Analytical modelling and design of partially CFRP-wrapped thin-walled circular NCFST stub columns under axial compression

Thin-Walled Structures 144 (2019) 106276

Contents lists available at ScienceDirect

Thin-Walled Structures journal homepage: www.elsevier.com/locate/tws

Full length article

Analytical modelling and design of partially CFRP-wrapped thin-walled circular NCFST stub columns under axial compression

T

Qihan Shena, Jingfeng Wanga,b,*, Yanbo Wangc, Fengqin Wanga a

School of Civil Engineering, Hefei University of Technology, Anhui Province, 230009, China Anhui Civil Engineering Structures and Materials Laboratory, Anhui Province, 230009, China c College of Civil Engineering, Tongji University, Shanghai, 200092, China b

ARTICLE INFO

ABSTRACT

Keywords: Normal-strength concrete filled steel tubular (NCFST) Carbon fiber reinforced polymer (CFRP) Axial compressive behaviour Numerical modelling Design formulas

The partial CFRP (carbon fiber reinforced polymer) wrapping scheme is widely used for strengthening engineering practices to obtain a moderate improvement in strength, whereas detailed investigations on partially CFRP-wrapped thin-walled circular normal-strength concrete-filled steel tubular (NCFST) stub columns are seldom presented. This paper aims to conduct a series of numerical analyses to figure out the axial compressive performance of circular NCFST stub columns wrapped by CFRP belts partially. A nonlinear finite element (FE) modelling focused on the surface interaction as well as the CFRP and thin-walled hollow steel section (HSS) confinement effects on the concrete infill is developed via ABAQUS solver and the accuracy is validated against the existing experimental data. Following this, a systemic parametric investigation is developed to explore the impact of steel yield stress, concrete compressive strength, diameter: thickness ratio, CFRP wrapping ratio and number of CFRP layer, etc. on the axial compressive properties of the partially CFRP-wrapped thin-walled circular NCFST stub columns. Elaborate investigations on the surface contact action, stress-strain response, typical axial force versus axial shortening curve and failure modes are presented to better figure out the axial compressive behaviour of the type of composite column. A discussion on the effective wrapping scheme of the partially CFRP-wrapped thin-walled circular NCFST stub column imposed with axial compressive force is described as well. Finally, two types of design formulas in compliance with the unified theory and the tubed concrete method are proposed to assess the axial compressive resistance of the partially CFRP-wrapped thinwalled circular NCFST stub column. The research may provide a considerable and scientific basis for employing CFRP materials for the CFST structures.

1. Introduction Concrete-filled steel tubular (CFST) columns possess high prospects of using as vertical supporting member in multi- and high-rise buildings thanks to their well-known superiorities in terms of high compressive strength, good ductility, sound economic sense and easy construction [1–6]. However, a series of issues including the outward local buckling and the corrosion of the thin-walled hollow steel section (HSS) are observed according to the application history of the CFST structures since 1960s. Thus, deteriorations in lateral confinement and load bearing capacity were observed, respectively. In order to overcome the abovementioned conditions, carbon fiber reinforced polymer (CFRP) belts were suggested to protect the exposed steel material away from the adverse external environment [7,8] and to provide extra axial compressive resistance for the CFST members.

*

Previously, numerous investigation works were performed to explore the mechanical performances of CFRP-strengthened reinforced concrete (RC) members under various loading conditions [9,10]. The outstanding properties of the CFRP materials in terms of high tensile stress, light weight and easy construction make them quite appropriate for the plain concrete and RC structures. According to the confined concrete theory defined by Mander et al. [11], some newly-built buildings intended to use CFRP tubes to strengthen the plain concrete of their column cores. However, the surveys demonstrated that the construction procedure of the CFRP-tubed concrete members was complicated to some extent, and therefore the cost of the engineering project was highly increased [12]. Besides, the brittle failure of CFRP-tubed concrete columns was another serious problem due to the low ductility property of CFRP materials. Although the inward local buckling of the hollow steel section (HSS) was prevented by the supporting impact

Corresponding author. 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.tws.2019.106276 Received 26 March 2019; Received in revised form 25 June 2019; Accepted 26 June 2019 0263-8231/ © 2019 Elsevier Ltd. All rights reserved.

Thin-Walled Structures 144 (2019) 106276

Q. Shen, et al.

Sundarraja [35] respectively launched several experiments on the partially CFRP-wrapped circular or square NCFST stub columns under axial pressure. Nevertheless, investigations on the detailed performance of the type of stub composite column concerning on the typical failure modes, the contact stress, the stress and strain response, the characteristic curve and the effective wrapping scheme were ignored by the previous studies. Compared to the experimental research programs, numerical modelling method was a promising and effective way to save time and cost and to present a comprehensive description of parametric effect. However, the systematic analysis on the mechanical responses of the partially CFRP-wrapped thin-walled circular NCFST stub column via the FE modelling approach had scarcely been stressed. This paper aims to explore the axial compressive properties of partially CFRP-wrapped thin-walled circular NCFST stub columns. Corresponding to the previous experimental work [26], an FE analysis modelling was developed and verified via the axial load (N) versus axial shortening (δ) relationships and failure modes, taking the material nonlinearity and the contact interaction into consideration. Following this, the effect of extensive parameters including steel yield stress, concrete compressive strength, diameter: thickness ratio, number of CFRP layer and CFRP wrapping ratio, etc. on the axial compressive performance of partially CFRP-wrapped concrete-filled thin-walled circular HSS stub columns was estimated. Unlike the experimental studies presented in Refs. [26,34,35], this paper focused on revealing the mechanical properties containing failure modes, stress-strain responses, interface contact stress and feature N-δ curve. Moreover, the effective wrapping scheme of the partially CFRP-wrapped thin-walled circular NCFST stub column under axial compression was detailed investigated. Finally, design formulae for predicting the axial compressive resistance of the type of stub composite column were respectively proposed according to the tubed concrete method and the unified theory.

provided by the concrete infill and the concrete compressive strength was improved by the outside HSS [13–15], the outward bugles of the HSS turned out to be the typical failure mode of the NCFST columns. With respect to those above limits, CFRP-wrapped CFST members offered a combining advantage, as the CFRP belts shielded the steel from the corrosive substances and provided strong confinement, while the steel tube improved the ductility behaviour. In addition, the CFRP could be twined around the steel tube conveniently thanks to the provided attachment surface. Therefore, the load carrying capacity, the ductility and the corrosion resistance of the CFRP-wrapped CFST column were highly modified compared to those of the CFRP-confined concrete column or the bare CFST column, which indicated that this type of composite column could be undoubtedly used as bridge piers and frame columns in offshore structures and high-rise buildings [12]. Nowadays, a host of research works mainly concerned on the static performance of the fully CFRP-wrapped normal-strength concrete-filled steel tubular (NCFST) beams and columns have been reported. Wang et al. [16], Choi and Xiao [17], Tao et al. [18], Li et al. [19], Dong et al. [20] and Ding et al. [21] respectively investigated the mechanical performances of the CFRP-wrapped axially-loaded NCFST stub and slender columns offering various slenderness ratios. Some experimental and finite element (FE) analyses on the flexural behaviour of fully CFRP-wrapped circular or rectangular thin-walled NCFST beams were respectively conducted by Zand et al. [22,23], Feng et al. [24] and Sundarraja and Prabhu [25], due to the excellent tensile property of the CFRP materials. All the investigations revealed that the axial and flexural load bearing capacities of the thin-walled NCFST members could be effectively mounted through using CFRP belts. Nevertheless, the axial compressive strength improvement of the type of slender composite column was obviously decreased due to the limited contribution of CFRP belts on its axial stiffness. The fully CFRP-wrapped NCFST slender column was failed in global buckling primarily without damaged CFRP indicating that the strength of CFRP wraps were not adequately used in NCFST slender columns. Same conclusion was obtained by Li et al. [19] and Shen et al. [26] as well. Considering that CFRP materials were often used to repair the damaged structures after various disasters, the compressive and flexural performances of the fully CFRP-wrapped NCFST columns exposed to fire (i.e. Chen et al. [27], Tao and Han [28] and Tao et al. [29]) and the responses of this type of composite columns under impact and cyclic load (i.e. Yu et al. [30], Alam et al. [31,32] and Shakir [33]) were therefore investigated as well. Despite that most of the studies mainly followed on the behaviour of fully CFRP-wrapped NCFST beams and columns, relative investigations indicated that using the partial CFRP wrapping arrangement for the compressed thin-walled NCFST stub column could also provide an adequate enhancement in load bearing capacity with respect to the fully wrapping scheme (i.e. Prabhu and Sundarraja [35], Prabhu et al. [34], Shen et al. [26] and Wang et al. [36]). Under several circumstances, the partial CFRP-wrapped arrangement would be an economic and effective substitute for the fully CFRP-confined NCFST column, when the strengthening objectives only demanded for a moderate rise in load resistance. Prabhu et al. [34], Shen et al. [26] and Prabhu and

