Compressive behavior of joint core confined with core steel tube for connection of polyvinyl chloride-carbon fiber reinforced polymer–confined concrete column and reinforced concrete beam

Abstract

The axial compression behavior of a new type of joint wherein the core concrete is confined by a core steel tube while the external concrete is confined by a ring stirrup is investigated in this study. Such a joint core is intended to connect a polyvinyl chloride-carbon fiber reinforced polymer–confined reinforced concrete column and reinforced concrete beam. The failure process and the effects of structural parameters on the mechanical behavior of the joint core are analyzed. Results indicate that the crushing of concrete in the joint core is the predominant failure modes of all specimens. The crack development speed is related to the specimen height and the reinforcement ratio of the core steel tube. The stirrup ratio does not significantly affect the crack development speed but can dominate the crack growth path partially during the crushing of the specimen. In addition, the ultimate bearing capacity of the joint core increases with the decrease in the specimen height, whereas it decreases as the stirrup ratio or reinforcement ratio of core steel tube decreases. Furthermore, a formula for predicting the ultimate bearing capacity of a joint core confined by a core steel tube is proposed based on dimensional analysis associated with the numerical simulations. This study is expected to provide preliminary guideline to facilitate such connection joint cores for structural systems.

Keywords

beam bearing capacity column failure mode joint polyvinyl chloride-fiber reinforced polymer–confined concrete stress–strain relation

Introduction

Brittle failure of joint core of beam–column connections for reinforced concrete (RC) structures may occur if the transverse shear reinforcement of the joint is insufficient or absent (Esmaeeli et al., 2016). Although various types of loading (such as gravity, shear, axial loads, and moment) may be exerted onto the joint and adjoining members of structures, the joint would experience severe axial and lateral loads. Therefore, the premature failure of joints restricts energy dissipation in the formation of plastic hinges, which introduces the risk of disastrous collapse of structures under lateral loading. The strong-joint–weak-member design concept is widely adopted for seismic design as the column–beam joint is crucial in guaranteeing the seismic performance of RC structures. In addition to the sufficient transverse shear resistance in the column–beam joint region, the adequate shear capacity of column is also necessary to avoid the brittle shear failure of RC structures (Ghobarah and Said, 2002).

The mechanical behavior of joint core connecting RC beams and columns with steel tubes has been investigated extensively. Han and Li (2010) conducted cyclic tests on six circular concrete-filled steel tubular (CFST) columns and steel beam joints, including four interior and two exterior joints. Their results showed that the exterior joint exhibited a more severe beam failure than the interior joint. Zhang et al. (2012) used the confinement of a steel cage anchored inside a joint zone and an octagonal ring beam located outside a column to compensate the reduced stiffness of a composite column owing to the interruption of an outer steel tube. Chen et al. (2014) conducted cyclic tests on beam–column specimens with a strengthening ring beam, and those specimens exhibited good seismic performances. To enhance the axial bearing capacity of column-to-beam connections, three different connection-strengthened techniques were designed in the connection zone (Zhou et al., 2017), namely strengthening stirrups (Type A), a tube with rectangular openings (Type B), and horizontal haunches (Type C). The experimental results showed that Type B and Type C connections were effectively strengthened, whereas the Type A connection had to be further strengthened owing to the lower axial bearing capacity compared with those of reference columns. Wang et al. (2015) introduced a type of connection between a CFST column and an RC beam through a transitional RC ring beam encircling the CFST column. Bi-directional cyclic tests highlighted the ductile performance and multidirectional characteristics of the force system. In addition, Tang et al. (2016) proposed a new type of connection between a square CFST column and an RC beam. The connection incorporated a strengthening joint system with a steel cage comprising multilayer steel meshes and radial pattern stirrups to strengthen the joint strength. Accordingly, the favorable seismic performance of such a connection was demonstrated experimentally.

Hitherto, beam–column joints have been limited to RC concrete and CFSTs, and the continuity as well as load-carrying capacities of joint cores have not been well developed. Over the last few decades, fiber-reinforced polymer (FRP) materials have been widely applied to repairing and strengthening activities owing to their high strength, light weight, strong fatigue resistance, and strong corrosion resistance (Eid and Paultre, 2017; Lee et al., 2010; Mohamed and Masmoudi, 2010; Teng et al., 2016; Zhu et al., 2005). Another typical engineering material is polyvinyl chloride (PVC), which is typically utilized in the construction industry as concrete molds or tubes owing to its light weight, low cost, and stable chemical properties (Hameed and Salih, 2011). Moreover, although the ductility of concrete columns can be improved using PVC tubes, the improvement in carrying capacity is not significant owing to the limited strength of PVC (Kurt, 1978). Therefore, PVC–CFRP-confined concrete (PFCC) column, which incorporates the advantages of FRP and PVC, have been extensively studied, for example, its static performance (Fakharifar and Chen, 2016; Toutanji and Saafi, 2002; Yu and Niu, 2010, 2013), seismic performance (Fakharifar and Chen, 2017; Yu et al., 2018), and durability (Toutanji and Saafi, 2001). Therefore, detailed information regarding PFCC columns is available, and a relatively complete research methodology and design system has been established.

However, current studies are primarily focused on the structural responses of individual components of PFCC columns. Studies regarding beam–column joints core are few, and the connection of PFCC columns with beams, which exists in other confined concrete columns (i.e. CFSTs and FRP tubes), has not been elucidated. To solve the connection mode of PFCC beam–column joints, a new joint connection mode of PFCC column and RC beams is proposed herein, in which a steel tube is built in the joint core and ring stirrups with specific spacing are arranged around the steel tube to confine the core concrete (as shown in Figure 1). Consequently, the compressive bearing capacity and shear resistance of the joint core can be improved significantly. In addition, the longitudinal reinforcement in the beams can penetrate the joint core without cutting off, which significantly improves the integrity of the structure and the bearing capacity of the joint core.

