plain concrete (PC) and RC members. Notable enhancement in strength could be obtained because of the triaxial compressive condition rendered by the CFRP confining stress. Based on this principle [9], several newly built structures even prepared to apply the CFRP tubes for the RC and PC columns. Nonetheless, relative surveys indicated that using the CFRP-tubed concrete members for buildings increased the cost because of its complicate construction procedure [10]. Moreover, brittle failure is another serious issue occurring due to the low ductility property of the CFRP composites. In terms of the concrete-filled steel tubular (CFT) column, although the inward local bugles of the steel tube were restricted by the supporting effect supplied by the core concrete, the outward local buckling of the steel tube became the typical failure pattern [11–15]. Considering these limitations, the CFRP-jacketed CFT column offers a good alternative with comprehensive advantages, as the hollow steel section could provide an attached surface for the CFRP jackets and improve the ductility behaviour of the column, while the CFRP belts could prevent the outward local buckling of the steel tube, shield the outside steel surface from the corrosive environment, and supply an extra confinement for the core concrete. Moreover, an easy construction step would be realized because the CFRP could be conveniently twinned around the

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Q. Shen et al. / Journal of Constructional Steel Research 166 (2020) 105925

hollow steel section. Hence, the mechanical properties of the CFRP jacketed CFT column including the load resistance, ductility, and corrosion behaviour would be much better than those of the pure CFT column and the CFRP-tubed concrete column [10], which indicates that this type of composite column is undoubtedly adept to be used as frame columns and bridge pillars in high-rise buildings and offshore structures [16]. Hitherto, a good number of literatures have focused on the static behaviour of the CFT columns and beams fully jacketed using the CFRP materials. Impressive research works on the mechanical responses of the axially loaded CFT short column fully jacketed by CFRP were meticulously reported by Tao et al. [17], Ding et al. [18], Dong et al. [19], Choi and Xiao [20] and many other researchers. The axial behaviour of the type of composite columns with various slenderness ratios was investigated as well [21–23]. The research results showed that both the axial strength and the deformation ability of the CFT short column were clearly enhanced by using the CFRP jackets [24,25], while the contribution to the slender CFT column was quite limited due to the little effect of the CFRP wraps on its axial stiffness. Flexural performance of the fully CFRP jacketed rectangular and circular CFT beams was studied as well, considering the superior tensile property of the CFRP composites [26– 28]. The examples revealed that the flexural resistance of the CFT beam was greatly improved by the longitudinally jacketed CFRP; nonetheless, the CFRP strips in the transverse direction offered limited influence [29,30]. Moreover, as the CFRP jackets were usually applied for repairing/strengthening the damaged structures living through various disasters, many scholars have studied the fire-exposed properties of the fully CFRP jacketed CFT members imposed with axial, eccentric, and flexural loads (i.e. Chen et al. [31] and Tao and Han [32]), and behaviour of the column subjected to cyclic and impact loads (i.e. Han et al. [33], Yu et al. [34], Alam et al. [35] and Shakir et al. [36]) . Although most of the researches concentrated on the response of the fully CFRP jacketed CFT columns and beams, the partial CFRP wrapping technology was commonly used in the RC structures (shown in Fig. 1). Related studies indicate that using the partial CFRP strengthening method could also supply an increased ample bearing-capacity to the RC members [37,38]. In certain cases when only a moderate improvement in strength was needed, the partial CFRP jacketing layout was an economic and promising choice to substitute for the fully CFRP jacketed CFT members [39]. Recently, Shen et al. [23,40], Prabhu et al. [41], and Prabhu and Sundarraja [42] explored the axial compressive properties of the partially CFRP jacketed circular and square CFT columns through experimental and numerical approaches. The results demonstrated that a dramatic improvement in strength could be observed by applying the partial jacketed CFRP jackets. Despite the eccentric compressive members, such as side and corner columns, being commonly used in

(a) Partially CFRP jacketed RC column

buildings, there exists a paucity of experimental and numerical studies focusing on the strengthening behaviour of the partially CFRP jacketed CFT columns under eccentric bearing force. The mechanical performance of the eccentrically loaded short and slender composite columns was totally ignored. In this study we investigate the behaviour of partially CFRP jacketed circular CFT column (shown in Fig. 2) imposed with eccentric bearing force. To this end, a total of 10 circular CFT short columns and 11 circular CFT slender columns partially jacketed by CFRP wraps subjected to eccentric compressive loads were tested and analysed. The influence of various parameters including the steel yield stress (fy), number of CFRP layers (n), load eccentricity (e), slenderness ratio (λ), and CFRP spacing (ws) on the eccentric compressive behaviour of the partially CFRP jacketed circular CFT column was investigated. Detailed mechanical responses in terms of the eccentric compressive load (N)-longitudinal shortening (δ) curve, failure modes, strain response, strength indexes, and ductility indexes were also revealed. Further exploration of the contact stress and the suitable wrapping program of partially CFRP jacketed circular CFT columns was carried out through a modified finite element (FE) modelling approach. Eventually, based on the analytical model built for the confining stress transferring mechanism of the partially CFRP jacketed CFT column, the design formulae to predict the resistances of the axially and eccentrically loaded circular CFT columns strengthened by CFRP jackets partially are presented.

2. Experimental investigation A total of 21 circular CFT columns (10 short columns and 11 slender columns) partially jacketed by CFRP composites (seen in Table 1) imposed with eccentric compression were included in the experimental program. Moreover, the strength resistance and ductility properties of the type of composite column are discussed and compared with the observations of axially loaded partially CFRP jacketed CFT columns described in the previous works of the authors [23,43]. All specimens have used the commercially available circular hollow steel sections (CHSSs) with a measured cross-section of 140 mm diameter and 6 mm thickness. The CFRP jackets with widths of 50 mm and 150 mm were used respectively for the short and slender columns. Specially, the length of the short column was uniformly set as three times its diameter to guarantee that the column was short enough and would not fail in overall instability, but would be sufficiently long to reflect the stress and strain distribution. The major test parameters in this study included the fy, n, ws, e, and λ. Detailed information of the test specimens is illustrated in Table 1.

(b) Partially CFRP jacketed RC beams and slabs

Fig. 1. Partial CFRP jacketing scheme used in RC structures.

Q. Shen et al. / Journal of Constructional Steel Research 166 (2020) 105925

Ds

Table 2 Material properties of the steel. Steel

CFRP wrapped zone

wf (CFRP width)

Q345

CFRP jacket

Number Yield tensile stress

1 2 3

Average Q235 1 2 3 Average

ws (CFRP spacing)

CFRP unwrapped zone

3

Ultimate tensile stress

Elastic modulus

fy (N/mm2)

fu (N/mm2)

Es (N/mm2)

346.2 349.5 350.1 348.6 236.8 240.7 244.9 240.8

479.4 487.4 495.2 487.3 380.3 379.6 377.7 379.2

2.01 × 105 2.02 × 105 2.02 × 105 2.02 × 105 1.98 × 105 1.98 × 105 1.97 × 105 1.98 × 105

Elongation at fracture (%)

13.2 14.1 14.1 13.8 14.9 15.8 15.3 15.3

CFRP jacket Steel tube

Circular CFT column

Core concrete Dc

However, it failed abruptly once the tensile stress reached about 3510 MPa. For the core concrete, its initial slum, slum flow, density, average cube compressive stress (fcu), and the elastic modulus (Ec) were respectively tested to be 242 mm, 560 mm, 2386 kg/m3, 31.2 N/mm2, and 30,521.3 N/mm2 in compliance with the code GB/T 50081 [45].

Fig. 2. Schematic view of partially CFRP jacketed CFT column.

2.2. Test setup and load apparatus 2.1. Material properties Two kinds of seamless CHSSs with measured yield strengths of 240.8 MPa and 348.6 MPa were applied for the test specimens. Their values for modulus of elasticity were 198 GPa and 202 GPa, respectively (shown in Table 2). The property of the CFRP tensile coupons was captured in accordance with the specification based on ASTMD 3039 [44]. The results demonstrated that the elastic modulus (Efrp) and average ultimate tensile strength (ffrp) of the CFRP jacket used in this experiment were respectively 243 GPa and 3510 MPa. Moreover, the average fracture strain (εfrp) of the CFRP jacket was measured as 1.44%. Details of the stress-strain relationships obtained from the tensile coupon tests are illustrated in Fig. 3. A distinct yield platform was found in the stress-strain relationship of the steel and finally the steel coupons failed in their ductility behaviour. Unlike the ductile property of the steel tensile coupons, the CFRP exhibited a brittle failure. The stress of the CFRP tensile coupon linearly improved with the increase in tensile strain.

