Deformation analysis of axially loaded weak PVC-fiber reinforced polymer confined concrete column-strong reinforced concrete beam joints reinforced with core steel tube

Abstract

This paper presents an experimental study on 11 weak PVC-FRP Confined Concrete (PFCC) Column-strong Reinforced Concrete beam joints reinforced with Core Steel Tube (CST) subjected to axial load. The influences of the joint height, joint stirrup ratio, Carbon Fiber Reinforced Polymer (CFRP) strips spacing, steel ratio and CST length on the failure mode, ultimate strength, and strain behavior of specimens are analyzed and discussed. Test results indicate that the failure mode of specimens is distinguished by the cracking of PVC tube, fracture of CFRP strips, yielding of stirrups, and longitudinal steel bars in the PFCC columns. Both the longitudinal steel bars and CST yield at the joint area, while there is no obvious damage on the joint. The ultimate stress of specimens decreases with the increment of CFRP strips spacing, while the other studied variables have little impact on the ultimate stress. As the CFRP strips spacing increases, the ultimate strain of specimens decreases, and the strain development accelerates. Considering the effect of joint dimension, a modified prediction model for the stress–strain relationship of axially loaded weak PFCC column-strong RC beam joints reinforced with CST is proposed and verified with good accuracy.

Keywords

Joint column PVC-fiber reinforced polymer confined concrete load capacity deformation stress–strain relationship steel tube stirrup ratio

Introduction

Fiber Reinforced Polymer (FRP) materials, including Carbon Fiber Reinforced Polymer (CFRP), Glass Fiber Reinforced Polymer (GFRP), and Aramid Fiber Reinforced Polymer, have the advantages of high corrosion resistance, large tensile strength, and excellent durability (Hollaway 2010). Such materials are widely used in the reinforcement of RC members, which significantly improves the compressive property (Lim and Ozbakkaloglu, 2013; Louk Fanggi and Ozbakkaloglu, 2015; Mohana, 2019; Pham and Hadi, 2013, 2014a; Xiao and Wu, 2003), bending performance (Attari et al., 2012; Fathuldeen and Qissab, 2019; Nordin and Täljsten, 2004; Shit and Roychowdhury, 2019), shear resistance capability (Al-Rousan, 2017; El-Sayed, 2014), seismic behavior (Antonopoulos and Triantafillou, 2003; Duran et al., 2018; Isleem et al., 2018; Marthong, 2019; Pantelides et al., 2008), and durability of members (Carloni et al., 2012). In recent years, some scholars have attempted to apply FRP materials in new structural systems, such as concrete-filled FRP tubes and PVC-FRP confined concrete structures (ElGawady and Dawood, 2012; Fam and Rizkalla, 2001; Mirmiran and Shahawy, 1997; Ozbakkaloglu, 2013; Saafi, 2001; Yu, 2007).

PFCC column is composed of prefabricated PVC-FRP tube, steel skeleton, and concrete, in which the prefabricated PVC-FRP tube is formed by winding FRP strips around PVC tube according to certain spacing (Yu 2007). In this way, it can make full use of stable performance and low price of PVC tube and effectively overcome the disadvantage of expensive FRP material. Numerous experimental studies and theoretical analyses have been conducted on the mechanical behaviors of PFCC columns, and fruitful achievements have been made. Yu and Niu (2013), Fakharifar and Chen (2016), and Ma and Jiang (2014) carried out experimental studies on PFCC columns under axial compression, and several variable parameters, such as layers of FRP strips, FRP strips spacing, and slenderness ratio, were considered in the experiments. Test results illustrated that the ultimate load capacity of PFCC columns improved as layers of FRP strips increased, while declined as slenderness ratio or FRP strips spacing increased. Yu (2007) and Jiang et al. (2012) investigated the mechanical properties of PFCC columns under eccentric load and indicated that the ultimate compressive strain of PFCC columns was much larger than that of ordinary concrete, and a formula for predicting the ultimate load capacity was also suggested. Ma et al. (2012) investigated the bending performance of PFCC columns, established a moment-curvature relation model, and suggested a simplified calculation formula for estimating the ultimate bending moment. Jiang et al. (2014) and Yu et al. (2018) conducted experiments to examine the seismic performances of PFCC columns and demonstrated that the hysteric curves were full and the PFCC columns exhibited good hysteric behaviors and ductility. Additionally, Toutanji and Saafi (2001) and Yu and Niu (2016) revealed the influences of environmental conditions, such as freeze and thaw, room temperature, wet and dry conditions, and alkali environment, on PFCC columns durability and indicated that, compared with the normal environment, the load capacity and strain of PFCC columns in the aforementioned different experimental environmental conditions decreased slightly, and the PFCC columns showed good durability.