Figure 1.

Arrangement of longitudinal bars in column and beam at joint core.

In this study, we aim to investigate the mechanical performance of the aforementioned emerging joint connection of a PFCC column and an RC beam. Seven specimens were designed to investigate the effects of specimen height, stirrup ratio ρ_sv, and reinforcement ratio of core steel tubes α_st on the axial compressive behavior (i.e. failure mode, bearing capacity, ultimate strain, and equivalent stress–strain relationship) of the joint. In addition, a formula for predicting the ultimate bearing capacity of the new joint connection is proposed.

Test program

Fabrication of specimens

Seven specimens composed of the joint core (as shown in Figure 1) were prepared. A core steel tube, ring stirrups, and longitudinal bars were configured in the joint core, as shown in Figure 2. The structural parameters considered in this study were the joint core height h; the stirrup ratio ρ_sv, which is defined as the content of stirrup per unit volume concrete; and the reinforcement ratio of core steel tube α_st, which is defined as the ratio of cross-sectional area of the steel tube and core concrete. The details of the structural designs for all the specimens are summarized in Table 1. The joint core specimens (labeled as C1–C7) have identical diameters of 200 mm, whereas the height was set to three values, that is, 180, 240, and 300 mm. All the specimens were reinforced with eight longitudinal bars of diameter 10 mm. The longitudinal bars were tied with ring stirrups of diameter 6 mm spaced at different distances along the specimen height. Therefore, ρ_sv of 1.18%, 1.71%, and 2.35% were allocated. The skeleton of the seven completed steel reinforcement cages is shown in Figure 3. The outside diameter of the core steel tube was 89 mm, whereas the thicknesses of core steel tube were 4, 6, and 8 mm. Correspondingly, the calculated α_st of the core steel tube were 21%, 34%, and 49%, respectively. The strength grade of the core concrete (as illustrated in Figure 2) was C55, whereas that of the external concrete was C35.

Figure 2.

Geometry and dimension of cross-section of the joint core confined with a core steel tube (units: mm).

Table 1.

Detailed design parameters of the specimens used in the test.

Specimen	h (mm)	D (mm)	t (mm)	Ring stirrup	ρ_sv (%)	α_st (%)
C1	180	200	8	3A6@40	2.35	49
C2	240	200	8	5A6@40	2.35	49
C3	300	200	8	6A6@40	2.35	49
C4	240	200	8	4A6@55	1.71	49
C5	240	200	8	3A6@80	1.18	49
C6	240	200	6	5A6@40	2.35	34
C7	240	200	4	5A6@40	2.35	21

Figure 3.

Illustration of steel reinforcement cages for joint core specimens.

Material properties

Concrete and steel bars

The compressive strength of concrete was determined according to the standard test of cubic standard specimens. Furthermore, the axial compressive strength that is generally applied to design RC structures was obtained by scaling reduction coefficients that are related to the concrete grade. The detailed mechanical properties of the concrete, ring stirrups, and longitudinal bars are summarized in Table 2.

Table 2.

Mechanical properties of the concrete (in compression) and steel bars (in tension).

Material	Axial compressive strength (MPa)	Yield stress (MPa)	Ultimate strength (MPa)	Elastic modulus (MPa)
Concrete (C35)	25.2	–	–	25,100
Concrete (C55)	35.1	–	–	29,600
Ring stirrup	–	291.30	504.30	194,000
Longitudinal bar	–	350.99	553.86	186,000

Core steel tubes

For the core steel tube, it is difficult to directly perform a tensile test on the entire tube to determine its tensile properties of steel tube. In this study, an equivalent method was adopted, in which a standard tensile specimen (GB/T228.1-2010, 2010) was acquired by cutting an original specimen from the core steel tubes. In addition, three different thicknesses of the steel tubes were subjected to axial compression tests to measure the elastic modulus and Poisson’s ratio. The failure modes of the steel tubes with different thicknesses are shown in Figure 4 and the corresponding stress–strain relationship curves are shown in Figure 5. The axial strain denoted ε_sa is the measured axial strain, whereas the lateral strain ε_sl is determined by the measured values. Correspondingly, the stress σ_s is calculated as the ratio of the axial force to the initial cross-sectional area of the steel tube. The strains of the three steel tubes with different wall thicknesses increased linearly at the initial stage of loading. As the load increased, the specimen gradually entered the elastoplastic stage. With a further increase of the load, the local bulge of the steel tube appeared gradually accompanied with a rapid degradation of the load carry capacity. The mechanical properties of the steel tubes obtained from tests are listed in Table 3.

Figure 4.

Failure modes of the steel tubes with wall thicknesses of (a) 4 mm, (b) 6 mm, and (c) 8 mm.

Figure 5.

Stress–strain relationship curves of the steel tubes with wall thicknesses of (a) 4 mm, (b) 6 mm, and (c) 8 mm.

Table 3.

Mechanical properties of the steel tubes.

Material	Thickness (mm)	Yield strength (MPa)	Ultimate strength (MPa)	Elastic modulus (MPa)	Poisson’s ratio
Steel tube	4	328.70	470.16	222,000	0.293
	6	301.37	455.56	199,000	0.326
	8	344.42	581.90	191,000	0.306

Test setup

The specimens were tested using a 5000-kN hydraulic compression machine. The experimental test setup and instrumentation are shown in Figure 6.

Figure 6.

The (a) schematic drawing and the (b) corresponding loading device used in the compression test.