Prior to casting the self-compacting concrete (SCC) into the CHSS, a 50 mm thickness steel plate was welded to the bottom of the CHSS. To realise the pinned connection of the column ends in the eccentric compression test, knife hinges were employed for the steel loading plates, and the knife hinge position on the plate was changed for different load eccentricities. Following this, the infill SCC was cast into the CHSS and was maintained in the laboratory. After 28 days of curing, a 50 mm thick steel plate was welded onto the other end of the CHSS. The vertical load (N) and longitudinal shortening (δ) of the composite column were extracted using an electro hydraulic servo system. Three linear variable displacement transducers (LVDTs) were arranged for the short columns to capture the δ of the column and the lateral deflection (μ) at the mid-height of the short column. Similarly, five LVDTs were utilised to capture the correlated deformation of the slender columns. The LVDT arrangements are depicted in Fig. 4. The strain responses of the CFRP jackets and the CHSS were reflected by the strain gauges arranged at the critical points. The short and slender columns

Table 1 Measured dimension of circular steel hollow tube, concrete and CFRP.

Series I

Parameter

Specimen

D × L × t/mm

e/mm

n

ws/mm

fcu

fy

fyu

Configuration

Steel strength

ES11 ES12 ES21 ES22 ES23 ES31 ES32 ES33 ES41 ES42 EL11 EL12 EL13 EL21 EL22 EL23 EL31 EL32 EL33 EL41 EL42

140 × 450 × 6 140 × 450 × 6 140 × 450 × 6 140 × 450 × 6 140 × 450 × 6 140 × 450 × 6 140 × 450 × 6 140 × 450 × 6 140 × 450 × 6 140 × 450 × 6 140 × 1200 × 6 140 × 1800 × 6 140 × 2300 × 6 140 × 2300 × 6 140 × 2300 × 6 140 × 2300 × 6 140 × 2300 × 6 140 × 2300 × 6 140 × 2300 × 6 140 × 2300 × 6 140 × 2300 × 6

30 30 30 30 30 30 30 30 10 50 30 30 30 30 30 30 30 30 30 10 50

3 3 0 1 5 3 3 3 3 3 3 3 3 0 1 5 3 3 3 3 3

50 50 0 50 50 0 30 150 50 50 100 100 100 0 100 100 0 150 250 250 250

31.2 31.2 31.2 31.2 31.2 31.2 31.2 31.2 31.2 31.2 31.2 31.2 31.2 31.2 31.2 31.2 31.2 31.2 31.2 31.2 31.2

240.8 348.6 348.6 348.6 348.6 348.6 348.6 348.6 348.6 348.6 348.6 348.6 348.6 348.6 348.6 348.6 348.6 348.6 348.6 348.6 348.6

379.2 487.3 487.3 487.3 487.3 487.3 487.3 487.3 487.3 487.3 487.3 487.3 487.3 487.3 487.3 487.3 487.3 487.3 487.3 487.3 487.3

Partially jacketed Partially jacketed No CFRP Partially jacketed Partially jacketed Fully jacketed Partially jacketed Partially jacketed Partially jacketed Partially jacketed Partially jacketed Partially jacketed Partially jacketed No CFRP Partially jacketed Partially jacketed Fully jacketed Partially jacketed Partially jacketed Partially jacketed Partially jacketed

CFRP layer

CFRP spacing

Load eccentricity Series II

Slenderness ratio

CFRP layer

CFRP spacing

Load eccentricity

Note: D and t are the diameter and thickness, respectively, of the circular steel tube wall; fcu is the average cube compressive strength of core concrete; fck is the characteristic compressive strength of core concrete, and fck = 0.67 fcu; fy and fyu are the yield strength and ultimate tensile strength of steel, respectively.

Q. Shen et al. / Journal of Constructional Steel Research 166 (2020) 105925

500

4000

400

3200

Stress (MPa)

Stresss (MPa)

4

300 200 100

Q235 Q345

0 0.00

0.05

0.10

0.15

2400 1600 Coupon1 Coupon2 Coupon3

800

0.20

Strain (a) Coupon tests results of steel

0 0.0

0.4

0.8

1.2

1.6

Strain (b) Coupon tests results of CFRP

Fig. 3. Stress-strain relationships of the steel and CFRP obtained from coupon tests.

were respectively set with 36 and 60 strain gauges, as illustrated in Fig. 5. To settle the column upright, a laser, a plumb bob, a shackle, and a water level were carefully used to centralise the specimen. The vertical force was imposed on a multi-stage loading method by an electro hydraulic machine with a capacity of 500 tons (shown in Fig. 6). Nearly every 0.1 times the eccentric load bearing capacity of the column (Nu) was applied to the end of the column for 2 min at a constant loading rate and each level of the force would be held for 2 min before the vertical load increased up to 0.6 Nu. Thereafter, every 0.05 Nu was imposed on the end of the column for 4 min at a constant loading rate until the pressure reached Nu. The test program would be stopped when the load decreased to 0.85 Nu or the specimen was severely damaged. 3. Experiment results and discussion 3.1. Axial load – displacement behaviour Fig. 7 illustrates the N-δ curves of the circular CFT column partially jacketed by the CFRP materials. The N-δ curves of the short columns exhibited an abrupt descent due to the sudden rupture of the CFRP jackets and the outward local bulges of the CHSS. Nevertheless, the N-δ curves of the partially CFRP jacketed circular CFT slender columns displayed N

D4

N

LVDT (lateral displacement) D5

Knife hinge

LVDT (vertical displacement) D1

D6 D2

D3

D7

D8

N

N

Stub column

Slender column Fig. 4. Layout of LVDTs.

the typical feature of global buckling. The vertical eccentric load increased almost linearly until the ultimate pressure load was approached. Then, it exhibited a sudden drop accompanied by a continuous increase in the lateral deflection. 3.2. Failure loads For the partially CFRP jacketed circular CFT short column, the test results revealed that its eccentric load bearing capacity improved with the increase in fy. The strength of the column offering an fy of 348.6 MPa (specimen ES12) was 10.5% higher than that of the column with an fy of 240.8 MPa (specimen ES11). As the confining stress heightened with an increase in n, the circular CFT short column also obtained a significant increase in the eccentric load bearing capacity. Compared with the pure circular CFT short column, the eccentric load bearing capacity of the circular CFT short column partially attached by 1, 3, and 5 layers of CFRP jackets improved by 6.3%, 22.0%, and 34.2%, respectively. When the circular CFT short column was partially jacketed by the same number of CFRP layers, increasing the spacing of CFRP jackets would clearly decrease the eccentric load bearing capacity because of the increase in the distance of the transferred path of the confining stress and the corresponding descent in the effective CFRP-steel confined concrete area. Therefore, the test eccentric load bearing capacities of the circular CFT short columns fully jacketed by the CFRP were respectively 6.4%, 10.3%, and 14.9% higher than those of the circular CFT short columns partially jacketed by CFRP belts with a spacing of 30 mm, 50 mm, and 150 mm. As the load eccentricity of the CFRP partially jacketed circular CFT short column increased, the eccentric load bearing capacity of the short composite column, which followed the axial force versus uniaxial bending moment rules of the common circular CFT short column, gradually reduced. Compared with the short composite column under axial compression presented in Ref. [23], the load resistances of the partially CFRP jacketed CFT short columns with load eccentricities of 10 mm, 30 mm, and 50 mm held the descents of 21.0%, 43.3%, and 59.3%, respectively. For the partially CFRP jacketed eccentrically loaded circular CFT slender column, the parameters including the λ, n, ws, and e were pitched to investigate their detailed effects. For the short composite column, similar developing laws were obtained along with the changes in the n, ws, and e. Nonetheless, λ turned out to be a much more significant influencing factor than n and ws,. The effects of n and ws weakened significantly, as the failure of the slender composite column was controlled by the instability failure. In terms of the circular CFT slender columns wrapped by spaced CFRP jackets, the eccentric load bearing capacities of the columns with λ of 34.3 and 51.4 (specimens EL11 and EL12) were respectively 27.2% and 8.1% higher than that of the column with λ of 65.7 (specimen EL13). However, the improvements in strength were only observed to be 0.8%, 8.7%, and 16.8% when n increased from 0 to 1, 3,

Q. Shen et al. / Journal of Constructional Steel Research 166 (2020) 105925

A

26

25

5

(51) (52)

(57) (58) A

24(54) 27(55) 23(53) 28(56)

30(60) 29(59)

20 19

26 25 B

C

14 A

A

18(36) 17(35)