2. Brief experimental introduction The corresponding experimental investigation program had been detailed reported in previous work [26]. Seven circular NCFST stub columns wrapped with CFRP belts and one bare NCFST column were tested and analyzed. Two strength grades of circular HSSs with dimensions of 140 mm in outer-diameter, 6 mm in tube-thickness and 450 mm in height were used for the specimens. Their average yield strengths were respectively 240.8 MPa and 348.6 MPa, and the average ultimate strengths were respectively 379.2 MPa and 487.3 MPa. The elastic moduli (Es) of the HSSs were respectively 198 GPa and 202 GPa. Parameters of CFRP wraps were width a=50 mm, thickness tf=0.167 mm, average fracture strain εFRP=1.44%, average ultimate tensile strength ffrp=3510 MPa and modulus of elasticity Efrp=243 GPa. Parameters of concrete infill were cube compressive strength fcu=31.2 MPa and modulus of elasticity Ec=30521.3 MPa. Detailed relative information of the test specimens is listed in Table 1. In order to apply the axial compressive pressure to the composite column, a hydraulic universal testing machine of 500 tons in loading capacity was used in this experiment. The strain response and

Table 1 Detail information of the specimens in Ref. [26]. Specimens

D/mm

L/mm

t/mm

n

a/mm

fy/MPa

fcu/MPa

ffrp/MPa

Configuration of CFRP

AS11 AS12 AS21 AS22 AS23 AS31 AS32 AS33

140 140 140 140 140 140 140 140

450 450 450 450 450 450 450 450

6 6 6 6 6 6 6 6

3 3 0 1 5 3 3 3

50 50 0 50 50 0 30 150

240.8 348.6 348.6 348.6 348.6 348.6 348.6 348.6

31.2 31.2 31.2 31.2 31.2 31.2 31.2 31.2

3510 3510 3510 3510 3510 3510 3510 3510

Partially wrapped Partially wrapped No CFRP Partially wrapped Partially wrapped Fully wrapped Partially wrapped Partially wrapped

2

Thin-Walled Structures 144 (2019) 106276

Q. Shen, et al.

Fig. 1. Loading setup.

displacement in lateral and longitudinal directions were recorded by the static strain testing system. The experimental set-up and the site photo are shown in Fig. 1. The experimental investigation demonstrated that the resistance of the axially-loaded thin-walled circular NCFST stub column was enormously enhanced by the partially-arranged CFRP wraps, whereas a sudden descent in axial force would be observed due to the abrupt rupture of CFRP. Detailed correlated experimental result of the type of axially-loaded composite column was exhibited in Ref. [26].

described by Wang and Han [41] was widely used to investigate the mechanical properties of the bare NCFST columns. The σ-ε model of this type of concrete (Model І) is expressed as follows:

(x

= ln (1 +

nom )

ftrue / E0

(2)

7

For common carbon steel, a nonlinear elastic-plastic constitutive model (depicted in Fig. 2a) presented by Han et al. [37] was widely adopted by plenty of scholars, such as Shen et al. [26], Yang et al. [38], Wang et al. [39] and Liu et al. [40]. For the elastic behaviour, both the Young's modulus (E0) and the Poisson's ratio (ν) need to be defined, which are respectively taken as 200000 MPa and 0.3. For the plastic behaviour, Wang and Han [41] suggested converting the nominal stress-strain relationships into true stress-log plastic strain curves to satisfy the requirement of ABAQUS modelling, which can be described as

pl ln

1) > 1) σ0=fc′, circular

= c + 800 NCFST,

0

0.210 6 ,

= 2,

= (2.36 × 10 5)[0.25+ ( 0.5) ] (fc )0.5 0.5 0.12 . fc′ is the cylinder compressive strength of the core concrete, and ξ is the confinement factor, ξ=Asfy/(Acfck); As, Ac are the section areas of the HSS and the concrete infill, respectively. fy is the yield stress of the HSS. fck is the characteristic compressive strength of the concrete, fck=0.67fcu. The initial elastic modulus of the confined concrete is taken as 4700 fc (N/mm2). For the CFRP wrapped region, the concrete model confined together by the steel and CFRP wraps (Model П) proposed by Teng et al. [42] was highly recommended by many researchers, such as Hu et al. [43], Choi and Xiao [17] and Yu et al. [44] to simulate the constitutive relation of the concrete in CFRP-wrapped NCFST members.

3.1. Model of steel

nom)

x 2 (x

x 1) + x (x

where, x=ϵ/ϵ0, y=σ/σ0, 6 For c = (1300 + 125fc ) 10 .

3. FE modelling

ftrue = fnom (1 +

2x

y=

c

fcc*

=

f cc*

(1b)

fco

where fnom and ftrue represent the nominal steel stress and true steel stress, respectively; nom and lnpl respectively represent the nominal strain and log plastic strain.

* cc

( x / cc* ) r 1 + ( x/

Ec

f cc* /

= 1 + 3.5

* cc

r

Because of the scarce numerical investigations on partially CFRPwrapped circular NCFST columns, the stress-strain (σ-ε) relationships for their confined core concretes were still unclear. Based on the configuration of CFRP wrapping scheme, the core concrete was divided into two parts in this paper: the wrapped zone and the unwrapped zone. Various confined concrete models were respectively used to simulate their constitutive relationships (seen in Fig. 2b). For the CFRP unwrapped zone, the confined concrete model

(3) (4)

r

(5)

fco 1.2

= 1 + 17.5

co

3.2. Model of concrete

* r cc )

Ec

r=

(1a)

r

=

2

,s t s

r

fco

(6)

+ 2Efrp t frp Dc

(7)

in which c and x are respectively the axial stress and strain of the core concrete confined by CFRP-steel; fcc* and cc* are respectively the peak axial stress and corresponding strain of the CFRP-steel confined concrete; r is a constant correlated to the brittleness of concrete; fco is the cylinder compressive strength of the unconfined concrete; co is the axial strain of the unconfined concrete at the peak compressive stress; r is the confining stress provided by the CFRP belts and the HSS, and ,s 3

Thin-Walled Structures 144 (2019) 106276

Q. Shen, et al.

Fig. 2. Constitutive models of steel tube and core concrete.

is the hoop stress of the HSS; is the hoop strain of the CFRP wraps; ts and tfrp are the thicknesses of the HSS and CFRP wraps; Dc is the outer diameter of the CFRP-wrapped circular NCFST column; Efrp is the elastic modulus of the CFRP. 3.3. Model of CFRP With regard to the CFRP wrap, it is generally considered as an orthotropic material. In its longitudinal direction, it exhibited an elastic behaviour before fractured, and has high tensile strength but can hardly stand any compressive pressure. In other directions, it would be damaged easily under tensile, compressive or shear force. Therefore, the elastic stress-strain relationship offering the option of “Engineering Constants” was used in this paper. According to the material property of CFRP wraps introduced in section 2, the Poisson's ratio, the modulus of elasticity, the fail stress and the fail strain were respectively assigned as 0.22, 243000 MPa, 3510 MPa and 0.0144. The damage of the CFRP materials was controlled by the ‘fail stress’ and the ‘fail strain’ options. When the tensile stress or the tensile strain of the CFRP exceeded the limit, the CFRP would be damaged in the form that the tensile stress of the CFRP suddenly changed from ultimate stress to 0.