Prior to the test, a small preloading was applied slowly on the specimens; subsequently, the load was removed gradually. During the test, a load interval of 100 kN was used during loading, and each load interval was maintained for approximately 2 min. After each load interval, the load was maintained for approximately 2 min. When the specimen yielded with a significant increase in the strain of the longitudinal bar and core steel tube, a displacement control loading at a constant rate of 0.6 mm/min was initiated. The tests were terminated after the load decreased to 85% of the ultimate bearing capacity.

Two displacement sensors were installed on the loading plate to measure the longitudinal deformation of different specimens, as shown in Figure 6. The average longitudinal deformation was acquired as the mean value of the two displacement sensors.

For joint core specimens (C1–C7), two strain gauges were placed at the middle height of the longitudinal bars located in the hoop direction of 0° and 180°, labeled with numbers 5 and 6 in Figure 7(a) as well as 7 and 8 in Figure 7(b). For specimens (C1, C4, and C5), in which three- and four-layer ring stirrups were arranged in the height direction, four strain gauges were placed on the first and second layers of the ring stirrup along the hoop direction of 0° and 180° owing to the symmetry of the specimens, as shown in Figure 7(a). Similarly, for the specimens (C2, C3, C6, and C7), in which five- and six-layer ring stirrups were arranged in the height direction, six strain gauges were placed on the first three layers of the ring stirrup along the hoop direction of 0° and 180°, as shown in Figure 7(b).

Figure 7.

Arrangement of the strain gauges for ring stirrups and longitudinal bars of the (a) specimens with three- and four-layer ring stirrups (C1, C4, and C5) and of the (b) specimens with five- and six-layer ring stirrups (C2, C3, C6, and C7).

A total of eight transverse and longitudinal strain gauges were placed on the surface of the core steel tube at the middle height to measure the transverse and longitudinal strains of the core steel tube, as shown in Figure 8.

Figure 8.

Schematic diagram of the arrangement of strain gauges for the core steel tube (a) in a front view and (b) in a top view.

Experimental results and analysis

Failure mode

Similar failure modes of all specimens were exhibited except a slight difference in the crack number and the crack growth orientations, as shown in Figure 9. At the early stage of loading, deformation was not evident, and the specimens exhibited an elastic behavior. As the load increased, the external concrete began to crack and the first vertical crack appeared on the side of the specimens. Observation of failure modes of the specimens with different structural parameters indicated the delayed appearance of the first concrete crack when the specimen height or the α_st of the core steel tube was high, whereas ρ_sv did not affect the concrete cracking. Subsequently, crack developed along the longitudinal direction of the specimen. The crack width and number of cracks increased gradually, and lateral short cracks were staggered with vertical cracks that occurred on the side of the specimen.

Figure 9.

Failure modes of seven specimens under axial compression: (a) C1, (b) C2, (c) C3, (d) C4, (e) C5, (f) C6, and (g) C7.

When the load was increased to 85%–90% of the ultimate bearing capacity, the specimen yielded accompanied with a significant increase in strain in the longitudinal bar and core steel tube. Subsequently, displacement control is performed. When the load was increased to the ultimate bearing capacity, the vertical cracks on the side of the specimens (i.e. C2, C5, C6, and C7) penetrated successively along the vertical direction of the specimens. The concrete within specimens (i.e. C1, C3, and C4) were not crushed after failure; however, a large number of vertical cracks and transverse cracks appeared.

Ultimate bearing capacity analysis

During the test, the stirrups, longitudinal bars, and core steel tube of the specimen labeled as C1 did not yield after failure. Specimen C1 was regarded as an unqualified sample owing to the failure of concrete pouring, and the experimental data were not used in the following analysis. Subsequently, some mechanical quantities were defined to evaluate the axial responses of the joints. The cracking load N_cr is defined as the value of the applied load, which initialized axial cracking on the external concrete. The yield load measured as the value corresponding to the turning point on the strain–load curve is denoted as N_y. The ultimate bearing capacity referring to the measured peak load value of specimen is marked as N_u. Correspondingly, ε_a is the axial ultimate strain of the specimen during axial compression. The experimental results of the remaining specimens under axial loading are shown in Table 4.

Table 4.

Experimental results of the load-carrying capacity of the specimens under axial loading.

Specimen	N_cr (kN)	N_y (kN)	N_u (kN)	ε _a
C2	231	1641	1762	0.0136
C3	248	1476	1618	0.0119
C4	228	1559	1694	0.0126
C5	182	1210	1368	0.0087
C6	195	1563	1696	0.0129
C7	171	1453	1586	0.0116

The ultimate bearing capacity of the specimen tended to decrease as the height of the specimen increased, as shown in Figure 10(a). This was primarily because the friction between the loading plate and the contact surface of the specimen effectively restrained the lateral deformation of the specimen. Furthermore, the confined effect of the core concrete increased as the specimen height decreased.

Figure 10.

Effects of the (a) specimen height, (b) ρ_sv, and (c) α_st of the core steel tube on the axial ultimate bearing capacity and axial deformation of the joint core.

The ultimate bearing capacity of the specimens depended on ρ_sv in which the ultimate bearing capacity increased with ρ_sv, as shown in Figure 10(b). The ultimate bearing capacity of specimen C2 improved to 394 and 68 kN compared with those of C5 and C4, respectively. The ring stirrups significantly restricted the lateral deformation of the core steel tube and core concrete during the loading. Furthermore, the confining effect of the ring stirrups of the specimen became more prominent with the increase in ρ_sv. Moreover, the effect of α_st of the core steel tube on the ultimate bearing capacity of the specimens was analyzed, as shown in Figure 10(c). As shown, the ultimate bearing capacity of the specimen increased slightly as the α_st of core steel tube increases. The ultimate bearing capacity of specimen C2 was 176 kN, which was 66 kN greater than those of C7 and C6 as the lateral deformation of the core concrete was confined by the steel tube.