12(30) 15(31) 11(29) 16(32) 14 13 A-A

B

8

7

B

C

1

C

13

B

C

7 B-B

B-B

(45) (46)

(39) (40)

18(48) 17(47)

15(43) 16(44)

D

8 7

(33) (34)

4(20) 3(19)

(a) Short column

10(38) 9(37)

D

6(36) 5(35)

2 1 C-C

12(42) 11(41) 8 7 D-D

C-C

9(25) 10(26) 8

A-A

14 13

(21) (22) (24)6 (23)5

2

14

19

(27) (28)

(33) (34)

13

20

21(50) 22(49)

E

2

1

E

4(32) 3(31) 2 1 E-E

(b) Slender column

Fig. 5. Layout of strain gauges. Note: The numbers in and out of the brackets are respectively the strain gauges of CFRP and steel tube.

and 5, respectively. Compared to the CFT slender column fully jacketed by 3 layers of CFRP, the eccentric load bearing capacities of the composite columns declined by 4.8%, 8.8%, and 14.7%, respectively. The n and ws showed slight influence on the eccentric load bearing capacity of the partially CFRP jacketed circular CFT slender column. The column would fail in global buckling before the CFRP reached its ultimate tensile stress indicating that the slender composite column could not use the excellent tensile property of the CFRP completely. Similar conclusion was obtained by Li et al. [22] as well. Changing the load eccentricities commonly exhibited a clear influence on the behaviour of the partially CFRP jacketed circular CFT slender column. With the e increasing from 0 mm to 10 mm, 30 mm, and 50 mm, the strength of the slender column reduced by 16.1%, 38.4%, and 53.5% respectively. 3.3. Failure modes Fig. 9 presents the overview failure photos of the partially CFRP jacketed circular CFT short and slender columns following the eccentric compressive tests. As expected, all the specimens exhibited large midheight deflections due to the existence of load eccentricity. Generally, the inward bulge of the CHSS was restrained by the supporting action provided by the core concrete. Therefore, the outward bulge became the major failure pattern of the CHSS. As for the eccentrically loaded short composite column, severe rupture in the CFRP jackets was observed due to the obvious lateral expansion of the concrete. To restrict the hoop extension, the CFRP jacket needed to fully utilize its excellent tensile strength. When the column was over-pressurized, the CFRP jacket around the mid-height of the column reached its fracture strain and ruptured subsequently. This phenomenon revealed that the outstanding CFRP tensile property was adequately utilised in the short columns, resulting in an evident enhancement in strength compared with the pure CFT column at the same load eccentricity. During the loading process, colloid peeling was first observed at the edge of the CFRP jackets. With the vertical load increasing, the lateral expansion exhibited a great degree of development. The hoop extension of the CFT

column at the unwrapped region was much larger than that at the wrapped zone because of the restraint provided by the fibre strips. Subsequently, the CFRP jackets were initially damaged from the verge of the fibre due to the emergence of excessive dilatation at the boundary between the wrapped and unwrapped zones. Finally, the CFRP jackets around the mid-height of the short column ruptured throughout their full sections and the specimen was eventually removed. In an attempt to determine the failure form of the concrete infill, the CFRP jackets and CHSS were removed following the testing. Both crumbling at the compressive side and tensile cracks at the tensile side of the core concrete were observed around the mid-height of the column, as illustrated in Fig. 8a. For the partially CFRP jacketed slender CFT columns under eccentric compression in this experiment, the failure patterns were observed by the consistent concrete cracking that slightly damaged the CFRP jackets and colloid peeling (shown in Fig. 8b). However, it should be noted that the slightly damaged CFRP could be found only in the column with moderate slenderness. On condition that the type of composite column held large slenderness, the slender column would fail firstly in global buckling mode before the over-pressurized concrete and large lateral expansion showed their appearances. Hence, the CFRP jackets exhibited no apparent experimental phenomena indicating that the CFRP scarcely devoted its excellent tensile strength. With the development of lateral deflection, lateral cracks on the tensile side of the slender composite column were observed and the intervals were approximately 20–50 mm. Crack distributions similar to that reported in Ref. [46] were obtained as well. 3.4. Height versus lateral deflection curves The typical column height (H) versus lateral deflection (μ) curves of the eccentrically loaded partially CFRP jacketed circular CFT slender columns under various axial compressive load levels were captured (seen in Fig. 10a), and all of them were in the shape of half-sine waves. Moreover, the result revealed that the deflection of the slender column

6

Q. Shen et al. / Journal of Constructional Steel Research 166 (2020) 105925

Fig. 6. Test site photos.

improved as n and e increased, whereas a reverse effect was observed with the increase in ws (illustrated in Fig. 10b–d). 3.5. Load -strain behaviour Fig. 11 shows the typical strain responses of the circular CFT short and slender columns partially jacketed by the CFRP. For the slender

column, the lateral and longitudinal strains of the CFRP jackets and the CHSS at their 1/4-, 1/2-, and 3/4- heights of the column were observed (specimen EL13) and the strains of the CFRP and CHSS at the top end, mid-height, and bottom end of the short column (specimen ES12) were also recorded. The CFRP fracture strain was 1.44 × 104 uε, and the CHSSs with fy values of 240.8 MPa and 348.6 MPa offered the corresponding yield

Q. Shen et al. / Journal of Constructional Steel Research 166 (2020) 105925

1800

1500 Eccentric load (kN)

Eccentric load (kN)

1800 rupture of CFRP 1200 900 600 ES11 ES12

300 0

1500

10 20 30 40 50 Longitudinal shortening(mm)

rupture of CFRP

900 ES31 ES32 ES12 ES33

600 300 0

10 20 30 40 50 Longitudinal shortening(mm)

(a3) Spacing of CFRP (a)

10 20 30 40 50 Longitudinal shortening(mm)

60

900 600

0

60

Eccentric load (kN)

1000

800 600 EL11 EL12 EL13 0

7 14 21 28 Longitudinal shortening(mm)

200 0

0

7 14 21 28 Longitudinal shortening(mm)

35

(b2) Number of CFRP layer (n)

1000

Eccentric load (kN)

1000 800 600 EL31 EL13 EL32 EL33 7 14 21 28 Longitudinal shortening(mm)

(b3) Spacing of CFRP (a)

EL21 EL22 EL13 EL23

400

1200

0

60

600

1200

200

10 20 30 40 50 Longitudinal shortening(mm)

800

35

(b1) Column slenderness (λ)

400

0

(a4) Load eccentricity (e) (a) Short columns

1000

200

ES41 ES12 ES42

300

1200

400

rupture of CFRP

1200

1200

Eccentric load (kN)

0

1500

Eccentric load (kN)

Eccentric load (kN)

300

1800

1200

0

ES21 ES22 ES12 ES23

600

(a2) Number of CFRP layer (n)

1500

Eccentric load (kN)

900

60

1800

0

rupture of CFRP

1200

0

0

(a1) Steel strength (fy)

0

7

35

800 600 400

EL41 EL13 EL42

200 0

0

7 14 21 28 Longitudinal shortening(mm)

(b4) Load eccentricity (e) (b) Slender columns

Fig. 7. Load (N) versus longitudinal shortening (δ) curves of short and slender columns.

35

8

Q. Shen et al. / Journal of Constructional Steel Research 166 (2020) 105925

Rupture of CFRP Colloid peeling

Crack of concrete

c

a

d

Concrete crumbling Local buckling

b (a) Short columns

Crack of concrete

Slight damage of CFRP

Colloid peeling

(b) Slender columns Fig. 8. Typical failure modes of partially CFRP jacketed circular CFT columns under eccentric compression.

strains of 1216 uε and 1726 uε, respectively. Assessing specimens ES12 and EL13 as examples, Fig. 10 depicts the longitudinal and transverse strain responses of the CFRP materials and CHSSs at the tensile, middle, and compressive sides. The experimental results reflected that the longitudinal strains at the tensile and compressive sides of the CHSS were generally symmetrical. In addition, the strains at the compressive and tensile sides were distinctly larger than those at the middle side under

ES11

ES22

ES23

ES32

ES33

the same load conditions. The compressive and tensile strains at the middle-height section were larger than those around the ends of the column or those at the 1/4- and 3/4-height sections. The differences in the CFRP strain responses at the mid-height sections of the short and slender columns were also investigated. According to the test results, the CFRP tensile strains at the mid-height section of the short column could reach their fracture strains with

ES42

ES21

ES41

(a) Short columns

EL31 EL21

EL23

EL11

EL41 EL22 EL33

EL13 EL42

EL12

(b) Slender columns Fig. 9. Overview failure photos of specimens after the test.

