Experimental Investigation and Design of Hollow Section, Centrifugal Concrete-Filled GFRP Tube Columns

Abstract

The compressive response of hollow section, centrifugal concrete-filled GFRP tube (HS-CFGT) members is examined experimentally and reported analytically in this paper. A total of 17 specimens separated into two groups were tested; the specimens in each group were of four different lengths and included thirteen straight columns and four tapered columns. The details of the test rigs, procedures as well as key test observations composed of ultimate-moment capacities, load-displacement curves, and failure modes were truthfully reported. The test results were analyzed to evaluate the influence of initial eccentricity on the structural performance. Therefore, the aim of this paper is: (1) to propose a proper coefficient, φ_e, reflecting the effect of initial eccentricity based on the Chinese design code; and (2) to determine a new confinement coefficient, k_cc = 1.10, for centrifugal concrete confined by GFRP tubes. Comparisons of the present design codes and specifications of confined concrete members with test results on 17 full-scale tube columns are also presented. Accordingly, new design equations, whose predictions generally agree well with the test results, are recommended to estimate the compressive capacity of the proposed HS-CFGT columns.

1. Introduction

Hollow section concrete columns have been used for off-shore structural columns, bridge piers, and electric poles due to their enhanced service performance, higher bending stiffness, and higher strength–weight ratios than solid section concrete columns [1,2,3,4,5,6,7,8]. In addition, due to the efficient utilization of materials, hollow section columns are of low cost and have internal space, thereby leading to an efficient construction system. The centrifugal technique has been used for concrete electric poles for many years. Thin-walled concrete-filled steel tubes have also been proposed and investigated [9,10]. With declining urban land resources, electric poles possessing an insulation property are needed, which means that the steel elements such as steel tubes and reinforcing bars should be avoided.

A novel type of electric pole, namely the hollow section concrete-filled GFRP tube (HS-CFGT), formed by concrete centrifugation in a GFRP tube, is proposed in this study. Compared with traditional concrete poles, it is much more advantageous: (1) GFRP tubes can be used as a concrete formwork in the fabricating stage; (2) GFRP tubes have excellent corrosion resistance and no cracking problems. There is also no previous steel corrosion problems owing to the absence of reinforcing bars embedded in the concrete; (3) HS-CFGT is lightweight and therefore is easy to transport, especially suitable for post-disaster reconstruction; (4) Since there is no steel reinforcement, the HS-CFGT is insulated, which avoids the problems of pollution flashover, lightning flashover, and wind flashover on overhead lines. The gear span of the transmission line could be significantly reduced, which would result in the minimization of urban land occupation. Moreover, there is a broad prospect for its application, as the cost of urban land occupation is much more expensive than that of producing electric poles.

Hollow section concrete tube columns are generally made by means of centrifugal technology. Thus, they possess several advantages, including saving time and labor costs, higher concrete quality, higher mechanization, and automation. During the last two decades, the structural behavior of centrifugal concrete members have been studied by scholars around the world [11,12,13,14,15,16,17,18,19]. Liu and Chen [11] developed a computer model to cover the full range of a progressive failure analysis of reinforced concrete tube columns and presented a proper stress–strain relationship for centrifugal concrete based on 39 column tests. Zhao et al. [15] described the compressive behavior of circular, hollow, centrifugal concrete-filled steel tubular short columns and proposed a new confinement coefficient reflecting the confinement effect of concrete strength. Zhang et al. [17] studied the structural behavior of precast, high-strength, centrifugal concrete tube columns, including failure modes, hysteresis behavior, and bearing capacity. However, due to the limited amount of research on hollow section centrifugal concrete-filled GFRP tube columns, they have almost no influence on the development of appropriate design formulae for current international standards, as well as on the effect of initial eccentricity.

Concrete-filled FRP columns have been extensively studied. During the last two decades, the effect of design parameters, including the manufacturing method of FRP tubes [5,6], the inner to outer diameter (i/o) ratio [20], section types [21], volumetric ratio (ρ_v) [22], concrete compressive strength (f_c′) [23], FRP tube thickness (t_f) [24], and slenderness effect (λ) [25,26,27,28] were studied for concrete-filled FRP tubes in order to predict the confined concrete compressive strength. However, few studies were focused on the centrifugal concrete-filled FRP tubes. In addition, stress–strain models of confined concrete were developed mainly for short, normal strength concrete and solid section columns confined with FRP jackets by different guidelines [29,30,31]. Moreover, these confinement models are not completely applicable to hollow section concrete columns strengthened by GFRP tubes that had been formed by a centrifugal technique, which are essentially partially filled columns.