The effects of the specimen height, ρ_sv, and α_st of the core steel tube on the axial ultimate strain of the joint core exhibited similar trends with those on the ultimate bearing capacity of the specimen, as illustrated in Figure 10. The axial ultimate strains of all the specimens considered under axial compression are listed in Table 4. As shown, the ultimate strain of specimen C2 increased by 56.3% compared with that of specimen C5, which further indicates that the ductility of the joint core improved significantly owing to the confining effect of the stirrup on the lateral deformation of the core concrete, especially for a specific specimen height.

Strain analysis

Strain in ring stirrup

The effect of structural parameters (i.e. specimen height, ρ_sv, and α_st of the core steel tube) on the strain in the stirrups is shown in Figure 11. The strain in the stirrups developed rapidly after the elastic stage after the yielding of the stirrups. As the specimen height decreased or the α_st of the core steel tube increased, the growth speed of the strain in the stirrups decelerated. Moreover, the ultimate strain in the stirrups near the middle height of the specimen increased significantly compared with that near the bottom of the specimen, which corresponds to a drum-shaped deformation of the core steel tube in the middle region. The ultimate strain in the stirrups increased as the specimen height increased or ρ_sv (or α_st of the core steel tube) decreased. This indicates that the confining effect of the core concrete became more prominent with the increase of the specimen height. Similarly, the confining effect of the stirrup and core steel tube on the core concrete became more prominent as the ρ_sv or α_st of the core steel tube increased. The ring stirrup and steel tube can collectively confine the lateral deformation of the core concrete. On such a double confinement, the ductility of the core concrete is highlighted and a relatively high ultimate strain can be achieved with the increase in the ρ_sv and α_st of the core steel tube.

Figure 11.

Effects of the (a) specimen height, (b) ρ_sv, and (c) α_st of the core steel tube on strain in ring stirrups.

Strain in longitudinal bar

The effects of the specimen height, ρ_sv, and α_st of the core steel tube on the strain of the longitudinal bar are shown in Figure 12. As shown, a linear relationship exists between the axial force and the strain of the longitudinal bar for all curves at the early stage of loading. After the yielding strength of the longitudinal bar is reached, the strain in the longitudinal bar developed rapidly with a slight increase in the load. Furthermore, the growth speed of the strain in the longitudinal bar decelerated as the specimen height decreased. By contrast, as the ρ_sv or α_st of the core steel tube decreased, the growth speed of strain in the longitudinal bar increased rapidly. Furthermore, the ρ_sv or α_st of the core steel tube exerted a more significant effect on the strain of the longitudinal bar than the specimen height. Generally, the joint core specimen favors damage owing to the premature crushing of the external concrete. Therefore, it is conducive to develop collaborative work of an external RC concrete and the core steel tube–confined concrete. Moreover, the ultimate strain in the longitudinal bar increased with the specimen height, whereas it exhibited a negative correlation with the ρ_sv or α_st of the core steel tube. Using C2 and C5 as examples, the ultimate strain in the longitudinal bar of C5 was approximately twice higher than that of C2, as shown in Figure 12(b). This could be attributed to the significant enhancement in the confining effect of the stirrup with the increase in ρ_sv.

Figure 12.

Effects of the (a) specimen height, (b) ρ_sv, and (c) α_st of the core steel tube on the strain in the longitudinal reinforcement.

Strain in core steel tube

The effects of structural parameters (i.e. the specimen height, ρ_sv, and α_st of the core steel tube) on the strain of the core steel tube are shown in Figure 13. The longitudinal compressive strain value was set as negative, whereas the tensile value of the lateral strain is positive. Similarly, the strains for all specimens indicated linear increase with axial load at the beginning of loading until the steel tube yielded. Both the longitudinal and lateral strains reached the yield strain of the steel tube before the ultimate strength of the specimen was reached, indicating the full utilization of the steel tube strength. Similar to the strain in the longitudinal steel, the ρ_sv and α_st of the core steel tube exerted a more significant effect on the strain of the core steel tube than the specimen height. It is clear that the longitudinal and lateral strains in the core steel tube increase with the specimen height, whereas those in the core steel tube increased as the ρ_sv or α_st of the core steel tube decreased. For specimens C2 and C7, the longitudinal strain of C2 was −3398 µε, whereas that of C7 was approximately four times of −12,734 µε. This indicates that the external RC concrete can effectively confine the lateral deformation of the core steel tube. In addition, for a certain height, the steel tube with thick thickness presents strong stability. Consequently, the load-bearing capacity and ductility of the specimen increased with the ρ_sv or α_st of the core steel tube.

Figure 13.

Effects of the (a) specimen height, (b) ρ_sv, and (c) α_st of the core steel tube on the strain in the core steel tube.

Equivalent stress–strain relationship analysis

For all specimens of the joint core, the equivalent stress of the specimen (σ_c) is defined as the ratio of the axial compression load to the area of the joint core compression zone. Correspondingly, the equivalent strain of the specimen (ε_c) is defined as the ratio of the axial compressive deformation to the initial specimen height.

The effects of the specimen height, ρ_sv, and α_st of the core steel tube on the stress–strain relationship of the specimen are illustrated in Figure 14. As shown, the equivalent stress increased linearly with equivalent strain at the early stage of loading. The parameters studied exerted little effect on the equivalent stress–strain curve of the specimen in the elastic stage. When the load was increased to induce the development of cracks within the concrete, the linear relationship between stress and strain deviated slightly. Moreover, the slope of the curve increased as ρ_sv or α_st of the core steel tube increased, whereas it decreased with the increase in the specimen height. The inflection point on the stress–strain curve indicates the onset of the specimen’s yield behavior. The strains increased rapidly with increase in the load at the yielding stage. After yielding, the strain developed continually with an approximately constant value of stress. The peak stress and the corresponding peak strain of the specimen decreased as the specimen height increased, whereas the peak stress and the corresponding peak strain of the specimen increased as ρ_sv and α_st of the core steel tube increased.