ES12

ES31

Q. Shen et al. / Journal of Constructional Steel Research 166 (2020) 105925

2000

2000

Height (mm)

2500

Height (mm)

2500

1500 1000

Sinusoid N/Nu=0.6 N/Nu=0.75 N/Nu=0.9 N/Nu=1.0

500 0

0

8

16 24 32 Lateral deflection (mm)

EL21 EL22 EL13 EL23

1500 1000 500 0

40

0

(a) Typical H-μ curves

10

20 30 40 Lateral deflection (mm)

50

(b) Number of CFRP layer (n)

2500

2500 EL31 EL13 EL32 EL33

1500

EL41 EL13 EL42

2000

Height (mm)

Height (mm)

2000

1000

1500 1000 500

500 0

9

0

0

10

20 30 40 Lateral deflection (mm)

50

0

(c) Spacing of CFRP (ws)

16

32 48 64 Lateral deflection (mm)

80

(d) Load eccentricity (e)

Fig. 10. The height versus lateral deflection curves of CFRP jacketed circular CFT slender column.

To estimate the eccentric load bearing capacities of the CFT columns attached by the partially jacketed CFRP, the strength index (SI) suggested by Ren et al. [46] and Wang et al. [43] was used in this section. It is defined as follows:

the SI of the composite column with 1 layer of CFRP decreased by 1.8%, whereas the SI of the column with 3 and 5 layers of CFRP increased by 3.6% and 10.7%, respectively. For the circular CFT columns jacketed by 3 layers of CFRP, the SIs of the short composite columns fully jacketed by the CFRP were almost equal to those of the composite columns with 30 mm, 50 mm, and 150 mm CFRP spacings, and the SIs of the slender composite columns wrapped with different spacing of CFRP jackets displayed the same trend. For the short columns attached by 3 layers of CFRP with 50 mm spacing, the SIs decreased by 27.8% and 40.5% as the value of e increased from 10 mm to 30 mm and 50 mm, respectively. For the slender columns wrapped by 3 CFRP layers with 100 mm spacing, the SIs decreased by 27.5% and 42.5% as e increased from 10 mm to 30 mm and 50 mm, respectively. For the slender columns with the same values of e, n, and ws, the SIs decreased by 6.4% and 8.0% as λ increased from 34.3 to 51.4 and 65.7, respectively. In general, the analysis showed that the SIs of the eccentrically loaded partially CFRP jacketed CFT columns were significantly influenced by e, whereas n, ws, λ, and fy exhibited only a slight impact on the SI.

SI ¼ Nue =Nuc

3.7. Ductility index

increasing eccentric pressure corresponding to the severe rupture of the CFRP jackets. Nevertheless, as the slender column was prone to failure owing to overall instability under a low level of axial pressure with respect to the short column, the expected hoop expansion could not be obtained in the column with large slenderness. Consequently, both the strains of CFRP and CHSS stayed in a much lower level compared to those of the short column. Hence, the CFRP jackets were only slightly damaged or even exhibited no such apparent phenomenon. All evidences in this study hinted that the lateral-wrapped CFRP jackets could take full advantage of the high tensile strength in short composite columns, whereas this property was stifled in the CFT slender column. 3.6. Strength index

ð1Þ

where Nuc is the axial load bearing capacity of the composite column reported in Ref. [23] and Nue is its eccentric load bearing capacity. Table 4 and Fig. 12 illustrate the strength indexes of the test specimens to reveal the effect of various parameters, including fy, n, ws, e, and λ. Compared with the partially CFRP jacketed axially-loaded circular CFT columns with steel yield stresses of 240.8 MPa and 348.6 MPa presented in Ref. [40], the SI of the short columns under eccentric compression decreased by 41% and 43%, respectively. For the pure circular CFT short column installed with an e of 30 mm, the SI values improved by 0%, 7.5%, and 11.3% when n increased from 0 to 1, 3, and 5, respectively. For the pure circular CFT slender columns with an e of 30 mm,

A ductility index (DI) was applied to assess the ductility of the specimens, which is defined as follows: DI ¼ δu =δy

ð2Þ

where δy is the longitudinal shortening corresponding to the yield load bearing capacity of the composite column and δu is the longitudinal shortening corresponding to its ultimate eccentric load bearing capacity. Table 4 and Fig. 13 display the DIs of the eccentrically loaded circular CFT short columns jacketed partially by the CFRP belts. The results revealed that the DI values of the short composite columns subjected to

Q. Shen et al. / Journal of Constructional Steel Research 166 (2020) 105925

1500

s=1276u

1200

frp=1.44%

Eccentric load (kN)

1200 900 600

εst1(εFt1) εst2(εFt2) εst3(εFt3) εsl1(εFl1) εsl2(εFl2) εsl3(εFl3)

sl1

Fl1

st1

Ft1

sl2

Fl2

st2

300

sl3

0 -20000

st3

-10000

0

Ft2

Eccentric load (kN)

10

900

600 εst1(εFt1) εst2(εFt2) εst3(εFt3)

300

εsl1(εFl1) εsl2(εFl2) εsl3(εFl3)

Fl3 Ft3

10000

0 -20000

20000

-10000

0

(a1) Middle section s=1276u

1200

Eccentric load (kN)

Eccentric load (kN)

1200 900 600

slc1

εslc2(εFlc2)

300 0 -20000

εstc3(εFtc3) εslc3(εFlc3)

-10000

Flc1

stc1

Ftc1

slc2

Flc2

stc2

Ftc2

slc3

Flc3

stc3

Ftc3

0

10000

600

slt1 stt1

εstt2(εFtt2) εslt2(εFlt2)

300 0 -20000

εstt3(εFtt3) εslt3(εFlt3)

-10000

0

Ft3

10000

εstc1(εFtc1) εslc1(εFlc1) εstc2(εFtc2)

20000

300

slc1

Flc1

stc1

Ftc1

slc2

εsl2(εFl2)

1200

Flt1 Ftt1

slt2

Flt2

stt2

Ftt2

slt3

Flt3

stt3

Ftt3

10000

Eccentric load (kN)

Eccentric load (kN)

600

Fl3

st3

εstc3(εFtc3) εslc3(εFlc3)

-5000

0

Flc2

stc2

Ftc2

slc3

Flc3

stc3

Ftc3

5000

10000

(b2) Compressive side

1200

εstt1(εFtt1) εslt1(εFlt1)

Ft2

sl3

Strain

frp=1.44%

900

Fl2

st2

900

(a2) Compressive side s=1276u

Ft1

sl2

frp=1.44%

s=1276u

0 -10000

20000

Strain

1500

Fl1

st1

(b1) Middle section

frp=1.44%

εstc1(εFtc1) εslc1(εFlc1) εstc2(εFtc2)

sl1

Strain

Strain

1500

frp=1.44%

s=1276u

20000

Strain

frp=1.44%

s=1276u

900 slt1

600

εstt1(εFtt1) εslt1(εFlt1)

Ftt1

slt2

Flt2

εslt2(εFlt2)

stt2

Ftt2

εstt3(εFtt3) εslt3(εFlt3)

slt3

Flt3

stt3

Ftt3

εstt2(εFtt2)

300

0 -20000

Flt1

stt1

-10000

0

10000

20000

Strain

(a3) Tensile side

(b3) Tensile side

(a) Short column

(b) Slender column

Fig. 11. Typical eccentric load (N) versus strain (ε) of partially CFRP jacketed circular CFT short and slender columns. Note: The strains in and out of the brackets are respectively the strains of CFRP and steel tube.

eccentric load were evidently lower than those of the axially loaded short columns presented in Ref. [23]. Moreover, the DIs of the composite columns improved with increased load eccentricity. The DIs of the partially CFRP jacketed circular CFT short columns with e values of 10 mm and 30 mm were respectively 33.9% and 23.7% lower than that of the column with an e value of 50 mm. The DI of the partially CFRP jacketed CFT short column with the fy of 240.8 MPa was higher than that of the column with the fy of 348.6 MPa. Moreover, owing to the large

deflection of the composite columns and the brittle failure of the CFRP, the DI of the short composite columns decreased faster with the increase in n, whereas ws showed little influence on the DI of the short composite columns when ws was smaller than 50 mm. The DIs of the eccentrically loaded CFT short columns partially jacketed by 1, 3, and 5 layers of the CFRP materials were respectively 35.1%, 41.6%, and 46.8% lower than that of the pure eccentrically loaded circular CFT short column.