Although bending is the dominant loading case for electric poles, the design of compressive capacity is still basic in engineering application. Understanding the axial compression behavior of HS-CFGTs (Figure 1) is fundamental for gaining an improved understanding of the behavior of hollow section concrete columns and for facilitating the wider structural application of FRP. In this paper, column tests on HS-CFGTs were conducted. Emphasis is placed on the proposed coefficient that reflects the effect of initial eccentricity and a new confinement coefficient of centrifugal concrete confined by GFRP tubes. Furthermore, comparisons of the present design codes and specifications with those of the experiment are presented. Finally, design equations for predicting the ultimate bearing capacity based on the test results are proposed.

2. Test Program

2.1. Test Specimens

Two series of column specimens were designed to examine the compressive performance of the proposed HS-CFGTs, including 13 straight test specimens and 4 tapered test specimens. A total of 13 HS-CFGT straight columns in four different lengths, namely 600 mm, 2000 mm, 3000 mm, and 4000 mm, were prepared in the first test group. Their measured geometrical dimensions are shown in

Table 1. Measured geometric dimensions and test results for straight HS-CFGT column specimens.

Specimen ID	L (mm)	Dtop (mm)	Dbottom (mm)	tf (mm)	tc (mm)	(ei)exp (mm)	(eu)exp (mm)	(eu)exp/ (ei)exp	Pu (kN)	εu	Failure Mode
G600-A	602	300	300	3.0	28.4	13.5	21	1.556	1992	0.0076	CCa
G600-B	601	300	300	3.0	30.1	13.4	26	1.940	2027	0.0076	CC
G600-C	597	300	300	2.8	30.0	0	2	---	2097	0.0085	CC
G600-D	589	300	300	3.1	32.0	1.3	11	1.183	2185	0.0094	CC
G2000-A	2000	300	300	3.0	32.0	8.0	13	1.625	2098	0.0038	CC
G2000-B	2000	300	300	3.0	30.1	5.5	12	2.182	2260	0.0038	CC
G2000-C	2000	300	300	3.1	32.1	5.1	11	2.157	2308	0.0037	CC
G3000-A	3005	300	300	3.1	30.0	7.1	23	3.239	1417	0.0032	CC
G3000-B	2997	300	300	3.1	31.1	7.2	21	2.917	1569	0.0042	CC
G3000-C	3001	300	300	3.0	31.2	5.6	49	5.179	1600	0.0034	CC
G4000-A	4005	300	300	3.1	31.2	10.8	67	6.204	1449	0.0027	CC
G4000-B	4003	300	300	3.0	32.3	10.7	64	5.981	1461	0.0022	CC
G4000-C	4001	300	300	2.9	32.0	12.2	49	4.016	1595	0.0030	CC

CC^a = crushed concrete.

, where L is the length of the specimen, t_f and t_c are the thickness of the external GFRP tube and the internal concrete tube, respectively (as shown in Figure 1).

The second test group comprised four tapered HS-CFGT columns, with each column being of a different length: 600 mm, 1200 mm, 2000 mm, and 3000 mm. The columns had the consistent taper angle γ along the length (as shown in Figure 2), with the inner concrete and outer GFRP tubes symmetrically centered without changing their thickness. The primary measured specimen parameters are summarized in

Table 2. Measured geometric dimensions and test results for tapered HS-CFGT column specimens.