Fig. 3. Typical FE modelling of the partially CFRP-wrapped thin-walled circular NCFST stub column under axial load.

composite column. Both the boundary conditions and the axial compressive force were applied to the loading plate via reference nodes. The displacements and rotations of the bottom loading plate were all fixed, while the displacement and rotation of the top loading plate were free and the axial displacement was imposed through z axis. The “Tie” option was applied to simulate that the loading plates were welded to the HSS, while surface-to-surface interaction was commonly used to model the contact action of steel-to-concrete interface (i.e. loading-plate-to-concrete interface and HSS-to-concrete interface). Based on the previous studies [26,36], the friction factor taken as 0.3 was applied for modelling the tangential direction behaviour and “Hard contact” action was used for simulating the normal direction behaviour. Considering that the CFRP wraps were perfectly bonded to

3.4. Description of FE model Similar to the investigation described in Ref. [36], 8-node linear brick elements with reduced integration (C3D8R) would be a reasonable element choice to simulate the deformation characteristic of the circular HSS and the core concrete. For the fiber wraps, using shell element (S4R) could not only simplify the FE model and save time for calculation, but also keep clear of no convergence. Typical numerical modelling of the partially CFRP-wrapped circular thin-walled NCFST column was depicted in Fig. 3. Two loading plates bonded to the top and bottom of the column were used to transfer the axial pressure to the full section of the type of 4

Thin-Walled Structures 144 (2019) 106276

Q. Shen, et al.

Table 2 Comparison between test [26,34] and FE results. Specimens

AS11

AS12

Nt/kN NFE/kN NFE/Nt Specimens Nt/kN NFE/kN NFE/Nt

2007 2352 1963 2331 0.98 0.99 CS-50-20-T1 989/983/975 951 0.96/0.97/0.98

AS21

AS22

2048 2141 2026 2072 0.99 0.97 CS-50-20-T2 1075/1055/1043 1026 0.95/0.97/0.98

AS23

AS31

2479 2594 2387 2521 0.96 0.97 CS-50-20-T3 1185/1209/1202 1192 1.01/0.99/0.99

AS32

AS33

2442 2151 2339 2073 0.96 0.96 CS-50-30-T1 965/962/970 916 0.95/0.95/0.94

CS-50-30-T2 1033/1012/1023 1009 0.98/1.00/0.99

CS-50-30-T3 1122/1145/1105 1106 0.99/0.97/1.00

Note: NFE represents the axial compressive resistance predicted by the FE modelling; Nt represents the test results.

the outside surface of the circular HSS and the interface between two layers cohered well. There barely exhibited any relative slippage. Therefore, the interactions between the CFRP layers and the contact action between CFRP and HSS were identified as “Tie” function.

specimens in Ref. [26] were all reflected in the corresponding FE models as well, including outward buckling of HSS, rupture of CFRP wraps and concrete crumbling. The satisfactory agreement indicated that the numerical modelling of partially CFRP-wrapped axially-loaded circular NCFST stub column established in this paper could be used as an effective and prospect approach to explore its mechanical properties.

3.5. Test validation

4. Parametric analysis

Based on the above steps, the typical FE model of partially CFRPwrapped circular thin-walled NCFST stub column under axial load was established. To validate its accuracy, comparisons between the existing experimental data [26,34] and the corresponding FE results were respectively illustrated in Table 2 and Fig. 4, including the axial force versus axial deformation relationships and the failure modes. The results revealed that the force versus deformation curves of the experiments performed satisfactory agreement with the FE results. Failure modes of the concrete-filled thin-walled circular steel tubular stub columns wrapped by CFRP partially were also compared with those of the FE models. It can be found that the failure modes of the tests matched well with the FE analytical results (shown in Fig. 5). Based on the investigation, the test failure patterns of the experimental

On the basis of the established FE modelling, the axial compressive response of partially CFRP-wrapped circular thin-walled NCFST stub columns offering extensive parameters was studied in this section. Thinwalled HSSs with small diameter: thickness ratios (D/t) were investigated specially in accordance with the correlated definitions in codes AS 4100 [45] and EC 4 [46]. Systemic parameters were discussed in this paper, which included: ● Steel yield stress: fy=235, 345, 420 and 550 MPa; and ● Concrete compressive strength: fcu=30, 40, 50 and 60 MPa; and ● CFRP ultimate tensile strength: ffrp= 1500, 2500, 3510 and

Fig. 4. Comparison between experimental curves [23,31] and FE results. 5

Thin-Walled Structures 144 (2019) 106276

Q. Shen, et al.

Fig. 5. Comparison on the failure modes between the experimental phenomena and the corresponding numerical observations.

4500 MPa; and ● Diameter: thickness ratio: α=D/t=10, 14, 20, 28.6, 40, 50, 70 and 100; and ● CFRP layer: n=0, 1, 2, 3, 4 and 5; and ● CFRP wrapping ratio: wp=aT/L=1, 8/9, 7/9, 6/9, 5/9, 4/9, 3/9 and 2/9 (aT is the total width of the CFRP belts wrapped on the NCFST column, L is the length of the column.); and ● Cross section: D × t = 100 × 2.0 mm, 140 × 2.8 mm, 200 × 4.0 mm, 400 × 8.0 mm and 600 × 12.0 mm.

Moreover, the information of the standard example in each group was specially identified in bold, which was used to identify the independent effect of each parameter. The numerical results are shown in Table 3. 4.1. The effect of steel yield stress (fy) The impact of steel yield stress on the axial force (N) - axial deformation (δ) relationship of partially CFRP-wrapped thin-walled stub

Table 3 Parametric analysis of partially CFRP-wrapped circular thin-walled NCFST stub column under axial compression. Examples

Dimensions D × t × L/mm

fy/MPa

fcu/MPa

fFRP/MPa

w

n

a

δy/mm

Ke/kN·mm−1

NFE/kN

AS-S-1 AS-S-2 AS-S-3 AS-S-4 AS-C-1 AS-C-2 AS-C-3 AS-f-1 AS-f-2 AS-f-3 AS-t-1 AS-t-2 AS-t-3 AS-t-4 AS-t-5 AS-t-6 AS-t-7 AS-t-8 AS-l-1 AS-l-2 AS-l-3 AS-l-4 AS-l-5 AS-l-6 AS-w-1 AS-w-2 AS-w-3 AS-w-4 AS-w-5 AS-w-6 AS-w-7 AS-w-8 AS-w-9 AS-cs-1 AS-cs-2 AS-cs-3 AS-cs-4 AS-cs-5

140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 1.4 × 450 140 × 2.0 × 450 140 × 2.8 × 450 140 × 3.5 × 450 140 × 4.9 × 450 140 × 7.0 × 450 140 × 10.0 × 450 140 × 14.0 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 100 × 2.0 × 200 140 × 2.8 × 280 200 × 4.0 × 400 400 × 8.0 × 800 600 × 12.0 × 1200

235 345 420 550 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345

50 50 50 50 30 40 60 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50

3510 3510 3510 3510 3510 3510 3510 1500 2500 4500 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510

50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 0 12.5 25 37.5 50 62.5 75 87.5 0 50 50 50 50 50

3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0 1 2 3 4 5 3 3 3 3 3 3 3 3 0 3 3 3 3 3