1.0

1.0

0.8

0.8

0.6

0.6

SI

SI

Q. Shen et al. / Journal of Constructional Steel Research 166 (2020) 105925

0.4 0.2 ES11

0.0

ES12

(a1) Steel strength (fy) 1.0

1.0

0.8

0.8

0.6

0.6

0.4

ES32

ES12

ES23

ES12

ES42

(a4) Load eccentricity (e) Short columns

1.0

1.0

0.8

0.8

0.6

0.6

SI

SI

ES41

ES33

(a)

0.4 0.2

0.4 0.2

EL11

EL12

0.0

EL13

(b1) Column slenderness (λ)

EL21

EL22

EL13

EL23

(b2) Number of CFRP layer (n)

1.0

1.0

0.8

0.8

0.6

0.6

SI

SI

ES12

0.4

0.0

ES31

(a3) Spacing of CFRP (a)

0.4

0.4 0.2

0.2 0.0

ES22

0.2

0.2

0.0

ES21

(a2) Number of CFRP layer (n)

SI

SI

0.4 0.2

0.0

0.0

11

0.0

EL31

EL13

EL32

EL33

(b3) Spacing of CFRP (ws)

EL41

EL13

EL42

(b4) Load eccentricity (e) (b)

Slender columns

Fig. 12. Strength indexes (SI) of circular CFT columns partially jacketed by CFRP under eccentric compression.

For the partially CFRP jacketed circular CFT slender columns, the DI values were approximately equal to 1 due to the failure mode of global buckling, while the longitudinal shortening of the slender composite column improved with increasing n and decreasing ws.

4. Numerical analysis In the numerical works conducted in Ref. [43], the contact stress and the effective wrapping arrangement of the partially CFRP jacketed circular CFT column under eccentric compression were totally ignored.

Q. Shen et al. / Journal of Constructional Steel Research 166 (2020) 105925

8.0

10

6.4

8

4.8

6

DI

DI

12

3.2 1.6

2

0.0

ES11

0

ES12

(a) Steel strength (fy) 8.0

8.0

6.4

6.4

4.8

4.8

3.2

ES22

ES12

ES23

3.2 1.6

1.6 0.0

ES21

(b) Number of CFRP layer (n)

DI

DI

4

0.0

ES31

ES32

ES12

ES33

(c) Spacing of CFRP (ws)

ES41

ES12

ES42

(d) Load eccentricity (e)

Fig. 13. Ductility indexes (DI) of circular CFT short columns jacketed by CFRP under eccentric compression.

Therefore, we have tried to establish a modified FE model to solve the above-mentioned questions. 4.1. The FE model Unlike the stress-strain relationship of the core concrete presented in the previous numerical works [23,43], a modified modelling of the partially CFRP jacketed circular CFT column under eccentric load was developed considering the differences in confined conditions. Based on the configuration of the CFRP wrapping arrangement, the core concrete can be divided into two parts: the wrapped zone and the unwrapped zone. Various confined concrete models were used to simulate their constitutive relationships (seen in Fig. 14a). The elastic-plastic stress-strain relationship was commonly used for the CHSS (illustrated in Fig. 14b). For the CFRP unwrapped zone, the confined concrete model (displayed in Fig. 14c) described by Wang and Han [47] was widely used to investigate the mechanical properties of the pure circular CFT columns. Details of this model were introduced in previous works [48]. For the CFRP wrapped region, the confined concrete model proposed by Teng et al. [49] was highly recommended by many researchers to simulate the behaviour of the concrete confined together by steel and the CFRP jackets (illustrated in Fig. 14d). The CFRP jacket is commonly deemed to be an orthotropic material. Along the fibre orientation, it exhibited an elastic behaviour before it was fractured. It demonstrated a high tensile strength but could barely bear any compressive force. Along the other directions, it could be easily damaged when subjected to tension, compression, or shear force. Hence, the linear-elastic constitutive relationship named as the “Engineering Constants” was used for the CFRP jacket in this study. In compliance with the material property of the CFRP jackets presented in this study, the elastic modulus, the Poisson's ratio, the fracture strain, and the fail stress were respectively entered as 243 GPa, 0.22, 0.0144 and 3510 MPa. The invalid limit of the CFRP jacket was controlled by the options of ‘fracture strain’ and ‘fail stress’. Once the strain or stress along the fibre orientation exceeded the fracture strain or fail stress, the CFRP jacket would be completely damaged or ruptured such that the tensile stress of the CFRP jacket abruptly changed from peak stress to 0.

The C3D8R solid element was used for the CHSS, concrete, and the loading plate, and the S4R shell element was applied for the CFRP jackets. To figure out the effective mesh size for the FE analysis, a sensitivity study on the FE modelling was conducted by assessing the ultimate strength of specimen ES12 (shown in Table 3). Coarse meshes that offered size larger than 15 mm were not considered due to the high loss in simulation accuracy. Using a 15 mm element size for the rigid-plate and a 10 mm element size for the CHSS, the concrete and the CFRP jacket provided a relatively effective computing procedure and appropriate accuracy. Applying smaller mesh sizes would increase the computing time and might result in a convergence issue. The eccentric force and the boundary conditions were exerted to the loading plates via the reference points (RPs) while the RPs were coupled to the knife hinges to simulate the eccentricity. The contact interaction and the boundary conditions of the eccentrically loaded circular CFT column partially jacketed by the CFRP materials were same as the settings presented in Ref. [43]. For the column, a global imperfection of L/1000 was applied, which was same as that in Ref. [23]. Based on the above details and the relative options defined in Ref. [23, 43], the typical FE model of the eccentrically loaded circular CFT short column jacketed partially by the CFRP wraps was developed as depicted in Fig. 15. Subsequently, comparisons between the existing test results and the corresponding numerical data were conducted to validate the accuracy of the FE model, and the details are displayed in Table 4 and Figs. 16–17. The results revealed that both the force versus deformation curves and failure modes of the FE models were in agreement with the experimental results. 4.2. Contact stress To acknowledge the interactions between the various components, the contact stress was a very important index for assessing their confinement states. Assessing the FE models corresponding to specimens ES12 and EL13 as examples, the contact stresses of the eccentrically loaded partially CFRP-jacketed circular CFT short and slender columns at their peak loads were captured and analysed in this section (seen in Fig. 18).

Q. Shen et al. / Journal of Constructional Steel Research 166 (2020) 105925

13

Fig. 14. Constitutive models of steel tube and core concrete.

Owing to the global buckling failure, the lateral expansion of the concrete infill in the slender column developed marginally. Therefore, the contact stress of the slender composite column (the blue dash line) was much lower than that of the short column (the black solid line). This phenomenon also revealed the inadequate confinement function supplied by the CFRP jackets, which resulted in a loss in the CFRP tensile strength. In terms of the contact stress between the CFRP jacket and the CHSS, the contact action at the mid-height of the column was higher than the contact stress around the ends of the column. This could be due to the restraint provided by the welded end plate. The lateral expansion of the CHSS around the end of the column was limited by the welded end plates. Similar results were observed for the distribution regulation of contact stress between the CHSS and the concrete infill as well. However, differences in the wrapped and unwrapped zones were discovered because the CFRP jackets limited the lateral deformation of the CHSS, and therefore, the core concrete could contact the CHSS more tightly, resulting in a high contact stress. In addition, the contact stress at the compressive side of the composite column was higher than that at the tensile side, which was attributed to the larger expansion of the concrete under higher compression stress.

use of a pre-tensioned CFRP jacket for the CFT columns was recommended to enhance the strengthening effect. According to the experimental analysis of n and ws, the strength improvements in the specimens ES23 and ES32, namely the circular CFT columns partially strengthened by the CFRP jackets, were basically similar to that of the specimen ES31, which was fully confined by the CFRP. Therefore, further investigations on designing an effective wrapping layout for the short composite column to enhance its eccentric load bearing capacity and to minimize the limited resources properly were done. Following this, an attempt to figure out the effective wrapping scheme for the eccentrically loaded CFRP jacketed circular CFT short column partially was conducted considering the effect of the steel tube thickness, CFRP spacing, and layer (depicted in Fig. 19). Assessing the type of short column with conditions of D × t × L = 140 × 2.8

4.3. Effective wrapping scheme Based on the observation of the slightly damaged CFRP jackets adjacent to the top and bottom ends of the column, it could be concluded that the high tensile strength of the CFRP jackets at those regions was not fully utilised. Therefore, employing a pre-tensioning force for the laterally jacketed CFRP has been suggested by some researchers. Rashid et al. [50] and Feng et al. [51] investigated the strengthening performance respectively of the RC and steel columns jacketed by pre-stressed CFRP. It was found that the strength of the column was clearly enhanced by setting the pre-stressed CFRP jackets. Based on the above studies, the

Fig. 15. FE modelling of partially CFRP jacketed circular CFT short columns under eccentric compression.