As mentioned above, there are numerous research studies on the mechanical behaviors of PFCC columns, yet few studies have concerned the connection of PFCC column and RC beam. So far, only Yu et al. (2019a, 2019b) conducted an experimental study on PFCC column-ring beam joint under axial load and analyzed the effects of joint parameters (i.e., stirrup ratio, reinforcement ratio, ring beam width, and height) and CFRP strips spacing on the mechanical behaviors of the joints.

To further study the connection of PFCC column and RC beam, in the present study, a new joint reinforced with CST is introduced to connect the PFCC column and RC beam. Abiding the concept of weak column and strong joint, 11 PFCC column-RC beam joints reinforced with CST are designed and tested. The influences of several studied variables, including joint height, joint stirrup ratio, CFRP strips spacing, steel ratio and CST length on the failure mode, and ultimate stress and strain evolution are analyzed and discussed. Then, a modified prediction model for the stress–strain relationship of axially loaded weak PFCC column-strong RC beam joints reinforced with CST is suggested.

Experimental program

Specimen design

HPB300-grade steel bars with diameters of 6 mm, 8 mm, and 10 mm are employed in this experiment. C35 strength-grade concrete is prepared for the specimens, and the protective layer thickness is 15 mm. CFRP strips with a width of 20 mm wrapped around two layers on the PVC tube at specified intervals (i.e., 40 mm and 60 mm) are adopted to confine the core concrete. The length of the PVC tube for the upper and lower columns is 500 mm, the outer diameter and wall thickness are 200 mm and 7.8 mm. The CST is made of Q235 steel, and the external diameter is 89 mm.

Different studied variables, such as joint heights (i.e., 300 mm, 240 mm, and 180 mm), joint stirrup ratios (i.e., 1.18% 1.71%, and 2.35%), CFRP strips spacing (i.e., 60 mm, 40 mm, and no winding), steel ratios (i.e., 49%, 34%, and 21%), and CST lengths (i.e., 360 mm, 300 mm, and 240 mm) are considered in this analysis. The detailed parameters of specimens are presented in Table 1. The reinforcement diagram is shown in Figure 1. For each subassembly, all members are cast at one time.

Table 1.

Parameters of PFCC column - RC beam joint reinforced with CST.

Specimen	Length of CST l/(mm)	Joint Height h/(mm)	Joint stirrup	Stirrup ratio of joint, % ρ	Steel ratio of CST, % α	$CFRP strips spacing s_{f}^{'} / (mm)$	Ultimate load capacity N ec/(kN)	$Ultimate deformation Δ_{e} / (mm)$
A1	240	240	A6@40	2.35	49	60	1428	14.36
A2	300	240	A6@40	2.35	49	60	1467	15.09
A3	360	240	A6@40	2.35	49	60	1481	15.07
A4	300	180	A6@40	2.35	49	60	1510	14.70
A5	300	300	A6@40	2.35	49	60	1434	15.04
A6	300	240	A6@55	1.71	49	60	1394	15.35
A7	300	240	A6@80	1.18	49	60	1380	15.59
A8	300	240	A6@40	2.35	34	60	1498	15.21
A9	300	240	A6@40	2.35	21	60	1460	15.56
A10	300	240	A6@40	2.35	49	No winding	1160	—
A11	300	240	A6@40	2.35	49	40	1621	20.22

α refers to the ratio of the cross-section area of steel tube to that of core concrete in steel tube.

Figure 1.

Details of specimens. (a) Elevation view of steel bar skeleton, (b) 1–1, (c) 2–2, (d) 3–3.

Basic properties of test materials

Three 100 × 100 × 100 mm³ concrete test blocks are prepared and tested after 28 days of curing based on Chinese code (GB/T 50081-2002, 2002), and the average measured cube compressive strength is 35.59 MPa. The elastic modulus of concrete is 2.44 × 10⁴ MPa. According to the Chinese code (GB/T 3354-2014, 2014), the average tensile strength of CFRP strips is 3903 MPa, the elastic modulus is 2.84 × 10⁵ MPa, and the average ultimate tensile strain is 0.0137. An axial compression test and tensile test are conducted on the PVC tube and PVC strips, respectively. The ultimate compressive strength and Poisson’s ratio of the PVC tube are 58.0 MPa and 0.44. The average ultimate tensile strength and elastic modulus are 62.4 MPa and 2.57 × 10³ MPa.