50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 80 70 60 50 40 30 20 0 50 50 50 50 50

2.17 2.05 2.00 2.00 2.19 2.12 2.03 2.01 2.01 2.02 1.64 1.69 1.79 2.05 2.10 2.22 2.31 2.31 3.12 1.93 1.94 2.05 1.96 1.99 2.08 2.06 2.01 2.10 2.05 2.11 2.09 2.12 2.08 0.83 1.79 1.65 2.81 2.81

1043.4 1064.2 1083.9 1089.9 929.2 987.5 1120.2 1043.8 1057.2 1071.9 863.5 925.8 1012.3 1063.2 1199.5 1341.5 1592.8 2050.5 997.4 1031.6 1096.6 1064.2 1082.1 1068.5 1103.2 1124.3 1037.1 1058.7 1064.2 1136.1 1105.8 1114.3 1118.2 684.69 1063.20 1953.56 5272.77 8998.07

1405.9 1658.3 1876.6 2200.8 1579.9 1616.2 1734.9 1535.9 1586.1 1770.9 1170.5 1322.7 1519.9 1658.3 2001.0 2417.1 2936.5 3484.5 1286.8 1405.7 1555.2 1658.3 1849.4 1987.3 2525.2 2313.6 2069.7 1851.7 1687.3 1557.2 1453.7 1363.4 1286.8 1015.7 1747.7 3133.1 10570.0 22499.3

Note: The b, n, a respectively stand for the width, layer and spacing of CFRP wraps; Ke represents the axial elastic stiffness of the column. 6

Thin-Walled Structures 144 (2019) 106276

Q. Shen, et al.

composite columns was depicted in Fig. 6a. The analysis revealed that the axial compressive resistance of the thin-walled circular NCFST stub column confined by CFRP wraps partially was enhanced by the increase of steel yield stress, whereas the axial elastic stiffness (Ke) practically kept invariant. With respect to the type of composite column with a steel yield stress of 345 MPa, the compressive resistance of the axiallyloaded column with a steel yield stress of 235 MPa reduced about 14.3%. In terms of the columns with steel yield stresses of 420 MPa and 550 MPa, their axial compressive resistances were promoted by 8.4% and 18.1% respectively compared to the composite column with a steel yield stress of 345 MPa.

respectively. Correspondingly, their axial elastic stiffness was decreased by 12.7% and 7.2%. When the concrete compressive strength rose up to 60 MPa, the axial compressive resistance and the axial elastic stiffness of the type of composite column respectively obtained improvements of 4.6% and 5.3%. 4.3. The effect of CFRP ultimate tensile strength (ffrp) The partially CFRP-wrapped axially-loaded concrete-filled thinwalled circular HSS stub columns with CFRP ultimate tensile strength of 1500, 2500, 3510 and 4500 MPa were investigated in Fig. 6c. The results showed that the axial compressive resistance of the type of thinwalled composite columns was enhanced by the increasing of CFRP ultimate strength, whereas the axial elastic stiffness of the columns was hardly influenced. With respect to the thin-walled circular NCFST stub column partially attached with CFRP belts offering a CFRP ultimate tensile strength of 1500 MPa, the axial compressive resistances of the columns with CFRP ultimate tensile strengths of 2500 MPa, 3510 MPa and 4500 MPa were respectively increased by 10.1%, 18.5% and 22.0%.

4.2. The effect of concrete compressive strength (fcu) Fig. 6b depicted the effect of concrete compressive strength on the axial compressive properties of the type of composite columns, including axial compressive resistance and axial elastic stiffness. The numerical results revealed that both them were significantly enhanced by the concrete compressive strength increasing. Compared to the column with a concrete compressive strength of 50 MPa, the axial compressive resistances of the columns offering concrete compressive strengths of 30 and 40 MPa were decreased by 4.7% and 2.5%,

Fig. 6. Influence of various parameters on the N-δ curves of partially CFRP-wrapped circular thin-walled NCFST stub columns under axial compression. 7

Thin-Walled Structures 144 (2019) 106276

Q. Shen, et al.

4.4. The effect of diameter: thickness ratio (α=D/t)

section area. In comparison with the column with dimensions of 100 × 2.0 × 200 mm, the axial compressive resistances of the columns offering dimensions of 140 × 2.8 × 280 mm, 200 × 4.0 × 400 mm, 400 × 8 × 800 mm and 600 × 12 × 1200 mm were respectively 2.34, 3.60, 17.96 and 28.20 times of the column with scale of 100 × 2.0 × 200 mm. Correspondingly, the axial elastic stiffness was 1.55, 2.85, 7.70 and 13.14 times of the counterpart.

The type of columns with diameter: thickness ratios of 10, 14, 20, 28.6, 40, 50, 70 and 100 (corresponding to the HSSs of 14, 10, 7, 4.9, 3.5, 2.8, 2 and 1.4 mm in thickness) were explored. Fig. 6d declared that the axial compressive resistance and axial elastic stiffness of partially CFRP-wrapped thin-walled circular NCFST stub columns rose up with the decrease of diameter: thickness ratio. The axial compressive resistances of the columns with diameter: thickness ratios of 100, 70 and 50 were respectively reduced by 20.3%, 11.5% and 4.1% compared to the composite column with a diameter: thickness ratio of 40, while the corresponding axial elastic stiffness was respectively decreased by 18.9%, 13.0% and 4.9%. With the diameter: thickness ratio of the columns decreasing from 40 to 28.6, 20, 14 and 10, their axial compressive resistances were respectively heightened by 15.1%, 36.5%, 68.5% and 116.9%, while the increases in axial elastic stiffness were observed to be 12.7%, 26.1%, 49.7% and 92.7%, respectively. Moreover, it should be stressed that the thin-walled steel tube of the axially loaded partially CFRP-wrapped circular NCFST stub column commonly failed with severely outward local bugles due to its instability feature. However, this local buckling located at the unwrapped zone would be gradually mitigated or even disappeared when the thick-walled steel tube was used.

5. Discussion 5.1. Failure patterns According to the test validation in section 3.5, failure patterns including rupture of CFRP wraps, outward buckling of HSS and concrete crumbling were respectively discovered in the FE models. Nevertheless, some other failure phenomena in terms of flexural buckling and concrete shear failure were observed as well based on the plenty of numerical analyses in section 4 (shown in Fig. 7). Detailed numerical investigation revealed that various failure phenomena and their occurrence orders were attributed to the change in CFRP wrapping ratio, CFRP layer (n), multiple confinement coefficient As f + Afrp ffrp ) and column slenderness. Generally, the failure of concrete ( y Ac fck

crumbling located at the unwrapped zone was commonly found in partially CFRP-wrapped axially-loaded thin-walled circular NCFST stub column because of the high axial compressive stress. Rupture of CFRP wraps was observed first in the fully-confined column, because the outward buckling of the HSS was substantially prevented by the uniform confinement provided by the CFRP. Then the buckling at the damaged CFRP region was emerged immediately owing to the absence of CFRP confinement. Unlike the fully CFRP-wrapped thin-walled NCFST stub column, failure region of the type of partially-confined column was located at the weak area (CFRP unwrapped zone) behaving as outward local buckling of HSS. Following this, the CFRP wraps were ruptured with further developed lateral expansion. Nevertheless, the deformation level of the local buckling would be lightened with the decrease of diameter: thickness ratio. When the thick-walled steel tube was used for the type of stub composite column, the outward bugles disappeared and only large lateral deformation was observed as the stability failure of the thin-walled steel tube was substitute for the strength failure of the thick-walled steel tube. By the column slenderness and CFRP spacing increasing, the partially CFRP-wrapped circular NCFST column showed the property of slender column and thus failed in flexural buckling mode without any damage of CFRP (seen in Fig. 7a). For the fully or partially CFRP-wrapped circular NCFST stub column with small multiple confinement coefficient and thin-walled HSS, shear failure of the type of column was observed due to the brittle feature of plain concrete (depicted in Fig. 7b).