Figure 14.

Effects of the (a) specimen height, (b) ρ_sv, and (c) α_st of the core steel tube on equivalent stress–strain relations of the joint.

Formula for predicting the ultimate bearing capacity

Basic principles

The superposition method has been widely used to calculate the strength of concrete-encased CFST stub columns (Han and An, 2014; Li et al., 2015; Wakabayashi, 1988), where the strengths of steel tube, core concrete, and external concrete were added directly. According to Chinese, American, and European codes, three methods can be used to calculate the ultimate strength of concrete-encased CFST columns (Han and An, 2014). However, the confinement of ring stirrups to external concrete was not considered, which may result in the conservative predicted results. Considering the effects of the specimen height (h), ρ_sv, and α_st on the bearing capacity of the joint core, the comprehensive impact coefficient (η_d) is proposed based on confined concrete theory. The basic assumptions adopted were as follows:

The increment of the concrete beyond ring stirrups to the bearing capacity is not considered.

The concrete in the core steel tube is subjected to the double restraint mechanism of the core steel tube and ring stirrups.

The core steel tube and the ring stirrups yielded after the specimens failed.

No relative slip occurred between the core steel tube and concrete.

The ideal elastic–plastic bi-linear model is adopted for the constitutive relationship of steel.

Ultimate bearing capacity

The external concrete is the concrete between the ring stirrup and core steel tube (as illustrated in Figure 2), A_c1 is the cross-sectional area of external concrete, A_c2 is the cross-sectional area of the core concrete. Figure 15 shows the force principle of the ring stirrup, which is similar to that of a spiral stirrup–confined concrete. Therefore, the ring stirrup–confined concrete can be considered as a spiral stirrup–confined concrete.

Figure 15.

Force balance of a ring stirrup.

The experimental results indicated that the core concrete confined by steel tube can support additional loads continually after the specimen failed. Hence, the occurrence of the ultimate bearing capacity of the core concrete and external concrete was not simultaneous. Therefore, $η_{d}$ was introduced to account for the confined effect of concrete. Consequently, based on the superposition principle and the aforementioned assumptions, the ultimate bearing capacity of the joint connection N_u can be expressed as

N_{u} = η_{d} (N_{u 1} + N_{u 2}) + f_{y, lb} A_{y, lb}

(1)

where N_u1 is the ultimate bearing capacity of the external concrete; N_u2 is the ultimate bearing capacity of the core concrete; f_y,lb is the yield strength of the longitudinal bar; A_y,lb is the total cross-sectional area of the longitudinal bars.

Calculation of N_u1

According to the forces balance shown in Figure 15, the radial compressive stress provided by the ring stirrups σ_r can be expressed as follows

σ_{r} = \frac{2 f_{y} A_{s}}{s d_{s}}

(2)

where A_s is the section area of a ring stirrup; s is the spacing of the adjacent layer ring stirrup; and d_s is the internal diameter of the ring stirrup. Substituting the expression of stirrup ratio $ρ_{sv} = 4 A_{s} / d_{s} s$ into Equation (2), the following expression could be obtained as

σ_{r} = \frac{1}{2} ρ_{sv} f_{y}

(3)

The relation between strength of the ring stirrup–confined concrete f_cc and that of the axial compressive concrete f_c can be expressed as follows (Cai, 1963)

f_{cc} = f_{c} + 4 σ_{r}

(4)

Substituting Equation (3) into Equation (4), the following equation is given

f_{cc} = f_{c} + 2 ρ_{sv} f_{y}

(5)

By introducing the ring stirrup reinforcement characteristic value $λ_{sv} = ρ_{sv} (f_{y} / f_{c})$ , Equation (5) can be rewritten as

f_{cc} = (1 + 2 λ_{sv}) f_{c}

(6)

Subsequently, by substituting the parameters determined in this article to Equation (6), the ultimate bearing capacity of external concrete N_u1 can be determined as

N_{u 1} = (1 + 2 λ_{sv, 1}) f_{c, e} A_{c 1}

(7)

where $λ_{sv, 1} = ρ_{sv} (f_{y, rs} / f_{c, e})$ ; f_c,e is the strength of axial compressive external concrete; f_y,rs is the yield strength of the ring stirrup.

Calculation of N_u2

According to Qian and Jiang (2011), the ultimate bearing capacity of the core concrete confined by core steel tube N_u2,c can be expressed as follows

N_{u 2, c} = (1 + 1.1 θ + \sqrt{θ}) f_{c, c} A_{sc}

(8)

where θ (=α_st·f_y,st/f_c,c) is confinement factor of core steel tube section; A_sc (= A_c2+A_st) is the cross-sectional area of the core steel tube and the core concrete. From Equation (7), the ultimate bearing capacity of the core concrete confined by the ring stirrup N_u2,s can be expressed as follows

N_{u 2, s} = (1 + 2 λ_{sv, 2}) f_{c, c} A_{c 2}

(9)

where $λ_{sv, 2} = ρ_{sv} (f_{y, rs} / f_{c, c})$ . Hence, the ultimate bearing capacity of core concrete N_u2 can be obtained as

N_{u 2} = (1 + 1.1 θ + \sqrt{θ}) f_{c, c} A_{sc} + (1 + 2 λ_{sv, 2}) f_{c, c} A_{c 2}

(10)

Description of numerical model

A finite element study was further performed to determine the dependence of η_d on the structural parameters. Numerical models of the joint cores were simulated using explicit finite element code ABAQUS/Explicit. The steel tube, longitudinal reinforcement, and stirrup were assumed to be elastic, perfectly plastic materials; their parameters are listed in Tables 2 and 3. The plastic damage model provided in ABAQUS for concretes was adopted. A stress–strain model that accounted for the circular confining effect, which was proposed by Han et al. (2007), was applied to characterize the core concrete properties in this study. A stress–strain relationship of stirrup-confined concrete suggested by Guo (2004) was adopted for the external concrete. The tensile properties of concrete in the plastic damage model were defined by the fracture energy method, and the parameters (i.e. fracture energy, tensile strength) were coincident with Nie et al. (2019).