14

Q. Shen et al. / Journal of Constructional Steel Research 166 (2020) 105925

1500

1200 900 600 Test FE

300 0

1200 900 600

5

10

15

20

25

30

35

Longitudinal shortening(mm)

Test FE

300 0

0

40

0

5

10

15

20

25

30

35

1200 900 600

0

40

1000

1000

600 400 Test FE 0

5

10

15

20

25

30

35

Longitudinal shortening(mm)

(c) Specimen EL11

40

Eccentric load (kN)

1000

Eccentric load (kN)

1200

800

800 600 400 Test FE

200 0

0

5

10

15

20

25

5

10

15

20

25

30

35

Longitudinal shortening(mm)

40

(f) Specimen ES31

1200

0

0

(b) Specimen ES12

1200

200

Test FE

300

Longitudinal shortening(mm)

(a) Specimen ES11

Eccentric load (kN)

Eccentric load (kN)

1800

1500

Eccentric load (kN)

1800

1500

Eccentric load (kN)

1800

30

35

800 600 400 Test FE

200 0

40

Longitudinal shortening(mm)

0

5

10

15

20

25

30

35

40

Longitudinal shortening(mm)

(d) Specimen EL13

(e) Specimen EL31

Fig. 16. Comparison on the eccentric load versus longitudinal shortening curves of the partially CFRP jacketed circular CFT columns obtained from tests and FE models.

× 450 mm, e/r = 0.25, ffrp = 3500 MPa, fcu = 50 MPa, and fy = 345 MPa for instance, the comparison of hundreds of models of eccentrically loaded fully and partially CFRP jacketed circular CFT short columns offering various CFRP layers from 1 to 10 and CFRP wrapping ratios (wfT/L, where wfT is the total length of the CFRP jacketed on the CFT column) from 2/9 to 1 is presented in Fig. 19a. The analysis revealed that the eccentric load bearing capacity of the CFRP jacketed circular CFT short column increased gradually with the increase in n, while the growth rate decreased with decreasing CFRP wrapping ratio. Although the strength of the short composite column increased with n, as every CFRP layer was added, the increase amplitude by adding every CFRP layer declined gradually deriving from the decreased intervals between the various. Moreover, the strength enhancement of the column with various CFRP layers showed only a small difference when the CFRP wrapping ratio came down to 3/9. Therefore, it was not suggested to strengthen the eccentrically loaded CFT short column with CFRP belts offering the wrapping ratio being smaller than 1/3. Similarly, the influence of the CFRP spacing and diameter-thickness ratio on the strengthening efficiency of the eccentrically loaded partially CFRP jacketed CFT short column was explored by a sample with conditions D × L = 140 × 450 mm, n = 3, ffrp = 3500 MPa, fcu = 50 MPa, and fy = 345 MPa as well. Detailed outcomes are depicted in Fig. 19b. It indicated that thinner the steel tube of the column was, higher the improvement in strength. The strengthening effect was limited when the diameter-thickness ratio was smaller than 20. Nonetheless, the disparity in the strength improvements between the various curves decreased significantly with decreasing CFRP wrapping ratio. Once the CFRP coverage ratio of the column was less than 3/9, the strength improvements between the various models hardly showed any differences. Eventually, the strengthening contribution of the CFRP jackets would become zero when the CFRP coverage ratio is reduced to 1/9. 5. Design recommendations Currently, the specifications EC4 [52], GB 50936 [53], AS5100.6 [54], AISC-360 [55], AIJ-SRC [56], and CAN/CSA S16–01 [57] do not cover the CFT columns partially strengthened by CFRP jackets, although simplified

design methods are available for pure CFT columns. Therefore, it is necessary to provide a design method to assess the load carrying capacity of the partially CFRP jacketed CFT short column. In this section, a design method for assessing the load bearing capacities of the partially CFRP jacketed circular CFT short and slender columns is presented on the basis of the partial CFRP-confined mechanical model. 5.1. Mechanical analysis of the confinement function of the partially jacketed CFRP To reasonably deduce the design formulae, we have to determine the mechanical behaviour of the confinement state of the partially CFRP jacketed CFT column. The CFRP jackets enhance the load bearing capacity of the CFT column by providing extra confining stress for the core concrete. Therefore, it is very crucial to acknowledge the stress condition of the core concrete. According to the load transferring mechanism presented by Hou et al. [58], Ding et al. [59], and Yang et al. [60], the diffusion path of the CFRP confining stress could be obtained considering the feature of the partial wrapping arrangement (shown in Fig. 20). Based on observations of the failure modes of the partially CFRP jacketed axially loaded CFT short column presented in Ref. [23, 40], the partially CFRP jacketed CFT short column bulged firstly at the unwrapped zone. This showed that the unwrapped region was the control section for the ultimate load bearing capacity. During the loading process, the confining stress provided by the CFRP jackets would transfer towards the unwrapped region. Based on the stress transferring rules defined in Ref. [58, 60], the confining stress offers the load-distributed path ratios of 1:2.5 in the steel component and 1:1 in the concrete part. Hence, the control section could be divided into three parts: 1) the steel tube part; 2) the steel-confined concrete part; and 3) the CFRPsteel-confined concrete part. Finally, the axial load bearing capacity of the partially CFRP jacketed circular CFT short column can be described as 0

Nu ¼ As f y þ Ac1 f ck þ Acc f cp

ð3Þ

where As, Ac1, and Acc respectively stand for the cross-sectional areas of

Q. Shen et al. / Journal of Constructional Steel Research 166 (2020) 105925

15

Rupture of CFRP

Local buckling on steel tube

(a1) Rupture of CFRP

(a2) Local buckling on steel tube wall

Concrete crumbling Concrete cracking

(a3) Cracks and crumbling of core concrete (a) Short column

Concrete cracking

Slight damage of CFRP

(b1) Rupture of CFRP

(b2) Cracks in core concrete (b) Slender column

Fig. 17. Observed and predicted failure modes of partially CFRP jacketed circular CFT short and slender columns.

16

Q. Shen et al. / Journal of Constructional Steel Research 166 (2020) 105925

13.2

13.5 14.0 14.6 15.2

12.6 12.2

14.8 11.9 11.5 11.1 11.0

16.6 19.1 21.6

11.7

22.5

11.0

23.2

10.2

23.7

10.8

9.6

23.8

10.3

15.0 16.0 16.8 17.5

23.5 24.1

13.2

18.1 19.1

13.2

10.9

20.4

10.4

20.6

20.3 21.1 21.5

9.5

21.8

8.9

C-C:steel-to-concrete 9.4

9.8

12.4 11.0

8.1

14.2

7.8

15.0

3.2

13.5

8.0

14.7

3.3

13.2

8.1

13.9

7.7

E-E:CFRP-to-steel

14.6

E-E:steel-to-concrete

13.8 14.0 14.2 15.3 16.0

7.2 16.3

11.5

11.6

8.6

13.9

3.7 3.4

10.0 10.2 10.7 11.1

8.9

10.8 11.9

4.5 4.1

13.2

18.8

10.1

C-C:CFRP-to-steel

12.6

17.7

10.7

20.1

11.4

17.4

11.8

19.7

6.4 7.2 7.7 8.9

14.1 15.2 15.2 16.9

13.1 12.8

18.6

5.5

22.8

A-A:steel-to-concrete

11.8

4.9

21.1 22.1

23.1

A-A:CFRP-to-steel

14.8

20.0

11.0

10.1

14.7 14.1

15.4 16.8 18.4 19.1

8.3 8.6 9.6 9.8

10.3 10.7

5.7 16.7

10.6

7.7

17.2

9.7 9.0

18.5

B-B:steel-to-concrete

11.9

5.2 5.1

17.9

8.7

11.7

5.5

17.4

8.7

11.0

5.7

12.6

5.0

12.7

D-D:steel-to-concrete

Tensile side

Compressive side

Fig. 18. The contact stress of the partially CFRP-jacketed circular CFT column (unit: MPa).

the CHSS, the steel-confined concrete and the CFRP-steel-confined concrete. fck and f’cp stand for the characteristic compressive strength of the steel-confined concrete and the confined strength of the CFRP-steelconfined concrete, respectively. In accordance with the explanation illustrated in Fig. 20, the cross-sectional areas of the various parts can

be written as:

As ¼

ðDc þ 2t Þ2 −D2c 4

CFRP wrapping ratio

CFRP wrapping ratio 7/9

5/9

3/9

1/9

n=10 n=9 n=8 n=7 n=6 n=5 n=4 n=3 n=2 n=1

3.5

Ns,e/Npure,e

3.0 2.5 2.0

2.5

1

7/9

5/9

3/9

1/9

75

100

D/t=100 D/t=50 D/t=40 D/t=28.6 D/t=20 D/t=14 D/t=10

2.0

Ns,e/Npure,e

4.0

1

ð4Þ

1.5

1.5 1.0

0

25

50

75

CFRP spacing (a) Number of CFRP layer

100

1.0

0

25

50

CFRP spacing (b) Diameter: thickness ratio

Fig. 19. The effect of various parameters on the strength enhancement of partially CFRP jacketed circular CFT short column under eccentric compression. Note: Ns,e and Npure,e respectively represent the eccentric compressive resistances of the circular CFT short column strengthened by CFRP wraps and the corresponding pure CFST column.