4.5. The effect of CFRP layer (n) The impact of CFRP layer ranging from 0 to 5 on the resistance of partially CFRP-wrapped axially-loaded thin-walled circular NCFST stub column was reflected in Fig. 6e. The axial compressive resistances of the composite columns with 1–5 layers of CFRP wraps were increased by 25.1%, 45.1%, 53.2%, 61.8% and 72.6% respectively in comparison with the bare NCFST column. Nevertheless, the axial elastic stiffness of the column was not sensitive to the change of CFRP layer. Therefore, the result proved that the axial compressive resistance of the partially CFRP-wrapped thin-walled circular NCFST stub column was highly promoted by the increase of CFRP layer. In addition, the amplitude of the sudden descent in their load-displacement curves resulting from the rupture of CFRP wraps was observed to be correlated to the number of CFRP layer as well. 4.6. The effect of CFRP wrapping ratio (wp) Fig. 6f illustrated the impact of CFRP wrapping ratio on the axial compressive properties of the partially CFRP-wrapped concrete-filled thin-walled circular HSS stub column. The FE analytical models with CFRP wrapping ratio ranging from 2/9 to 1 were established. The analytical results proved that the axial compressive resistance of the column was heightened obviously by the increase of CFRP wrapping ratio, but the axial elastic stiffness scarcely showed any change. Compared to the partially CFRP-wrapped thin-walled circular NCFST short column with CFRP wrapping ratio of 5/9, the axial compressive resistances of the columns with CFRP wrapping ratio of 1, 8/9, 7/9 and 6/ 9 were respectively increased by 49.7%, 37.1%, 22.7% and 9.7%. With the CFRP wrapping ratio decreasing from 5/9 to 4/9, 3/9 and 2/9, the axial compressive resistance of the column respectively offered descents of 7.7%, 13.8% and 19.2%. 4.7. The effect of section area (Asc) To investigate the size effect on the axial compressive resistance of partially CFRP-wrapped thin-walled circular NCFST stub columns, the columns with sizes (D × t × L) ranging from 100 × 2.0 × 200 mm to 600 × 12.0 × 1200 mm were respectively studied (shown in Fig. 6g). The results revealed that the axial compressive resistance and axial elastic stiffness of the partially CFRP-wrapped thin-walled circular NCFST stub columns were obviously promoted by the increase of the

Fig. 7. Typical failure modes of partially CFRP-wrapped circular thin-walled NCFST stub column under axial compression. 8

Thin-Walled Structures 144 (2019) 106276

Q. Shen, et al.

Fig. 8 as well. (1) The elastic stage (OA). The curve was developed in a linear progression. The concrete and the HSS undertaken the axial force separately and behaved in elastic behaviour, while the CFRP wraps stayed in low tensile condition. The results demonstrated that the elastic stage of the axially loaded thin-walled circular NCFST stub column fully or partially attached with CFRP belts was almost the same with that of the bare NCFST column. (2) The elastic-plastic stage (AB). With the longitudinal stress and strain increased with the axial shortening, the concrete and HSS stepped into their nonlinear plastic stages, respectively. In addition, the contact stress was observed with the lateral deformation increasing. The HSS was yielded finally when the curve arrived at point B. (3) The plastic hardening stage (BC). The axial force would keep increasing after the HSS reached its yield stress because of the hardening behaviour of mild steel. High contact stress of the interface between the concrete infill and the HSS was observed resulting in the enhancement on the confinement effect and the compressive resistance of the core concrete. The numerical results revealed that both the ultimate axial stress of the HSS and the core concrete were highly improved by wrapping CFRP materials. Moreover, the longitudinal shortening corresponding to the maximum axial force of the type of the stub composite column was increased with the CFRP wrapping ratio, which represented that the deformation capacity of the column was obviously enhanced. (4) The abrupt descent stage (CD). After the column reached its maximum load, the CFRP wraps finally arrived at their fracture strain and ruptured suddenly resulting in an abrupt descent beyond the

Fig. 8. Typical N-δ curve of CFRP-wrapped NCFST stub columns.

5.2. Typical N-δ curve Based on the numerical analysis, a typical N-δ relationship of the partially CFRP-wrapped concrete-filled thin-walled circular HSS stub column was figured out considering the material property and geometric feature. The curve was investigated to be comprised of five parts. Moreover, the N-δ responses of the bare thin-walled circular NCFST stub column and the column fully-wrapped by CFRP belts were depicted in

Fig. 9. The contact stress of the partially CFRP-wrapped axially-loaded thin-walled circular NCFST stub column. 9

Thin-Walled Structures 144 (2019) 106276

Q. Shen, et al.

peak load. The decrease amplitude was correlated to the CFRP wrapping ratio and the multiple confinement coefficient. The larger CFRP wrapping ratio and multiple confinement coefficient, the higher descent is. (5) The horizontal stage (DE). The axial force would keep constant in this stage. Much severe outward buckling of the HSS was discovered because of the disappearance of the confinement provided by CFRP wraps. Although using CFRP wraps for the circular NCFST stub column would result in a sudden descent in axial reaction force due to the rupture of CFRP, the residual axial strength of the fully or partially CFRP-wrapped circular NCFST stub column was still a little higher than that of the bare NCFST stub column.

consistent with the transverse strain (εTS) response. Finally, the σTS showed a sudden rise at point D owing to the failure of CFRP. For the concrete infill, the distribution law of its longitudinal stress (σLC) and strain (εLC) was similar to that of σLS. Both the σLC and σTC showed that the core concrete was in triaxial compressive condition. During AB and BC stages, the σLC at the wrapped zone was much higher than that at the unwrapped zone thanks to the excellent confinement supplied by the CFRP belts. Because of the combined constraints provided by the welded loading plate and CFRP wraps, the highest σLC and σTC were basically located at the column ends. In addition, the strain response of the concrete indicated that the maximum deformation of the concrete stayed at the unwrapped region around its mid-height region, due to its weakest confinement. For the CFRP wrap, it should be noted that the fibers barely undertook any axial force, while only lateral confinement was provided. Therefore, only its transverse stress (σTF) was captured during the loading phrase. When the axial load reached points A and B, the σTF at the middle of CFRP wrap was much lower than that at the edge of the CFRP. At the peak load, the edge of the CFRP wrap ruptured firstly and the ultimate tensile stress developed to its mid-part. Beyond the peak load, the CFRP wraps around the mid-height of the composite column were destroyed completely, while the fibers at the end of the column kept working.

5.3. Contact stress The contact stress is an intuitive index for reflecting the constrained state of the core concrete. Assessing the standard model AS-S-12 for example, the contact pressure of the partially CFRP-wrapped thinwalled circular NCFST stub column at various cross-sections and loading stages (i.e. the feature points A, B and C) was captured as shown in Fig. 9. The FE analytical results showed that the contact stress of the partially CFRP-wrapped axially loaded thin-walled circular NCFST stub column stayed at a low level when the column was loaded at its elastic and elastic-plastic stages. The contact stress of the column increased continuously through the loading process, while most of the increase was finished during the plastic hardening stage. Moreover, the contact stress at the 1-1, 3-3 and 5-5 cross-sections was much higher than that at the other cross-sections because of the perfect confinement action supplied by the CFRP wraps. Therefore, the outward bulges of the thinwalled HSS at the CFRP-confined zones were effectively prevented by the high tensile strength CFRP. The investigation also demonstrated that the contact stress at the mid-height of the column was a little larger than that at the end of the column. This contact stress response could perfectly explain that the rupture of CFRP and the outward bulges were firstly discovered around the mid-height of the column, which was corresponded to the experimental phenomenon described in Ref. [26].