The stress–strain curve of circular steel tube–confined concrete under compression suggested by Han et al. (2007) is expressed as

\frac{σ_{c}}{σ_{0}} = {\begin{matrix} 2 (\frac{ε}{ε_{0}}) - {(\frac{ε}{ε_{0}})}^{2} & ε \leq ε_{0} \\ {\begin{matrix} 1 + (\frac{θ^{0.745}}{2 + θ}) [{(\frac{ε}{ε_{0}})}^{0.1 θ} - 1], & (θ \geq 1.12) \\ \frac{ε / ε_{0}}{β {(ε / ε_{0} - 1)}^{2} + ε / ε_{0}}, & (θ < 1.12) \end{matrix} & ε > ε_{0} \end{matrix}

(11)

with related parameters being similar to those mentioned in Nie et al. (2019)

β = {(2.36 \times 1 0^{- 5})}^{[0.25 + {(θ - 0.5)}^{7}]} f_{c} \times 3.51 \times 10^{- 4}

(12)

σ_{0} = [1 + (- 0.054 θ^{2} + 0.4 θ) {(\frac{24}{f_{c}})}^{0.45}] f_{c}

(13)

ε_{0} = 1300 + 12.5 f_{c} + [1400 + 800 (\frac{f_{c}}{24}) - 1] θ^{0.2} (μ ε)

(14)

where f_c is the concrete cylinder strength and θ is the confinement factor of core steel tube section.

For the concrete confined by ring stirrups, the stress–strain relationship based on the proposed model by Guo (2004) was adopted

\frac{σ_{c}}{σ_{0}} = {\begin{matrix} α_{1} (\frac{ε}{ε_{0}}) + (3 - 2 α_{1}) {(\frac{ε}{ε_{0}})}^{2} - (α_{1} - 2) {(\frac{ε}{ε_{0}})}^{3}, & ε \leq ε_{0} \\ \frac{ε / ε_{0}}{α_{2} {[{(ε / ε_{0})}^{2} - 1]}^{2} + ε / ε_{0}}, & ε > ε_{0} \end{matrix}

(15)

where α₁ and α₂ are the shape parameters of plain concrete, which are defined as

α_{1} = 1.7 (1 + 1.8 λ)

(16)

α_{2} = 2 (1 - 1.75 λ^{0.55})

(17)

Moreover, the ε₀ and σ₀ of the confined concrete depend on the confined index of ρ_sv, λ = ρ_svf_y/f_c, that is

ε_{0} = {\begin{matrix} (1 + 2.5 λ) ε_{p}, & λ \leq 0.32 \\ (- 6.2 + 25 λ) ε_{p}, & λ > 0.32 \end{matrix}

(18)

σ_{0} = {\begin{matrix} (1 + 0.5 λ) f_{c}, & λ \leq 0.32 \\ (0.55 + 1.9 λ) f_{c} & λ > 0.32 \end{matrix}

(19)

where f_c is the concrete cylinder strength, and ε_p the yield of the first stirrup (Liu et al., 2012), which is calculated as

ε_{p} = 0.004 + \frac{0.9 ρ_{sv} f_{y}}{300}

(20)

The core concrete, external concrete, and steel tube were modeled with C3D8R (an eight-node linear brick, reduced integration, hourglass control) solid elements, whereas the steel bar was meshed with T3D2 truss elements. Surface-to-surface contact was exerted between the steel tube and concrete, whereas an embedded region constraint was applied between the reinforcement and external concrete.

The deformation evolution of the joint core with the structural parameters of specimen C2 under compression is illustrated in Figure 16. It indicates that the strain within the longitudinal reinforcement bars and external core developed much quicker than that within the core concrete and steel tube at the initial stage. Therefore, the ultimate strains of the external concrete and longitudinal bars would be reached first. Benefiting from the core concrete, the localized fold and concave buckling of the steel tube were effectively restricted; hence, the remaining structure still exhibited considerable load-bearing capacity, which resulted in the well development of strength and ductility of the joint core. The constituent members may have contributed differently to the ultimate strength of the joint core. Therefore, the distribution of ultimate bearing capacities of the members to the specimen should be considered.

Figure 16.

The contours of equivalent strain of the joint core under compression loading (V = 0.5 m/s) in a semi-sectional view.

Comprehensive impact coefficient η_d

Based on the analysis of the experimental results, the ultimate bearing capacity of the joint connection N_u is related to the specimen height h, ρ_sv, and α_st of the core steel tube. Dimensional analysis was applied to determine η_d, and the dimensional form of η_d can be expressed as a function of dimensionless parameters θ, ρ_sv, and h/D

η_{d} = f (θ, ρ_{sv}, \frac{h}{D})

(21)

Investigation of the dependence of η_d on ρ_sv indicated that coefficient η_d was basically independent of ρ_sv, as shown in Figure 17(a). This may be explained by the limited effect of the stirrup confinement on the contribution of coordinative work of the external concrete and core concrete. Therefore, Equation (21) can be simplified as

η_{d} = f (θ, \frac{h}{D})

(22)

Figure 17.

Variations of η_d with (a) ρ_sv and (b) h/D.