Specimen ID	L (mm)	Dtop (mm)	Dbottom (mm)	tf (mm)	tc (mm)	(ei)exp (mm)	(eu)exp (mm)	(eu)exp/ (ei)exp	γ	Pu (kN)	εu	Failure Mode
GT600-A	602	300	308	3.5	30.0	5.1	9.6	1.882	0.38°	2131	0.0099	CC
GT1200-A	1200	300	316	3.5	30.0	0.0	0.5	---	0.38°	2524	0.0065	CC
GT2000-A	2000	300	327	3.5	30.1	1.2	3.3	2.750	0.38°	2244	0.0040	CC
GT3000-A	3001	300	340	3.4	30.1	4.4	6.0	1.364	0.38°	2527	0.0030	CC

, where D_top is the diameter of the measured cross section of a column at its smallest end, while D_bottom is that of a column at the biggest end (see Figure 1 and Figure 2). Noticeably, D_top and D_bottom for the straight columns in the first test group are equal.

The thickness of the hollow-core concrete tube and the GFRP tube is presented both in Table 1 and Table 2. It is worth mentioning that the thickness t_f and t_c are the average measured thickness at different sections along the length; this is because each specimen group section varied slightly along their length due to the centrifugal techniques. The labelling system for specimens begins with ‘G’ or ‘GT’, which respectively represent straight or tapered GFRP-tube testing specimens, followed by a number ‘600′, ‘1200′, ‘2000′, ‘3000′, or ‘4000′ to signify their length, and the suffix letter differentiating the specimen from the group filled with the same length.

2.2. Material Properties

The specimens were fabricated by casting concrete into preformed circular GFRP tubes. GFRP tubes were prepared using a manual wet layup process that involved wrapping unsaturated polyester resin-impregnated fiber sheets around precision-cut templates. The unsaturated polyester resin was allowed to cure at standard temperature for at least 24 h before the GFRP tubes were removed from their molds. All these tubes were manufactured from unidirectional sheets. Their properties, which include the Young’s modulus E_f and the tensile strength f_fu, are provided by the manufacturer and are shown in

Table 3. Material properties of GFRP.

Tube Type	Nominal Thickness (mm)	Stacking Sequence	Efl (GPa)	fflt (MPa)	Fflc (MPa)	Efh (GPa)	ffht (MPa)
GFRP	3	(89°)	36.9	731	232	9.3	55
GFRP	3.5	(89°)	37.2	731	232	9.6	56

. In addition, the material properties of the GFRP composites were established through flat coupon tests, in accordance with Chinese standard GB/T 31,539 (2015) [32].

As verified, the high-performance concrete possesses superior compressive strength, bending resistance, and fracture resistance compared to ordinary concrete grades; reactive powder concrete (RPC) was also employed in the studied HS-CFGT specimens. The mixing proportions of concrete infill used in these test samples are shown in

Table 4. Concrete mix design.

fcu (MPa)	Mix Proportions (Relative to the Weight of 525 Cement)
	Cement	Water	Superfine Cement	1μm Quartz Powder	2.5 mm Quartz Sand	0.5 mm Quartz Sand	SFb	SPc
120	1.0	0.28	0.25	0.38	1.56	0.18	0.32	0.010

SF^b = silica fume; SP^c = superplasticizer.

. The measured strengths of the mixed concrete, whose properties were obtained by concrete cube tests, were 120 MPa.

2.3. Specimen Preparation

In this preparation process, particular attention is paid to the HS-CFGT column specimens. First, RPC is placed in a steel mold and centrifugally stirred to form a hollow-core concrete tube, and then the precast GFRP tube is used to wrap the concrete tube to obtain the electric pole, as shown in Figure 2. In addition, when fabricating the tapered columns, the steel mold is set with a taper ratio γ = 0.38°. With respect to the characteristics of transmission-line columns under load conditions, the traditional concrete poles are usually formed by centrifugal process, which is not only able to reduce the dead weight, but can also help to improve the compactness of the concrete. The same centrifugal device was used to fabricate the other HS-CFGT specimens. The steam curing process in the centrifugal technique is favorable to curing the RPC.

2.4. Test Setup and Instrumentation

A total of 17 column tests on the HS-CFGT specimens were carried out in this study. A servo-controlled hydraulic-testing machine with a 10,000 kN capacity was used to apply axial compressive force to the specimens. The typical HS-CFGT column test setups are illustrated in Figure 3a. A variable diameter support (see Figure 3c) was clamped near each end of the specimen with a circular outer tube in order to prevent an ‘elephant foot’ failure caused by test end effects. Small gaps on the top surface of the concrete arose due to concrete shrinkage, which was filled by a thin layer (<1 mm) of plaster. An initial load of approximately 2 kN was then applied to the top surface until the plaster hardened. This ensured that the load was simultaneously applied across the whole cross section. Load control was adopted to drive the actuator since it could allow the test to be continued beyond the ultimate load.