5.5. Effective wrapping scheme Based on the numerical analyses on the mechanical properties of the partially CFRP-wrapped axially loaded thin-walled circular NCFST stub column, it was found that the axial compressive resistance of the thinwalled NCFST stub column could be obviously enhanced by wrapping CFRP belts partially. However, it is of great necessity to figure out the effective wrapping scheme to better apply CFRP materials for the NCFST structures. According to the observation in Ref. [36], a greater strength enhancement index would be obtained by wrapping the same amount of CFRP wraps for the NCFST column with a thinner HSS. For the specimen AS12 in Ref. [26], its strength enhancement was 14.8%. However, the values of the strength enhancement would respectively increased up to 26.7%, 29.1%, 30.0%, 31.1% and 33.1% when the thickness of the HSS decreased from 6.0 mm to 4.9 mm, 3.5 mm, 2.8 mm, 2.0 mm and 1.4 mm. Therefore, the wrapping scheme of CFRPstrengthened thin-walled circular NCFST stub column is suggested in this paper. Similar findings were also observed by Tao and Han [28]. The investigation in section 4.5 also indicated that the axial compressive resistance of the type of composite column was gradually promoted by the increase of CFRP layer and the decrease of CFRP spacing. In order to figure out the strengthening efficiency of the CFRP strips presented in interval layout in detail, hundreds of numerical models were developed to obtain the effect of CFRP layer, diameter: thickness ratio and CFRP wrapping ratio of the column on the strength enhancement index. Taking the stub column with conditions of D × t × L=140 × 2.8 × 450 mm, fy=345 MPa, fcu=50 MPa and ffrp=3500 MPa for example, Fig. 11a gives the research results of fully and partially CFRP-wrapped thin-walled circular NCFST stub columns offering various CFRP layers from 1 to 10. The analysis revealed that the axial compressive resistance of the CFRP-wrapped thin-walled circular NCFST stub column was gradually heightened by the increase of CFRP layer, while the growth rate decreased obviously with the decrease of CFRP wrapping ratio. Moreover, the descent of the enhancement dropped much faster when the CFRP wrapping ratio was reduced to less than 8/9. The strengthening efficiency provided by every CFRP layer was gradually descent at the same CFRP wrapping ratio. When the CFRP wrapping ratio reduced less than 3/9, the strengthen improvements of the axially-loaded circular NCFST stub column with various CFRP layers only exhibited a small difference. Similarly, the impact of diameter: thickness ratio and CFRP spacing

5.4. Stress and strain response To better understand the stress and strain response of the partially CFRP-wrapped axially loaded thin-walled circular NCFST stub column, the stress and strain of the model AS-S-12 in longitudinal and lateral directions were respectively captured in Fig. 10. The stress value of the column at loading point A, B, C and D was displayed in form of curves in a rectangular coordinate, and the strain of the column at its peak load was shown by the results distribution. For the HSS, the results reported that the high longitudinal stress (σLS) was mainly located at the top and bottom ends. σLS of the wrapped and unwrapped zones was almost the same at point A indicating that the CFRP wraps seldom made any contribution for the axially-loaded stub composite column. With the load increasing, the σLS was gradually increased before the peak load, and the stress at the wrapped region was obviously higher than that at the unwrapped region. After the CFRP wraps were ruptured, the σLS exhibited an abrupt descent. At point D, the higher σLS at the unwrapped zone may result from the severe damage of the concrete meaning that more axial force would be undertaken by the steel component in this field. The longitudinal strain (εLS) distribution at the maximum load displayed that the largest εLS was majorly stayed around the mid-height of the column's unwrapped zone, which finally resulted in outward local buckling. In transverse direction, the transverse strain (σTS) kept increasing throughout the loading phrase. The σTS around the end of the column was much lower than that at other regions because of the constraint provided by the welded loading plate. Before the peak load, σTS at the unwrapped part was higher because of the absence of CFRP confinement. This was 10

Thin-Walled Structures 144 (2019) 106276

Q. Shen, et al.

Fig. 10. The stress and strain response of the partially CFRP-wrapped thin-walled circular NCFST stub column under axial compression.

11

Thin-Walled Structures 144 (2019) 106276

Q. Shen, et al.

Fig. 11. The effect of various parameters on the strength enhancement of partially CFRP-wrapped circular NCFST stub column under axial compression.

on the strengthening efficiency of the partially CFRP-wrapped axially loaded circular NCFST stub column was discussed by an example with conditions of D × L=140 × 450 mm, fy=345 MPa, fcu=50 MPa, ffrp=3500 MPa and n=3 as well. Detailed result was illustrated in Fig. 11b. It demonstrated that the thinner the HSS of the column is, the larger improvement would be observed. While disparity in strength enhancement decreased obviously with the decrease of CFRP wrapping ratio. When the coverage ratio of CFRP wraps was smaller than 4/9, the strength improvements of the partially CFRP-wrapped axially loaded circular NCFST columns with various CFRP layers and diameter: thickness ratios hardly exhibited any differences. Finally, the contribution on the strength improvement would be zero, when CFRP coverage ratio decreased to 1/9.

Therefore, σL,s can be shown as: L,s

r

=

=

fy2

3 s

2(1

s)

r

f

fc0

2

s

fc0

2

2 s

3

r

f

fc0

2

r

fc0

= 0.47 s + 0.5

,s

kp = 0.186 + 1.77wp

+

f,sc

s)

ffrp

+ 2.4

r

fc0

(11)

f

(12)

(13)

0.353

f,sc

0.347wp2 + 0.08

(14) 2 f,sc

0.191wp

f,sc

=

Afrp ffrp Ac fck + As fy

(16)

6.2. Unified theory approach Different from the simple superposition principle, the unified theory approach suggested by Han [37] regards the steel, the concrete infill and the CFRP wraps of the column as one composite material. For the axially loaded circular NCFST stub column, the simplified design provision put forward by Han [37] is expressed as

(8)

f

2(1

f

2

(15)

,s

2

+

Nu,TP = Ac fc + 1.7As fy + 1.7k p Afrp ffrp

(7a)

2

(10)

Considering that the thin-walled circular NCFST stub column was wrapped partially, a reduction in confinement provided by CFRP belts would be obtained which was distinct from the fully CFRP-wrapped NCFST stub column. Therefore, the reduction factor (kp) was used for weakening the continuous and uniform distributed confinement in order to simulate the partial wrapping scheme. The design formula for this type of composite column can be described as follows:

r

fco

fy

Finally,

(6a)

2 ,s

1

s

Nu,T = Ac fc + 1.7As fy + 1.7Afrp ffrp

where fco is the compressive strength of the unconfined concrete; σr is the confining stress supplied by the HSS and CFRP belts. In compliance with the Von Mises yield criterion and Saint-Venant's principle, σr and σL,s can be expressed as: L,s

f

It is easy to figure out that

dNu,T =0 d r

where fcc is the compressive strength of the confined concrete, σL,s is the axial stress of the HSS. In terms of the fully CFRP-wrapped axially loaded circular NCFST stub column, Ding et al. [21] gave a detailed derivation on its design formula. Hereinto fcc can be described as:

fcc = fco 1 + 3.4

r

2

The tubed concrete theory is initially presented by Mander et al. [11] and Richard et al. [47], and it is widely recommended by many researchers [42]. Based on the mechanical analysis developed in section 5, it was easily to figure out that axial resistance was composed of two parts which were contributed by the HSS and the confined concrete. Hence, its design formulae can be described as follows:

+ Ac fcc

2

3

Nu,T = Ac fc 1 +

6.1. Tubed concrete method

L,s

1

where ξs and ξf are the confinement indexes of the HSS and CFRP wraps, ξs=Asfy/Acfco, ξf=Afrpffrp/Acfco. Hence, the axial compressive resistance of the fully CFRP-wrapped circular NCFST stub column can be written as:

6. Prediction of axial compressive resistance

Ncs,p = As

=

(9)

where ρs and ρf are respectively the steel ratio and CFRP ratio of the cross section, ρs=As/Asc, ρf=Afrp/Asc; σθ,s is the hoop stress of the HSS.