Similarly, the effect of height to diameter ratio h/D on η_d was further analyzed under different levels of confinement factors of the core steel tube. It was discovered that η_d exhibited a parabolic locus with respect to h/D for a given θ, as shown in Figure 17(b). Therefore, an empirical expression of η_d can be assumed as follows

η_{d} = g_{1} (θ) {(\frac{h}{D})}^{2} + g_{2} (θ) \frac{h}{D} + g_{3} (θ)

(23)

where g₁(θ), g₂(θ), and g₃(θ) are three unknown functions of θ. Subsequently, the variation of the aforementioned unknown functions with θ was investigated, as shown in Figure 18. As shown, g₁(θ) and g₂(θ) exhibited nearly linear increase tendencies, whereas g₃(θ) can be regarded as a constant value. Therefore, the expression of the three functions can be expressed as follows

{\begin{matrix} g_{1} (θ) = 0.03785 θ + 0.9766 \\ g_{2} (θ) = 0.1072 θ + 0.2094 \\ g_{3} (θ) \approx 1.000 \end{matrix}

(24)

Figure 18.

Variations of g₁(θ), g₂(θ), and g₃(θ) with θ of the core steel tube.

Subsequently, by substituting Equations (7), (10), (23), and (24) into Equation (1), a revised formula for predicting the ultimate bearing capacity of joint connection under axial compression was obtained as follows

\begin{matrix} N_{u} = η_{d} [(1 + 2 λ_{sv}) f_{c, e} A_{c 1} + (1 + 1.1 θ + \sqrt{θ}) f_{c, c} A_{sc} \\ + (1 + 2 λ_{sv, 2}) f_{c, c} A_{c 2}] + f_{y, lb} A_{s, lb} \end{matrix}

(25)

Verification for the proposed formula

The calculation results (N_u-c) and experimental results (N_u-e) of the ultimate bearing capacity were compared, as listed in Table 5. The ratio of N_u-e and N_u-c was between 0.883 and 1.094. In addition, the average and standard deviation of the ratio were 1.018 and 0.076, respectively. Therefore, the ultimate bearing capacity of the joint that was analytically estimated by the proposed formula agreed well with the experimental results.

Table 5.

Comparison between the calculation results and the experimental results.

Specimen	h (mm)	D (mm)	ρ_sv (%)	α_st (%)	N_u-e (kN)	N_u-c (kN)	N_u-e/N_u-c
C2	240	200	2.35	49	1762	1611	1.094
C3	300	200	2.35	49	1618	1635	0.990
C4	240	200	1.71	49	1694	1578	1.074
C5	240	200	1.18	49	1368	1550	0.883
C6	240	200	2.35	34	1696	1614	1.051
C7	240	200	2.35	21	1586	1558	1.018
Average	–	–	–	–	–	–	1.018
Standard deviation	–	–	–	–	–	–	0.076

Conclusion

Experimental studies on seven specimens of joint cores confined with core steel tubes subjected to axial compression were performed in this study. The effects of the specimen height, ρ_sv, and α_st of the core steel tube on the failure mode, bearing capacity, ultimate strain and equivalent stress–strain relationship were analyzed. Based on the experimental results and theoretical analysis, the following conclusions were obtained:

The failure modes of all specimens subjected to axial compression were the crushing of concrete in the joint core. Expansion occurred on the concrete in the middle of the specimens, and considerable vertical cracks on the side of the specimens penetrated along the longitudinal direction of the specimens.

The ultimate bearing capacity of joint cores confined with core steel tubes increased as the specimen height decreased, whereas the ultimate bearing capacity decreased as ρ_sv or α_st of the core steel tube decreased.

The strains in the longitudinal bar, ring stirrups, and core steel tube increased linearly at the early stage of loading. The growth speed of the strains in the longitudinal bar, ring stirrups, and core steel tube decreased gradually as the specimen height decreased, whereas it increased as ρ_sv or α_st of the core steel tube decreased at the yielding stage. After yielding, the strains in the longitudinal bar, ring stirrups, and core steel tube increase rapidly with the increase in load.

The effect of the specimen height, ρ_sv, or α_st of the core steel tube on the stress–strain relationship of the specimen was not evident at the elastic stage. After yielding, the strain developed rapidly with a nearly constant stress. The peak stress and the corresponding peak strain of the specimen increased as the specimen height decreased, whereas the peak stress and the corresponding peak strain of the specimen decreased as the ρ_sv or α_st of core steel tube decreased.

A formula for predicting the ultimate bearing capacity of the new joint connection was proposed based on the superposition principle and confined concrete theory. A dimensional analysis associated with numerical calculations was performed to determine the quantitative expression of η_d.

Footnotes

Appendix

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by Natural Science Foundation of China (Nos 51578001, 51608003, and 51878002), Natural Science Foundation granted by Department of Education, Anhui Province (No. KJ2015ZD10), Key Research and Development Plan of Anhui Province (No. 1704a0802131), and the Outstanding Young Talent Support Program of Anhui Province (No. gxyqZD2016072). This work was also supported by the Anhui Collaborative Innovation Project (No. GXXT-2019-005).

ORCID iDs

Feng Yu

Yucong Guan

Shilong Wang

References

Cai

(1963) Local compressive strength of concrete and reinforced concrete. China Civil Engineering Journal 36: 1–10 (in Chinese).

Chen

Cai

Bradford

, et al. (2014) Seismic behaviour of a through-beam connection between concrete-filled steel tubular columns and reinforced concrete beams. Engineering Structures 80: 24–39.

Eid

Paultre

(2017) Compressive behavior of FRP-confined reinforced concrete columns. Engineering Structures 132(2): 518–530.

Esmaeeli

Danesh

Tee

, et al. (2016) A combination of gfrp sheets and steel cage for seismic strengthening of shear-deficient corner RC beam-column joints. Composite Structures 159: 206–219.