Q. Shen et al. / Journal of Constructional Steel Research 166 (2020) 105925

17

Core concrete CFRP-steel-confined concrete

wf

CFRP jacket

CFRP jacket 1:2.5

2.5t

45°

ws -5t

ws

Dc-ws +5t 1:1

Control section

(ws -5t)/2

2.5t

Steel-confined concrete Dc-ws +5t

Steel tube Steel tube

Dc Dc+2t t

t

Dc

Fig. 20. The distributed location of the control section in the partially CFRP jacketed circular CFT column under axial compression.

ð5Þ

ðws ≥ 5t Þ

ðDc ≤ ws −5t Þ ðDc N ws −5t N 0Þ ðDc N 0 ≥ ws −5t Þ

0

0

f cp ¼

1þ2

0

f co

! 0

ð7Þ

 f co

0

where ffrp and tfrp respectively stand for the ultimate tensile strength and the thickness of the CFRP jackets. The wf stands for the width of the CFRP jackets. To validate the accuracy of the design formulae for assessing the axial load bearing capacity of the partially CFRP jacketed circular CFT short column, some existing experimental data of the axially loaded circular CFT short columns fully and partially jacketed by CFRP [17,23,41,61] were compared with those of the predicted results (depicted in Fig. 22a). The comparison showed that the results assessed by Eqs. (3)–(9) agreed well with the data obtained by the experiments. 5.2. Design formulae for assessing the eccentric load bearing capacity

According to the Ref. [24], the f cp can be defined as:

fl

0

where f co is the unconfined strength of the concrete and f l stands for the confining stress of the steel-CFRP-confined concrete part. Based on the load transferring laws introduced above, an equilibrium equation between the confining stress of the inside surface of the steel tube at the CFRP wrapped zone and the confining stress of the steel-CFRP-confined concrete part is established (seen in Fig. 21).

After determining the calculation approach for the axial load bearing capacity of the partially CFRP jacketed circular CFT short column, the eccentric load bearing capacity of the column could be easier to present in compliance with the M-N correlation theory. Based on the design theory presented by Han [62], a simplified approach for predicting the load bearing capacity of the eccentrically loaded CFRP wrapped circular CFT (ws-5t)/2

fl

fl

0

fl ¼

ðws N 5t Þ

ð8Þ

where fl stands for the confining stress of the inside surface of the steel tube at the CFRP wrapped zone.

45°

fl

Dc

ws +5t

ðws ≤ 5t Þ

fl

Dc-ws +5t

fl  f l  w f þ 5t : w f þ ws

fl

fl

ws+wf

0

Hence, f l can be described as: 8 <

ð9Þ

ð6Þ

where ws stands for the spacing of the CFRP jackets and Dc stands for the outer diameter of the core concrete. Based on the calculation formulae, ws should be smaller than Dc + 5 t (ws b Dc + 5 t) to ensure that the CFRP jackets could make a contribution to the core concrete. Otherwise, the axial and eccentric compressive strength of the partially CFRP jacketed CFT column would should no improvement with respect to those of the pure CFT column. This could perfectly explain the findings on the effective wrapping scheme displayed in Section 4.3.

0

  8 2f frp  t frp  w f þ 2 f y  t  w f þ 5t > >   > ðws ≥ 5t Þ < Dc  w f þ 5t   fl ¼ > 2f frp  t frp  w f þ 2 f y  t  w f þ ws > >   ðws b 5t Þ : Dc  w f þ ws

Dc-ws +5t

8 0 > > > > < πðDc −ws þ 5t Þ2 Acc ¼ 4 > 2 > > > : πDc 4

Similarly, fl can be determined by the load-distributed rules for the steel component and therefore can be written as:

ðws b 5t Þ

1: 1

Ac1

8 0 > < h i ¼ π D2c −ðDc −ws þ 5t Þ2 > : 4

fl

Fig. 21. Confining stress transferring mechanism of the core concrete in the axially loaded partially CFRP jacketed circular CFT column.

18

Q. Shen et al. / Journal of Constructional Steel Research 166 (2020) 105925

6000

4000

4000

+10%

Shen et al [23] Li et al [22] This paper

3200 -10%

-10%

Nu,c2(kN)

5000

Nu,c1(kN)

+10%

Tao et al [17] Prabhu et al [41] Shen et al [23] Che et al [61]

3000 2000

Average=0.97 COV=0.05

2400 1600 Average=0.92 COV=0.01

800

1000 0

0 0

1000

2000

3000

4000

5000

6000

0

800

1600

Ne(kN)

2400

3200

4000

Ne(kN)

(a) Comparison between the existing experimental data

(b) Comparison between the existing experimental data

of the axially loaded circular CFT short columns

of the axially/eccentrically loaded circular CFT short

fully/partially jacketed by CFRP and the corresponding

and slender columns fully/partially jacketed by CFRP

predicted results.

and the corresponding predicted results.

Fig. 22. Comparison between the existing experimental data and the predicted results. Note: Ne stands for the experimental data of the circular CFT columns jacketed by CFRP in Ref. [17, 22, 23, 41, 61] and this paper; Nu,c1 stands for the predicted results calculated by Eqs. [3–9]; Nu,c2 stands for the predicted results calculated by Eqs. [10–29].

column can be expressed as follows:   8 1 N a1 M > > < φN þb  M ¼1 u u 1  2     > N N 1 M > : −b1  −c1  þ  ¼1 Nu Nu d1 Mu

  N=Nu ≥ 2φ3  ηo 

3

N=N u ≥ 2φ  ηo

ð10Þ

in which ηo and ζo represent the coefficients related to the steel-to-concrete confinement factor (ξ); N stands for the eccentric pressure; M stands for the uniaxial bending moment, M = N (e + Li); and Li stands for the initial imperfection. For the short column, Li = 0 and for the slender column, Li = L/1000; L stands for the column effective length; Nu stands for the axial load bearing capacity of the CFRP jacketed circular CFT short column; NE stands for the Euler critical force; and, λp and λo are the critical slenderness ratios of the circular CFT column corresponding respectively to the elastic-plastic buckling failure and the elastic buckling failure. Nu is obtained by Eqs. (3)–(9). Therefore, the flexural resistance (Mu) of the partially CFRP jacketed circular CFT column needs to be determined to figure out the eccentric load bearing capacity. However, according to the investigations presented in the literatures (i.e. Tao et al. [30,32] and Wang et al. [43]), it was observed that the strengthening improvement in the flexural strength of the column was quite limited for lateral wrapped CFRP jackets. Therefore, the Mu of the laterally CFRP jacketed circular CFT column could be approximately treated as that of the pure circular CFT column and can be described as:

b1 ¼

1−ζ o φ3  η2o

ð12Þ

c1 ¼

2  ðζ o −1Þ ηo

ð13Þ

N NE

 ð14Þ

NE ¼ π 2  Esc  Asc =λ2 −1:15

ζ o ¼ 0:18ξ  ηo ¼

φ¼

ð15Þ

þ1

0:5−0:245  ξ −0:84 0:1 þ 0:14  ξ

ð16Þ ðξ ≤ 0:4Þ ðξ N 0:4Þ

8 <

1 a2  λ2 þ b2  λ þ c2 : d2 =ðλ þ 35Þ2

a2 ¼

ðλ ≤ λo Þ   λ b λ ≤ λp  o  λ N λp

  1 þ 35 þ 2  λp −λo  e  2 λp −λo

ð17Þ

ð18Þ

ð19Þ

b2 ¼ e−2  a2  λp

ð20Þ

c2 ¼ 1−a2  λ2o −b2  λo

ð21Þ

!#  0:3  0:05 235 25 α  d2 ¼ 13500 þ 4810  ln  fy f ck þ 5 0:1

"

e¼

−d2

3 λp þ 35

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð420ξ þ 550Þ=½ð1:02ξ þ 1:14Þ  f ck 