Ncu,sc = (1.14 + 1.02 ) fck Asc 12

(17)

Thin-Walled Structures 144 (2019) 106276

Q. Shen, et al.

Fig. 12. Comparison between predictions of design formulas and test and numerical data.

For the concrete column fully confined by CFRP wraps, the design recommendation for predicting its axial compressive resistance proposed by Yu [48] was designed as

Ncu,fc = (1 + 1.15

frp ) fc A c

(2)

(18)

where ξfrp is the confinement factor representing the interaction between the concrete and the CFRP wraps, frp = Afrp ffrp /(Ac fc ) ; fc is the cylinder strength of the concrete. Although the presentations of Eqs. (17) and (18) are quite concise, their accuracy for predicting the strength of the circular NCFST stub column and the CFRP-confined concrete stub column had been validated by large amounts of experimental results. Based on these design thoughts, the prediction approach to assess the axial compressive resistance of the fully CFRP-wrapped thin-walled circular NCFST stub column is presented by Tao et al. [18].

Ncu,f = (1 + 1.02 s) fc Asc + 1.15

frp fc A c

(19)

= As fy /(Ac fc )

s

(20)

Based on the above design recommendations, the reduction on the CFRP confinement was considered in terms of the partially CFRPwrapped approach. The method designed for assessing the axial compressive resistance of the partially CFRP-wrapped thin-walled circular NCFST stub column was presented as

Nu,UP = (1.14 + 1.02 ) fck Asc + 1.15 p

= 1.672 + 0.969wp

= Asfy/(Acfck)

1.433

f,sc

p frp fc A c

+ 0.465wp2 + 0.276

(3)

(21) 2 f,sc

(22)

(4)

(23)

The axial compressive resistance predicted by the tubed concrete method and the unified approach was compared against the experimental and numerical data as illustrated in Fig. 12. The result showed that the axial compressive resistance calculated by the formulae (Nu,TP, Nu,UP) coincided well with the test (Nu,t) and FE results (NFE). In compliance with the scope of the experimental and numerical analysis, the design methods are appropriate for the axially loaded partially CFRP-wrapped circular NCFST stub columns on condition that fy=235–550 MPa, fcu=30–60 MPa, ffrp=1500–4500 MPa, α=D/t=10–100, n=0–10, wp=0–1 and D × t=100 × 2.0 mm–600 × 12.0 mm.

(5)

7. Conclusions This paper conducted a detailed research on the analytical modelling and design of partially CFRP-wrapped axially loaded thin-walled circular NCFST stub columns. Based on the limited numerical observations, the following conclusions was obtained.

considering the local CFRP-wrapped feature. The accuracy of the FE model was validated via the existing experimental results [26,34]. Based on the parametric investigation on the axial compressive performance of partially CFRP-wrapped thin-walled circular NCFST stub column, it can be observed that its axial compressive resistance was evidently enhanced by the increase of the steel yield stress, the concrete compressive strength, the CFRP ultimate tensile strength, the number of CFRP layer, the CFRP wrapping ratio and the section area, whereas opposite findings were obtained with the diameter: thickness ratio growing. Compared to the bare circular NCFST stub column (model AS-l-1), the enhancement in axial compressive resistance would increase up to 54.4% when the 5 layers of CFRP belts were applied for the partially CFRP-wrapped thin-walled circular NCFST (model AS-l-6). Assessing the fully CFRP-wrapped circular NCFST stub column (model AS-w-1), its axial compressive resistance was almost doubled that of the bare NCFST stub column. With the CFRP wrapping ratio decreasing to 1/9, the enhancement nearly reduced to 0. Failure modes of the partially CFRP-wrapped axially loaded thinwalled circular NCFST stub columns included the rupture of CFRP wraps, the outward bulges of thin-walled HSS, concrete crumbling, concrete shear failure and flexural buckling of the column. Detailed numerical analysis revealed that the failure patterns and their occurrence orders were attributed to the changes in CFRP wrapping ratio, the CFRP layer, the multiple confinement coefficient and the column slenderness. According to the detailed discussion on the effective wrapping scheme of the partially CFRP-wrapped NCFST stub column under axial load, using CFRP belts for the thin-walled NCFST column was highly recommended to obtain a significant strength improvement. Moreover, the CFRP wrapping ratio of the type of composite column was not suggested to be smaller than 3/9. Based on the tubed concrete method and the unified theory, design formulas for predicting the axial compressive resistance of partially CFRP-wrapped thin-walled circular NCFST stub column were proposed and validated against the previous experimental data obtained by various scholars and numerous FE results in this paper. The comparison result declared that the calculation approaches presented in this paper could provide an accurate assessment method for the axial compressive resistance of this type of composite column.

Conflicts of interest The authors declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.

(1) A numerical modelling of partially CFRP-wrapped thin-walled circular NCFST stub column subjected to axial pressure was developed 13

Thin-Walled Structures 144 (2019) 106276

Q. Shen, et al.

Acknowledgments [23]

This work described in paper is supported by the National Natural Science Foundation of China (Project 51478158) and the New Century Excellent Talents in University (Project NCET-12-0838), which is greatly appreciated. The authors would also like to acknowledge the assistance of Mr. Wei Wang, Dr. Xuebei Pan and Beibei Li of Hefei University of Technology. The authors have declared that no conflict of interest exists.

[24] [25] [26]

References

[27]

[1] J.F. Wang, Q.H. Shen, Numerical analysis and design of thin-walled RECFST stub columns under axial compression, Thin-Walled Struct. 129 (2018) 166–182. [2] Q.H. Shen, J.F. Wang, W.Q. Wang, Z.B. Wang, Performance and design of eccentrically-loaded concrete-filled round-ended elliptical hollow section stub columns, J. Constr. Steel Res. 150 (2018) 99–114. [3] J.F. Wang, F.Q. Wang, Q.H. Shen, Numerical modelling and design recommendation of axially-loaded thin-walled RCFST slender column, Thin-Walled Struct. 135 (2019) 210–226. [4] F.X. Ding, G.A. Yin, L.Z. Jiang, Y. Bai, Composite frame of circular CFST column to steel-concrete composite beam under lateral cyclic loading, Thin-Walled Struct. 122 (2018) 137–146. [5] Z.B. Wang, Z. Tao, Q. Yu, Axial compressive behaviour of concrete-filled doubletube stub columns with stiffeners, Thin-Walled Struct. 120 (2017) 91–104. [6] Y.X. Hua, L.H. Han, Q.L. Wang, C. Hou, Behaviour of square CFST beam-columns under combined sustained load and corrosion: Experiments, Thin-Walled Struct. 136 (2019) 353–366. [7] R. Wang, L.H. Han, Z. Tao, Behaviour of FRP-concrete-steel double skin tubular members under lateral impact: experimental study, Thin-Walled Struct. 95 (2015) 363–373. [8] Z.B. Wang, Q. Yu, Z. Tao, Behaviour of CFRP externally-reinforced circular CFST members under combined tension and bending, J. Constr. Steel Res. 106 (3) (2015) 122–137. [9] J.J. Zeng, Y.C. Guo, W.Y. Gao, J.Z. Li, J.H. Xie, Behaviour of partially and fully FRPconfined circularized square columns under axial compression, Constr. Build. Mater. 152 (2017) 319–332. [10] Z. Tao, J.G. Teng, L.H. Han, L. Lam, Experimental Behaviour of FRP-Confined Slender RC Columns under Eccentric Loading, Advanced Polymer Composites for Structural Applications in Construction, (2004), pp. 203–212. [11] J.B. Mander, M.J.N. Priestley, R. Park, Theoretical stress-strain model for confined concrete, J. Struct. Eng. 114 (8) (1988) 1804–1823. [12] J.P. Liu, T.X. Xu, Y.H. Wang, Y. Guo, Axial behaviour of circular steel tubed concrete stub columns confined by CFRP materials, Constr. Build. Mater. 168 (2018) 221–231. [13] C.X. Dong, A.K.H. Hwan, J.C.M. Ho, A constitutive model for predicting the lateral strain of confined concrete, Eng. Struct. 91 (2015) 155–166. [14] M.H. Lai, J.C.M. Ho, Confinement effect of ring-confined concrete-filled-steel-tube columns under uni-axial load, Eng. Struct. 67 (2014) 123–141. [15] M.H. Lai, J.C.M. Ho, A theoretical axial stress-strain model for concrete-filled-steeltube columns, Eng. Struct. 125 (2016) 124–143. [16] Q.L. Wang, Z. Zhao, Y.B. Shao, Q.L. Li, Static behavior of axially compressed square concrete filled CFRP-steel tubular (S-CF-CFRP-ST) columns with moderate slenderness, Thin-Walled Struct. 110 (2017) 106–122. [17] K.K. Choi, Y. Xiao, Analytical model of circular CFRP confined concrete-filled steel tubular columns under axial compression, Journal of Composite for Construction, ASCE 14 (1) (2010) 125–133. [18] Z. Tao, L.H. Han, J.P. Zhuang, Axial loading behaviour of CFRP strengthened concrete-filled steel tubular stub columns, Adv. Struct. Eng. 10 (1) (2007) 37–46. [19] N. Li, Y.Y. Lu, S. Li, L. Liu, Slenderness effects on concrete-filled steel tube columns confined with CFRP, J. Constr. Steel Res. 143 (2018) 110–118. [20] C.X. Dong, A.K.H. Kwan, J.C.M. Ho, Axial and lateral stress-strain model for concrete-filled steel tubes with FRP jackets, Eng. Struct. 126 (2016) 365–378. [21] F.X. Ding, D.R. Lu, Y. Bai, Y.Z. Gong, Z.W. Yu, M. Ni, W. Li, Behaviour of CFRPconfined concrete-filled circular steel tube stub columns under axial loading, ThinWalled Struct. 125 (2018) 107–118. [22] A.W.A. Zand, W.H.W. Badaruzzaman, A.A. Mutalib, S.J. Hilo, The enhanced