Fakharifar

Chen

(2016) Compressive behavior of FRP-confined concrete-filled PVC tubular columns. Composite Structures 141: 91–109.

Fakharifar

Chen

(2017) FRP-confined concrete filled PVC tubes: a new design concept for ductile column construction in seismic regions. Construction and Building Materials 130: 1–10.

GB/T228.1-2010 (2010) Metallic Materials-Tensile Testing-Part 1: Method of Test at Room Temperature. Beijing: China Standards Press (in Chinese).

Ghobarah

Said

(2002) Shear strengthening of beam-column joints. Engineering Structures 24(7): 881–888.

Guo

(2004) Theory and Application of Strength and Constitutive Equation of Concrete. Beijing: China Architecture & Building Press (in Chinese).

10.

Hameed

Salih

ZGM

(2011) A study of some mechanical behavior on a thermoplastic material. Journal of Al-Nahrain University 14(3): 58–65.

11.

Han

(2014) Performance of concrete-encased CFST stub columns under axial compression. Journal of Constructional Steel Research 93(1): 62–76.

12.

Han

(2010) Seismic performance of CFST column to steel beam joint with RC slab: experiments. Journal of Constructional Steel Research 66(11): 1374–1386.

13.

Han

Yao

Tao

(2007) Performance of concrete-filled thin-walled steel tubes under pure torsion. Thin-Walled Structures 45(1): 24–36.

14.

Kurt

(1978) Concrete filled structural plastic columns. Journal of the Structural Division 104: 55–63.

15.

Lee

Chiou

Shih

(2010) Reinforced concrete beam–column joint strengthened with carbon fiber reinforced polymer. Composite Structures 92(1): 48–60.

16.

Han

, et al. (2015) Circular concrete-encased concrete-filled steel tube (CFST) stub columns subjected to axial compression. Magazine of Concrete Research 68(19): 1–16.

17.

Liu

Jia

(2012) Study of constitutive relations for steel-hoop-confined concrete material. Industrial Construction 42: 188–191 (in Chinese).

18.

Mohamed

Masmoudi

(2010) Flexural strength and behavior of steel and FRP-reinforced concrete-filled FRP tube beams. Engineering Structures 32(11): 3789–3800.

19.

Nie

Wang

, et al. (2019) Ultimate torsional capacity of steel tube confined reinforced concrete columns. Journal of Constructional Steel Research 160: 207–222.

20.

Qian

Jiang

(2011) Calculation method for axial compressive strength of steel tube-reinforced concrete composite columns. Engineering Mechanics 28: 49–57 (in Chinese).

21.

Tang

Cai

Chen

, et al. (2016) Seismic behaviour of through-beam connection between square CFST columns and RC beams. Journal of Constructional Steel Research 122: 151–166.

22.

Teng

Casalboni

, et al. (2016) Behavior and modeling of fiber-reinforced polymer-confined concrete in elliptical columns. Advances in Structural Engineering 19(9): 1359–1378.

23.

Toutanji

Saafi

(2001) Durability studies on concrete columns encased in PVC–FRP composite tubes. Composite Structures 54(1): 27–35.

24.

Toutanji

Saafi

(2002) Stress-strain behavior of concrete columns confined with hybrid composite materials. Materials and Structures 35: 338–347.

25.

Wakabayashi

(1988) Japanese standards for the design of composite buildings. In: Dale Buckner

Viest Ivan

(eds) Composite Construction in Steel and Concrete. New York: ASCE, pp. 53–70.

26.

Wang

Chen

Chan

, et al. (2015) Three-dimensional cyclic performance on new ring-beam connection between concrete-filled tubular column and reinforced-concrete beams. Advances in Structural Engineering 18(8): 1287–1302.

27.

Niu

(2010) Stress-strain model of PVC-FRP confined concrete column subjected to axial compression. International Journal of Physical Sciences 15: 2304–2309.

28.

Niu

(2013) Experimental study on PVC-CFRP confined reinforced concrete short column under axial compression. Journal of Building Structures 34: 129–136 (in Chinese).

29.

Niu

, et al. (2018) Experimental study on PVC-CFRP confined concrete columns under low cyclic loading. Construction and Building Materials 111: 287–302.

30.

Zhang

Zhao

Cai

(2012) Seismic behavior of ring beam joints between concrete-filled twin steel tubes columns and reinforced concrete beams. Engineering Structures 39(6): 1–10.

31.

Zhou

Cheng

Liu

, et al. (2017) Behavior of circular tubed-RC column to RC beam connections under axial compression. Journal of Constructional Steel Research 130: 96–108.

32.

Zhu

Ahmad

Mirmiran

(2005) Effect of column parameters on axial compression behavior of concrete-filled FRP tubes. Advances in Structural Engineering 8(4): 443–450.

Compressive behavior of joint core confined with core steel tube for connection of polyvinyl chloride-carbon fiber reinforced polymer–confined concrete column and reinforced concrete beam

Abstract

Keywords

Introduction

Test program

Fabrication of specimens

Material properties

Concrete and steel bars

Core steel tubes

Test setup

Experimental results and analysis

Failure mode

Ultimate bearing capacity analysis

Strain analysis

Strain in ring stirrup

Strain in longitudinal bar

Strain in core steel tube

Equivalent stress–strain relationship analysis

Formula for predicting the ultimate bearing capacity

Basic principles

Ultimate bearing capacity

Calculation of Nu1

Calculation of Nu2

Description of numerical model

Comprehensive impact coefficient ηd

Verification for the proposed formula

Conclusion

Footnotes

Appendix

Declaration of conflicting interests

Funding

ORCID iDs

References

Calculation of N_u1

Calculation of N_u2

Comprehensive impact coefficient η_d