The mechanical properties of steel bars and CST are measured depending on Chinese code (GB/T 228.1-2010, 2010). The yield strengths of steel bars with diameters of 6 mm, 8 mm, and 10 mm are 291.29 MPa, 276.52 MPa, and 350.98 MPa, respectively. The corresponding tensile strength and elastic modulus are 504.29 MPa, 429.71 MPa, and 553.85 MPa and 1.93 × 10⁵ MPa, 1.80 × 10⁵ MPa, and 1.83 × 10⁵ MPa. The yield strengths of CST with wall thicknesses of 4 mm, 6 mm, and 8 mm are 328.71 MPa, 301.38 MPa, and 344.43 MPa, respectively. The corresponding tensile strength are 470.15 MPa, 455.57 MPa, and 581.91 MPa, respectively. The corresponding elastic modulus and Poisson’s ratios are 2.23 × 10⁵ MPa, 1.98 × 10⁵ MPa, and 1.92 × 10⁵ MPa and 0.294, 0.325, and 0.305, respectively.

Measurement scheme

To measure the axial deformation of the specimens, two LVDTs (linear variable differential transformers) are placed on the lower loading plate, as shown in Figure 2(a), and another four LVDTs are arranged to monitor the joint axial deformation. Eight strain gauges are pasted along circumferential and longitudinal directions at middle position of CST, as shown in Figure 3(a). Ten strain gauges are attached on the two longitudinal bars. In the joint zone, six strain gauges are arranged on the upper three layers of stirrups. Four strain gauges are symmetrically attached on the stirrups in the PFCC columns (upper and lower), as shown in Figure 3(c). Eight strain gauges are attached along the axial direction on PVC tubes at middle position of PFCC columns, and another eight strain gauges are arranged along the circumferential direction on CFRP strips. Two pairs of strain gauges arranged at 90° are attached at middle position of the joint concrete. More details are depicted in Figure 3(b).

Figure 2.

Test setup. (a) Schematic diagram, (b) Photograph of loading device.

Figure 3.

Strain gauge arrangement (a) Arrangement of strain gauges of CST, (b) Arrangement of strain gauges of PVC-CFRP tube, (c) Arrangement of strain gauges of steel bars.

Loading scheme

As depicted in Figure 2(b), an electron-hydraulic servo compressive machine (Type YAW-5000F) is employed to conduct the monotonic static loading test. Two steel column caps are utilized to prevent the failure of the PFCC columns end in advance. Preloading with 5% of the predicted ultimate load capacity is first carried out to make sure that the device works well. Two loading schemes, load-controlled (speed of 50 kN/min) and displacement-controlled (speed of 0.5 mm/min), are employed. The test starts with the load-controlled scheme and each load step (load increment is 10%) is maintained for 2 min. After reaching 90% of the ultimate load capacity, the displacement-controlled scheme is applied.

Analysis of test results

Failure mode

The failure processes of all PFCC column-beam joints reinforced with CST are basically identical and are composed of three stages, that is, elastic, crack development, and damage stages. At the early loading stage, the stirrups, longitudinal steel bars, and CST exhibit elastic behavior, and the appearance of the specimens has no significant variation. As the load increases, several cracks appear at the connection between the PFCC column and joint, and the specimen enters the second stage. As the load continues to increase, the longitudinal steel bars yield, and then the PFCC column stirrups yield. As the load increases to 80%–85% of the ultimate load capacity, the CST in the joint yields. As the load reaches approximately 90% of the ultimate load capacity, the specimen comes into the damage stage. Some CFRP strips are broken in the middle of the upper PFCC columns, and the PVC tubes are cracked, as the load attains the ultimate load capacity. Several slight vertical cracks emerge on the joint concrete surface. Eventually, the specimen fails, the joint does not reach its ultimate load capacity, and the PVC tube and CFRP strips of the lower PFCC column are not damaged. The typical failure mode is depicted in Figure 4.

Figure 4.

Failure mode of PFCC beam-column joint with CST. (a) Overall form, (b) Failure mode of column(c) Crack of joint.

Stress analysis

Figure 5 shows the influence of studied variables, such as joint height $h$ , joint stirrup ratio $ρ$ , CFRP strips spacing $s_{f}^{'}$ , steel ratio $α$ , and CST length $l$ on the ultimate stress of specimens, in which, $σ$ represents the ultimate stress of specimens, determined by the ratio of ultimate axial load to the column section area. Apparently, $h, l, α, and ρ$ have no obvious influence on the ultimate stress of specimens, as depicted inFigure 5(a)–(d). This may be because the failure of specimens is caused by the damage of PFCC columns, and these four studied variables have no significant influence on the ultimate load capacity of PFCC columns. The ultimate stress of specimens increases as $s_{f}^{'}$ decreases, as illustrated in Figure 5(e). For instance, the ultimate stress of the specimen with a CFRP strips spacing of 40 mm is 1.1 times larger than that with a CFRP strips spacing of 60 mm. This is mainly because the confining effect of the PVC-CFRP tube on concrete increases with the decrease of CFRP strips spacing.