[28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48]

14

performance of CFST beams using different strengthening schemes involving unidirectional CFRP sheets: an experimental study, Eng. Struct. 128 (2016) 184–198. A.W.A. Zand, W.H.W. Badaruzzaman, A.A. Mutalib, S.J. Hilo, Rehabilitation and strengthening of high-strength rectangular CFST beams using a partial wrapping scheme of CFRP sheets: experimental and numerical study, Thin-Walled Struct. 114 (2017) 80–91. R. Feng, Y. Chen, J.G. Wei, J.Y. Huang, J.F. Huang, K. He, Experimental and numerical investigations on flexural behaviour of CFRP reinforced concrete-filled stainless CHS tubes, Eng. Struct. 156 (2018) 305–321. M.C. Sundarraja, G.G. Prabhu, Finite element modeling of CFRP jacketed CFST members under flexural loading, Thin-Walled Struct. 49 (2011) 1483–1491. Q.H. Shen, J.F. Wang, J.X. Wang, Z.D. Ding, Axial compressive performance of circular CFST columns partially wrapped by carbon FRP, J. Constr. Steel Res. 155 (2019) 90–106. Y. Chen, K. Wang, K. He, J.G. Wei, J. Wan, Compressive behavior of CFRP-confined post heated square CFST stub columns, Thin-Walled Struct. 127 (2018) 434–445. Z. Tao, L.H. Han, Behaviour of fire-exposed concrete-filled steel tubular beam columns repaired with CFRP wraps, Thin-Walled Struct. 45 (2007) 63–76. Z. Tao, L.H. Han, J.P. Zhuang, Cyclic performance of fire-damaged concrete-filled steel tubular beam-columns repaired with CFRP wraps, J. Constr. Steel Res. 64 (2008) 37–50. T. Yu, Y.M. Hu, J.G. Teng, Cyclic lateral response of FRP-confined circular concretefilled steel tubular columns, J. Constr. Steel Res. 124 (2016) 12–22. M.I. Alam, S. Fawzia, X.L. Zhao, A.M. Remennikov, M.R. Bambach, M. Elchalakani, Performance and dynamic behaviour of FRP strengthened CFST members subjected to lateral impact, Eng. Struct. 147 (2017) 160–176. M.I. Alam, S. Fawzia, X.M. Liu, Effect of bond length on the behaviour of CFRP strengthened concrete-filled steel tubes under transverse impact, Compos. Struct. 132 (2015) 898–914. A.S. Shakir, Z.W. Guan, S.W. Jones, Lateral impact response of the concrete filled steel tube columns with and without CFRP strengthening, Eng. Struct. 116 (2016) 148–162. G.G. Prabhu, M.C. Sundarraja, Y.Y. Kim, Compressive behavior of circular CFST columns externally reinforced using CFRp composites, Thin-Walled Struct. 87 (2015) 139–148. G.G. Prabhu, M.C. Sundarraja, Behaviour of concrete filled steel tubular (CFST) short columns externally reinforced using CFRP strips composite, Constr. Build. Mater. 47 (2013) 1362–1371. J.F. Wang, Q.H. Shen, F.Q. Wang, W. Wei, Experimental and analytical studies on CFRP strengthened circular thin-walled CFST stub columns under eccentric compression, Thin-Walled Struct. 127 (2018) 102–119. L.H. Han, Concrete Filled Steel Tubular Structures—Theory and Practice, third ed., Science Press, Beijing, 2016 (in Chinese). H. Yang, F.Q. Liu, T.M. Chan, W. Wang, Behaviours of concrete-filled cold-formed elliptical hollow section beam-columns with varying aspect ratios, Thin-Walled Struct. 120 (2017) 9–28. J.F. Wang, Q.H. Shen, H. Jiang, X.B. Pan, Analysis and design of elliptical concretefilled thin-walled steel stub columns under axial compression, International Journal of Steel Structures 18 (2018) 365–380. F.Q. Liu, Y.Y. Wang, T.M. Chan, Behaviour of Concrete-Filled Cold-Formed Elliptical Hollow Sections with Varying Aspect Ratios, Thin Walled Struct. 110 (2017) 47–61. F.C. Wang, L.H. Han, Analytical behavior of special-shaped CFST stub columns under axial compression, Thin-Walled Struct. 129 (2018) 404–417. J.G. Teng, Y.M. Hu, T. Yu, Stress-strain model for concrete in FRP-confined steel tubular columns, Eng. Struct. 49 (2013) 156–167. Y.M. Hu, T. Yu, J.G. Teng, FRP-confined circular cocnretet-filled thin steel tubes under axial compression, J. Compos. Constr. 15 (5) (2011) 850–860. T. Yu, B. Zhang, Y.B. Cao, J.G. Teng, Behaviour of hybrid FRP-concrete-steel double-skin tubular columns subjected to cyclic axial compression, Thin-Walled Struct. 61 (2012) 196–203. AS4100-1998, Steel Structures, Standards Australia, Sydney, 1998. Eurocode 4, Design of Composite Steel and Concrete Structures-Part 1-1: General Rules and Rules for buildings.1994-1-1:2004, CEN, Brussels, 2004. F.E. Richard, A. Brandtzaeg, R.L. Brown, The Failure of Plain and Spirally Reinforced Concrete under Combined Compressive Stresses. Bulletin 190, University of Illinois Engineering Experimental Station, Champaign, 1929. Q. Yu, reportBehaviors of FRP-Confined Concrete Columns, Dissertation for the Master Degree in Engineering, Harbin Institute of Technology (in Chinese).