The axial displacement δ of testing columns was measured by two 50 mm range linear variable differential transformers (LVDTs) arranged at the upper end of the testing machine and in the same position near the platen. The layout of the LVDTs and strain gauges for all specimens is illustrated in Figure 3b. In addition, a dial displacement gauge was arranged at the mid span of the columns, with lengths of 3000 mm and 4000 mm, in order to obtain the lateral deformation for the longer series. Meanwhile, localized strain developments were monitored by strain gauges attached at the selected position of the specimens. For specimens with lengths of 600 mm and 1200 mm, four pairs of strain gauges were attached at the mid length of the column and evenly around the outer tube, where each pair respectively affixed to the longitudinal and transverse directions. For specimens with lengths of 2000, 3000, and 4000 mm, 12 strain gauges were separately attached at points that were 1/4, 1/2, and 3/4 of the column length, while each pair was affixed to the two orthogonal directions and around the tube, as the former. The strain gauge readings were also used to eliminate the elastic deformation of the end platens from the end-shortening measurements of the LVDTs, and to determine the true average axial strain values.

3. Test Results and Discussion

3.1. Failure Modes

The typical failure modes of test specimens are shown in Figure 4 and Figure 5. Similar failure modes were observed for both straight and tapered HS-CFGT columns. The HS-CFGT columns, which were subjected to compressive loading, showed an initial behavior similar to that of solid CFFT columns. The early loading stage observed neither obvious damage nor slight crack along the column height. Then, the straight specimens as well as the tapered ones almost remained in a straight line and seemed to have no observed lateral deformation, keeping their cross section flat. Eventually, The HS-CFGT columns failed when the load reached the peak point, with the GFRP outward deformation occurring simultaneously, near the top end of the tapered columns and both the two ends of the straight columns (see Figure 4 and Figure 5).

3.2. Ultimate Condition

The ultimate condition of each specimen, which consists of the ultimate compressive strength (P_u) recorded upon failure of the specimen and the corresponding axial strain (ε_u), is reported in Table 1 and Table 2. Figure 6 presents the representative load–axial displacement relationships of straight column specimens, while Figure 7 depicts the load–axial displacement relationships of tapered specimens. The load–axial displacement relationship contains an ascending branch so that the ultimate strength (P_u) is the maximum strength, as reported in Table 1 and Table 2. The ultimate axial strain (ε_u) of each specimen is the measured strain corresponding to the ultimate strength. It is shown that the ultimate axial strain decreases with the increasing column lengths, which may indicate that the strengths of the materials used also decreased.

3.3. Axial Load–Axial Displacement Behavior

Figure 6 depicts the load–axial displacement curves of the straight HS-CFGT columns. The axial displacements here are the average values of the LVDT readings. The pictures illustrate the influence of the column length on the bearing capacity of the tested members, which demonstrates that the longer the length of the column, the smaller the ultimate load it could have. In other words, as the length of the straight specimens increases, the bearing capacity of these specimens may decrease.

Figure 7 depicts the load–axial displacement curves of the tapered HS-CFGT columns and illustrates the influence of the column length on the bearing capacity of the testing members. As the tapered column length increases, their bearing capacity does not decrease as obviously as that of straight members; that is, the effect of column length on tapered members is not as much as that on straight members. At the same time, upon comparison of straight columns and tapered columns with the same lengths, the ultimate bearing capacity of tapered columns is higher than that of straight columns.