λo ¼ π

ð11Þ



ð24Þ



a1 ¼ 1−2φ2  ηo

d1 ¼ 1−0:4 

qffiffiffiffiffi λp ¼ 1743= f y

ð22Þ

ð23Þ

ð25Þ

Mu ¼ γm f sc Wsc

ð26Þ

f sc ¼ ð1:14 þ 1:02ξsc Þf ck

ð27Þ

Table 3 Comparison of different mesh size in precision and computing time. Mesh size of rigid plate (mm)

Mesh size of steel tube (mm)

Mesh size of concrete (mm)

Mesh size of CFRP (mm)

The error of the maximum strength

Computing time (h)

15 15 15 15 10 15 15 15

15 15 15 10 10 10 10 5

15 15 10 10 10 10 5 5

15 10 10 10 10 5 5 5

7.1% 5.7% 4.4% 3.2% 3.1% 2.9% 2.8% 2.8%

0.32 h 0.41 h 0.48 h 0.50 h 0.58 h 0.79 h 0.88 h 0.95 h

Q. Shen et al. / Journal of Constructional Steel Research 166 (2020) 105925

19

Table 4 Comparison on experimental, FE analytical and predicted results. ES11

ES12

ES21

ES22

ES23

ES31

ES32

ES33

AS12 [23]

ES41

ES42

δy/mm δu/mm Nu,t/kN SI DI NFE/kN NFE/Nu,t Nu,c/kN Nu,c/Nu,t

3.1 15.3 1186.2 0.54 4.9 1162.5 0.98 1067.6 0.90

3.2 14.5 1325.1 0.57 4.5 1282.7 0.97 1179.3 0.89

3.1 23.9 1086.0 0.53 7.7 1085.4 1.00 1020.8 0.94

3.1 15.6 1154.0 0.53 5.0 1119.6 0.97 1050.3 0.91

3.4 14.0 1457.5 0.59 4.1 1428.4 0.98 1282.6 0.88

3.3 14.3 1523.9 0.59 4.3 1462.9 0.96 1417.2 0.93

3.3 14.5 1411.0 0.58 4.4 1368.7 0.97 1284.0 0.91

2.4 13.8 1270.3 0.59 5.8 1244.9 0.98 1105.2 0.87

2.69 15.87 2324.6 1.00 5.9 2313.6 1.00 2254.9 0.97

3.0 11.4 1847.0 0.79 3.9 1828.8 0.99 1662.6 0.90

2.6 15.5 991.0 0.47 5.9 942.1 0.95 832.4 0.84

δy/mm δu/mm Nu,t/kN SI NFE/kN NFE/Nu,t Nu,c/kN Nu,c/Nu,t

EL11 8.3 8.3 989.1 0.63 959.4 0.97 890.2 0.90

EL12 11.0 11.0 840.6 0.59 807.0 0.96 765.0 0.91

EL13 12.8 12.8 777.3 0.58 738.4 0.95 715.1 0.92

EL21 11.8 11.8 715.4 0.56 679.6 0.95 651.0 0.91

EL22 12.7 12.7 721.1 0.55 685.0 0.95 641.8 0.89

EL23 14.6 14.6 835.8 0.62 819.1 0.98 735.5 0.88

EL31 15.2 15.2 816.2 0.59 815.3 1.00 701.9 0.86

EL32 12.4 12.4 762.4 0.58 731.9 0.96 648.0 0.85

EL33 12.0 12.0 735.2 0.57 713.1 0.97 661.7 0.90

AL13 [23] 14.5 14.5 1330.0 1.00 1262.6 0.95 1223.6 0.92

EL41 14.0 14.0 1070.3 0.80 1059.6 0.99 1016.8 0.95

EL42 15.3 15.3 612.1 0.46 587.6 0.96 514.2 0.84

Mean

SD

CoV

0.98

0.015

0.015

0.90

0.034

0.037

0.97

0.016

0.017

0.89

0.031

0.034

Note: Nu,t and NFE are the experimental and FE analytical results, respectively; Nu,c are the results predicted by the design formulas; SD and CoV are the standard deviation and the coefficient of variation.

γm ¼ 1:1 þ 0:48 ln ðξsc þ 0:1Þ

ð28Þ

Wsc ¼ πD3 =32

ð29Þ

where Wsc stands for the section modulus of the circular CFT column and γm stands for its bending strength index. After confirming the variables in the above formulas, the eccentric load bearing capacity of the partially CFRP jacketed circular CFT column is finally presented. Fig. 22b and Table 4 display the predicted strength versus the experimental load. The results indicated that the eccentric load bearing capacities calculated using the formulas compared well with the experimental results. Therefore, the design recommendations presented in this study could be used to accurately assess the axial and eccentric load bearing capacities of the partially CFRP jacketed circular CFT column. 6. Conclusions Based on the limited experimental and analytical results of this research, the following conclusions were drawn: (1) For the eccentrically loaded CFRP jacketed CFT short columns in a partial wrapping program, the typical failure patterns primarily consisted of the outward bulges of the CHSS, CFRP rupture, colloid peeling, concrete cracking, and crumbling. Moreover, the local buckling on the CFRP jacketed circular CFT short columns was basically located at the unwrapped region. This phenomenon indicated that using CFRP materials for the circular CFT short columns could significantly limit the development of the outward local buckling. (2) The failure modes of the eccentrically loaded CFRP partially jacketed circular CFT slender columns mainly included global buckling, slight damages of the CFRP, and local tensile cracking of the core concrete. However, the CFRP strain response demonstrated that the strength of the CFRP jackets could not be fully used in the slender columns. Slightly damaged CFRP could only be found in the composite column with moderate λ, while no such apparent phenomenon was observed when the column offered large λ. Similar observations could be found in Ref. [22, 23] as well. Therefore, strengthening the CFT slender column by CFRP jackets in a partial and lateral wrapping arrangement was not suggested. (3) The N-δ curves for the circular CFT short or slender columns partially jacketed by the CFRP wraps exhibited the characteristic of

an abrupt decline beyond the peak load, which was a resultant of the CFRP rupture and global buckling. (4) A modified FE model of the partially CFRP jacketed circular CFT column under eccentric bearing force was established and validated against by the experimental data. The contact stress and the effective wrapping scheme for the composite column were investigated. Using the CFRP jackets for the circular CFT short column was highly recommended for obtaining a significant strength improvement. According to the analysis of the confining stress transferring mechanism of the partially CFRP jacketed CFT column under compression, the ws of the column should not be larger than Dc + 5 t. (5) Considering the partial wrapping feature and the confining stress transferring mechanism, design formulas for assessing the load bearing capacities of the partially CFRP jacketed circular CFT columns under axial and eccentric compression were presented and validated using the results from experimental data. The comparison revealed that the results predicted by the design formulae compared well with the experimental results. Acknowledgments This work was supported by the National Natural Science Foundation of China (Project 51478158) and the New Century Excellent Talents in University (Project NCET-12-0838); the authors greatly appreciate the supports. Particular gratitude is also extended to Prof J. Y. Richard Liew at the National University of Singapore and Dr. Yanbo Wang at the Tongji University. References [1] A. Siddika, M.A.A. Mamun, R. Alyousef, Y.H.M. Amran, Strengthening of reinforced concrete beams by using fiber-reinforced polymer composites: a review, J. Build. Eng. 25 (2019), 100798. [2] J. Cai, Z.Q. He, Axial load behavior of square CFT stub column with binding bars, J. Constr. Steel Res. 62 (5) (2006) 472–483. [3] J.G. Teng, T. Yu, D. Fernando, Strengthening of steel structures with fiber-reinforced polymer composites, J. Constr. Steel Res. 78 (2012) 131–143. [4] J.J. Zeng, G. Lin, J.G. Teng, L.J. Li, Behavior of large-scale FRP-confined rectangular RC columns under axial compression, Eng. Struct. 174 (2018) 629–645. [5] J.Z. Wang, L. Cheng, J.L. Yang, Compressive behavior of CFRP-steel composite tubed steel-reinforced columns with high-strength concrete, J. Constr. Steel Res. 150 (2018) 354–370. [6] X.J. Lao, X.L. Han, J. Ji, B.B. Chen, The compression behavior of CFRP-repaired damaged square RC columns, Constr. Build. Mater. 223 (2019) 1154–1166. [7] R.K. Varma, J.A.O. Barros, J.M. Sena-Cruz, Numerical model for CFRP confined concrete elements subject to monotonic and cyclic loadings, Compos. Part B 40 (2009) 766–775.

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