When comparing the bearing capacity of specimens between G600 and G2000 in Figure 6, their differences are not significant. When comparing that of G2000, G3000, and G4000, the bearing capacity of the compressive columns evidently decreases as their length increases. One probable reason for the phenomenon above is that the overall buckling of the long column reduced the bearing capacity of the columns. Another foreseeable factor is the initial eccentricity e_i, which results from the theoretical geometric center of the component A₁ and the actual geometric center of the component A₂ due to the uneven thickness of the concrete tube by the existing centrifugal technology, as shown in Figure 8. There is distance between the geometric center of the column section and the centers of the GFRP tube section (loading point). That is, there is an initial eccentricity for the column section, as shown in Figure 9, which leads to the decrease of the column’s bearing capacity when it is subjected to compression. In the elastic stage of loading, the initial eccentricity (e_i)_exp of the specimen is obtained according to the deviation of the axial displacement count in LVDT readings, and the ultimate eccentricity (e_u)_exp is obtained from LVDT readings corresponding to the ultimate strength. The ratio of (e_u)_exp/(e_i)_exp indicates the eccentricity of loading. The measured initial eccentricity (e_i)_exp, the ultimate eccentricity (e_u)_exp, and the loading eccentricity of both the straight and tapered specimens are summarized in Table 1 and Table 2, respectively.

In the loading process of the straight specimen, the initial loading eccentricity generally increased. This trend becomes clearer as the column length increases, indicating that the development of loading eccentricity is much more considerable for longer straight columns (3000 mm and 4000 mm). Compared with straight specimens, the initial eccentricity and ultimate eccentricity of tapered columns are significantly smaller and their loading eccentricity is much closer, which indicates that the development of loading eccentricity for tapered specimens is slower than it is for straight ones.

3.4. Axial Load–Axial Strain Behavior

Figure 10 depicts the load–axial strain curves of the straight specimens, while Figure 11 presents the load–strain curves of the tapered specimens. They illustrate the change law of the axial strain of the short column and the long column. Here, the axial strain in Figure 10 and Figure 11 is the average value of the vertical strain gauges attached to the columns. With the increase of the member length, the ultimate axial strain of the straight specimen decreased significantly, implying that the ultimate stress and corresponding compressive strength decreased accordingly. Additionally, the curves of the tapered columns exhibited a similar trend to that of their straight counterparts.

3.5. Axial Load–Lateral Deflection Behavior

Figure 12 depicts the load–lateral deflection curves of the straight test members and illustrates the influence of the specimen length on the lateral deflection. The lateral deflection was obtained from readings of the horizontal LVDTs for specimens with lengths of 3000 and 4000 mm and by comparing G3000-A, G3000-B, G4000-A, and G4000-C. It was found that as the specimen length increased, the lateral displacement exhibited no obvious difference. It is also visible that the maximum lateral deflection value is even less than the initial eccentricity value, which reveals that initial eccentricity has more considerable influence on column strength than on column length in this study.

3.6. Effect of Initial Eccentricity

The uneven thickness of the concrete caused by the centrifugal technique resulted in the loading eccentricity, which ranged from 0 to 13.5 mm in this work, as shown in Table 1 and Table 2. Generally, it measured value increases following not only the lengthening column, but also the increasing load. The value of ultimate eccentricity divides initial eccentricity (e_u)_exp/(e_i)_exp (see Table 1 and Table 2), which fairly increases with the column length and is typical in straight column specimens, as shown in Figure 13. In addition, since the loading eccentricity brings an extra bending moment to the column section, the longer column at the ultimate condition is much more likely to fail, as a beam column does. In this case, the effect of initial eccentricity should be carefully considered in the design of ultimate strengths.

4. Design Methods

The existing international design criteria for concrete-filled composite structures, as presented in DL/T 5030 [29], AASHTO [30], and ACI 440.2R [31], are evaluated to predict the bearing capacity of HS-CFGT columns. Although those standards do not correspond to HS-CFGTs, their applicability were first evaluated. The expressions of three design codes and specifications are presented in the following sections. More details can be found in [29,30,31]. The estimation was based on the measured geometric dimensions and material properties of the test specimens, and the safety factor was set to unity.

4.1. DL/T 5030 Technical Code

The DL/T 5030 technical code is for centrifugal, concrete-filled, thin-wall steel tubular structures, and it uses the design equations for both straight and tapered columns, as expressed in following equations:

$$N_u={\phi }_l{\phi }_{\mathrm{e}}(A_{\mathrm{s}}{f}_y+1.3A_c{f}_{\mathrm{c}}^{\prime })$$

(1)

$${\phi }_l=\frac{1-0.011\sqrt{\frac{L_e}{D}-8}}{1+0.00135{(\frac{L_e}{D}-8)}^2}$$

(2)

$${\phi }_{\mathrm{e}}=\frac{1+0.14\frac{e_i}{D}}{1+2.3\frac{e_i}{D}+4(0.2+0.23\frac{1.3A_c{f}_c^{\prime }}{A_s{f}_y}){(\frac{e_i}{D})}^2}$$

(3)

where φ_l is a reduction factor considering the effect of slenderness; φ_e is a reduction factor considering the effect of initial eccentricity; L_e is the effective length of the column; D is the outer diameter of the steel tube and is equal to D_top in this study; A_s is the area of the steel tube and is equal to A_f in this study; f_y is the yield strength of steel and is equal to f_flc in this study.

The confinement effect of steel tubes on concrete was considered as 30% enhancement of concrete compressive strength. Furthermore, effect of initial eccentricity was also considered in the design equations. When compared to the experimental results, the prediction value N_1pred of the DL/T 5030 [29] predictions are non-conservative, showing that the mean ratio of N_u,test/N_DL/T for straight members is equal to 0.64, and the mean ratio for tapered members is equal to 0.77, respectively (as presented in

Table 5. Comparisons between theoretical predictions and experimental results of straight members.

Specimen ID	Nu,test (kN)	NDL/T (kNm)	Nu,test/ NDL/T	NAAS (kNm)	Nu,test/ NAAS	NACI (kNm)	Nu,test/ NACI	Nprop (kNm)	Nu,test/ Nprop
G600-A	1992	2662	0.75	2231	0.89	1396	1.43	1983	1.00
G600-B	2027	2773	0.73	2338	0.87	1470	1.38	2087	0.97
G600-C	2097	3050	0.69	2361	0.89	1473	1.42	2082	1.01
G600-D	2185	3183	0.69	2473	0.88	1550	1.41	2191	1.00
G2000-A	2098	3012	0.70	2332	0.90	1466	1.43	1985	1.06
G2000-B	2260	2940	0.77	2338	0.97	1470	1.54	1911	1.18
G2000-C	2308	3103	0.74	2479	0.93	1555	1.48	2007	1.15
G3000-A	1417	2857	0.50	2349	0.60	1465	0.97	1716	0.83
G3000-B	1569	2927	0.54	2417	0.65	1512	1.04	1753	0.90
G3000-C	1600	2949	0.54	2406	0.67	1517	1.05	1737	0.92
G4000-A	1449	2823	0.51	2424	0.60	1516	0.96	1563	0.93
G4000-B	1461	2750	0.53	2350	0.62	1479	0.99	1520	0.96
G4000-C	1595	2808	0.57	2444	0.65	1553	1.03	1542	1.03
Mean			0.64		0.78		1.24		1.00
Cov			0.100		0.139		0.221		0.093

Note: N_DL/T, N_AAS, N_ACI, and N_prop represent the predictions proposed by DL/T 5030 [29], AASHTO [30], ACI 440.2R [31], and the present study, respectively.

and

Table 6. Comparisons between theoretical predictions and experimental results of tapered members.

Specimen ID	Nu,test (kN)	NDL/T (kNm)	Nu,test/ NDL/T	Nprop (kNm)	Nu,test/ Nprop
GT600-A	2131	3036	0.70	2421	0.88
GT1200-A	2524	3150	0.80	2393	1.05
GT2000-A	2244	3130	0.72	2357	0.95
GT3000-A	2527	2976	0.85	2241	1.13
Mean			0.77		1.00
Cov			0.061		0.095

). That is to say, those coefficients in the design equations validated against steel tubular columns may be inapplicable to GFRP tubular columns.

4.2. AASHTO Guide Specifications

AASHTO [30] provides the design equations for Concrete-Filled FRP tubes with straight axial members, as expressed in following equations:

$$N_n=\frac{\pi D_i^2}{4}0.85f_{cc}^{\prime }+\pi D{t}_f{E}_{fl}{\epsilon }_{ccu}$$

(4)

$$f_{cc}^{\prime }=f_{co}^{\prime }+3.3{\psi }_f{f}_l$$

(5)

$$f_l=\frac{2E_{fh}t{\epsilon }_{fe}}{D}$$

(6)

$${\epsilon }_{ccu}={\epsilon }_c^{\prime }[1.5+12\frac{f_l}{f_{co}^{\prime }}{(\frac{{\epsilon }_{fe}}{{\epsilon }_c^{\prime }})}^{0.45}]$$

(7)

$${\epsilon }_c^{\prime }=(\frac{f_{co}^{\prime }}{E_c})(\frac{n}{n-1})$$

(8)

$$n=0.8+\frac{f_c^{\prime }}{2.5}$$

(9)

$$E_c=1265\sqrt{f_c^{\prime }}+1000$$

(10)

where D_i is the inner diameter of the FRP tube; E_fl is the design longitudinal tensile modulus of the tube; ψ_f is a reduction factor equal to 0.95; ε_fe is the effective strain in the tube at the ultimate compressive capacity of the CFFT; E_fh is the design modulus of the tube in the hoop direction; E_c is the elastic modulus of concrete; f_cc^′ is the confined concrete strength; f_l is the confinement pressure; f_co^′ is the cylinder concrete strength and for high-strength concrete f_co^′ = f_c^′.

Both the factors of concrete strength and FRP tubes are considered in these equations. The predicted value N_AAS of AASHTO [30] yielded rather unsafe and scattered axial compressive resistance predictions for straight members, showing the mean ratio of N_u,test/N_AAS equal to 0.78 and COV equal to 0.139, as presented in Table 5. Since the design equations in AASHTO [30] are appropriate for solid section concrete-filled FRP tubes, the confinement effect of FRP tubes on the concrete strength may be overestimated.

4.3. ACI 440.2R-08 Guide

Chapter 12 of the ACI 440.2R-08 [31] design guidelines for straight members deals with the strengthening of RC members subjected to axial force by FRP jackets. The equations given are strictly advisable for the axial compressive strength of short, solid section, normal weight concrete members confined with an FRP jacket. The approach adopted by the current ACI 440.2R [31] for the maximum confined concrete compressive strength (f_cc^′) is based on a model calculation proposed by Lam and Teng (2003) [33], as expressed in following equations:

$$N_u=\varphi N_n=0.8\varphi [0.85f_{cc}^{\prime }(A_g-A_{st})+f_y{A}_{st}]$$

(11)

$$f_{cc}^{\prime }=f_{co}^{\prime }+{\psi }_{f}3.3{\kappa }_a{f}_l$$

(12)

$$f_l=\frac{2E_{f}n{t}_f{\epsilon }_{fe}}{D}$$

(13)

$${\epsilon }_{fe}={\kappa }_{\epsilon }{\epsilon }_{fu}$$

(14)

where A_g = gross area of the concrete section; A_st = total area of longitudinal reinforcement; κ_ε = efficiency factor equal to 0.55.

It is shown that the prediction value from ACI equations [31] is very conservative, with a mean ratio N_u,test/N_ACI of 1.24 and a corresponding COV of 0.221, as shown in Table 5. The reason for the conservative prediction is that the compressive strength of FRP tubes is neglected in the ACI equations. The contribution of FRP tubes to compressive strength is minor for solid section concrete-filled columns, however, it is not the case for hollow section concrete-filled columns. The reason is that concrete no longer takes up the overwhelming majority of the column section; furthermore, the strength of the enhanced concrete is smaller for hollow section columns compared with their solid section counterparts due to the different confinement effects.

4.4. Proposal Equations

Since the equations in current design rules are not favorable for HS-CFGT columns, it is indispensable to put forward new design equations. Based on the analysis above, the compressive strength of GFRP tubes should be seriously considered in the proposed equations. Thereby, the ultimate capacity (N_u) of HS-CFGT columns could be divided in two terms, i.e., the strength of outer GFRP tubes (N_f) and the strength of hollow concrete tubes (N_c), as shown in Equations (15)–(17).

$$N_u={\phi }_l{\phi }_e[N_f+N_c]$$

(15)

$$N_f=A_f{f}_{fc}$$

(16)

$$N_c=k_{cc}{A}_c{f}_c^{\prime }$$

(17)

Compared with solid section concrete-filled columns, enhanced concrete strength due to the confinement effect is relatively small for hollow section concrete-filled columns. However, the confinement effect should still be considered, and the coefficient k_cc in the equation is the representation. Although Lignola [34] proposed the theoretical model for the strength enhancement of hollow section concrete-filled columns, it needs to undergo an iteration process. There are limited types of cross sections in electric power engineering, therefore, k_cc is calculated here as 1.10, which is the most typical for electric poles.

The effect of initial eccentricity should be seriously considered for hollow section concrete-filled columns. Here, e_i is assigned 400/L, as proposed by EC 2 [35] for initial eccentricity in concrete structure design, owing to the lack of sufficient data about the value nowadays. Equations for straight and tapered HS-CFGT columns are proposed as Equations (18) and (19), respectively, as the effect of initial eccentricity on straight and tapered columns are different. Finally, an equation for the effect of column slender ratio is proposed, as shown in Equation (20). Equations (18)–(20) are similar to the design equations in the DL/T 5030 Technical code and are validated against the test results in this study.

$${\phi }_{e,s}=\frac{0.78+0.07\frac{e_i}{r}}{1+1.15\frac{e_i}{r}+(10.2+22.3\frac{1.1A_c{f}_c^{\prime }}{A_f{f}_{flc}^{}}) {(\frac{e_i}{r})}^2}$$

(18)

$${\phi }_{e,t}=\frac{0.88+0.07\frac{e_i}{r}}{1+1.15\frac{e_i}{r}+(1.2+1.5\frac{1.1A_c{f}_c^{\prime }}{A_f{f}_{flc}^{}}) {(\frac{e_i}{r})}^2}$$

(19)

$${\phi }_l=\{\begin{array}{l}1,if0\le L/D_{top}\le 8\\ \frac{1.2-0.15\sqrt{\frac{L}{D_{top}}-8}}{1+0.002{(\frac{L}{D_{top}}-8)}^2},if8\le L/D_{top}\end{array}$$

(20)

where φ_e is the reduction factor considering the initial eccentricity based on a regression analysis; for straight columns, φ_{e =} φ_e,s; for tapered columns, φ_{e =} φ_e,t, φ_l is the reduction factor for the effect of column slenderness, and r is the outer radius of the GFRP tube, which is equal to D_top/2.

The theoretical prediction employing the proposed forms is compared with the test results of N_u,test in Table 5 and Table 6 for both straight and tapered columns, respectively. The mean ratio of N_u,test/N_prop for straight HS-CFGT columns is 1.00, with its corresponding COV of 0.093, while for tapered HS-CFGT columns the mean ratio and COV of N_u,test/N_prop are 1.00 and 0.095, respectively. It can be seen that the prediction of the proposed equations generally agree well with the test results.

5. Conclusions

In this paper, the axial compressive response of hollow section concrete-filled GFRP tube columns (HS-CFGTs) was studied. A total of 13 straight columns and 4 tapered columns were prepared and tested to failure. Applicability of current design rules for HS-CFGT columns were evaluated against the test results. A new design method was proposed, and its prediction generally agrees with test results well. The test results and discussions have led to the following conclusions:

(1)

The straight HS-CFGTs and tapered HS-CFGTs generally behave in a comparable manner before the GFRP tube failure. The outward deformation of the GFRP tube, which was vulnerable in HS-CFGT columns, controlled the failure mode of both straight and tapered columns.

(2)

The initial imperfection caused by the unevenly thick centrifugal concrete layer, i.e., initial eccentricity should be seriously considered. The initial eccentricity has a considerable effect on the bearing capacity of straight columns, and the longer the member, the more significant the effect.

(3)

As the length of the specimen increases, it is shown that the lateral deflection value is even less than the initial eccentricity, indicating that the initial eccentricity has much more obvious influence than column lengths for columns up to 4000 mm.

(4)

A coefficient (φ_e) that accounts for the initial eccentricity is proposed to predict the ultimate bearing capacity of the HS-CFGTs. A coefficient (φ_l) for the effect of column slenderness is also proposed.

(5)

Current design rules ignore the longitudinal compression capacity of FRP tubes and overestimate the confinement effect of FRP on core concrete. Therefore, it is not completely advisable for the proposed HS-CFGT columns.