Figure 5.

Effects of various parameters on the ultimate stress of specimens. (a) Length of CST, (b) Steel ratio of CST, (c) Stirrup ratio of joint, (d) Joint height, (e) CFRP strips spacing.

Strain analysis

Carbon fiber reinforced polymer strips tensile strain

The influences of studied variables on the CFRP strips tensile strain are shown in Figure 6. Clearly, $l$ , $h$ , $ρ$ , and $α$ have no significant effect on the CFRP strips tensile strain, as demonstrated in Figure 6(a)–(d). This may come from that the damage of the PFCC columns dominates the failure of the specimens in this study, and the joint parameters (i.e., $l$ , $h$ , $ρ$ , and α) are not very related to the CFRP strips tensile strain. As depicted in Figure 6(e), the strain development of CFRP strips lessens as $s_{f}^{'}$ decreases. As previously reported in Pham and Hadi (2014b), this phenomenon is mainly attributed to the diminution of CFRP strips spacing, the confinement of CFRP strips on PVC confined column increases, the stiffness of the CFRP composite increases, thereby alleviates the strain development of CFRP strips.

Figure 6.

Effects of various parameters on tensile strain of CFRP strips. (a) Length of CST, (b) Joint height, (c) Stirrup ratio of joint, (d) Steel ratio of CST, (e) CFRP strips spacing

PVC tube compressive strain

Figure 7 reveals the influences of various studied variables on the PVC tube compressive strain. Similar to the effect on the CFRP strips tensile strain, four parameters associated with the joint including $l$ , $h$ , $ρ$ , and $α$ have no obvious effect on the PVC tube compressive strain, as illustrated in Figure 7(a)–(d). As the $s_{f}^{'}$ decreases, the development rate of the PVC tube compressive strain decreases, as demonstrated in Figure 7(e). The reason is that the decrease of $s_{f}^{'}$ increases the confining effect of PVC-CFRP tube on concrete core and slows down the transverse strain development of concrete.

Figure 7.

Effects of various parameters on compressive strain of PVC tube. (a) Length of CST, (b) Joint height, (c) Stirrup ratio of joint, (d) Steel ratio of CST, (e) CFRP strips spacing

Longitudinal steel bars strain

Figures 8–12 depict the influences of the various studied variables on the longitudinal steel bars strain. It is apparent that the effect of joint correlation parameters, such as $l$ , $ρ$ , $h$ , and $α$ , on the PFCC column longitudinal steel bars strain is not distinct, as illustrated in Figures 8(a)–11(a). As can be seen from Figure 12(a), with the decreases of $s_{f}^{'}$ , the PFCC column longitudinal steel bars ultimate strain increases. The decrease of $s_{f}^{'}$ enhances the confining effect of CFRP strips on concrete core, thereby improves the load capacity of specimens and correspondingly raises the PFCC column longitudinal steel bars stress. Taking specimens A2 and A11 as examples, the ultimate strain of specimen A11 with a CFRP strips spacing of 40 mm is 1.28 times larger than that of specimen A2 with a CFRP strips spacing of 60 mm.

Figure 8.

Effect of length of CST on strain of longitudinal steel bar. (a) Strain of longitudinal steel bar in column, (b) Strain of longitudinal steel bar in the connection between column and joint, (c) Strain of longitudinal steel bar in joint.

Figure 9.

Effect of Stirrup ratio of joint on strain of longitudinal steel bar. (a) Strain of longitudinal steel bar in column, (b) Strain of longitudinal steel bar in the connection between column and joint, (c) Strain of longitudinal steel bar in joint.

Figure 10.

Effect of joint height on strain of longitudinal steel bar. (a) Strain of longitudinal steel bar in column, (b) Strain of longitudinal steel bar in the connection between column and joint, (c) Strain of longitudinal steel bar in joint.

Figure 11.

Effect of steel ratio of CST on strain of longitudinal steel bar. (a) Strain of longitudinal steel bar in column, (b) Strain of longitudinal steel bar in the connection between column and joint, (c) Strain of longitudinal steel bar in joint.

Figure 12.

Effect of CFRP strips spacing on strain of longitudinal steel bar. (a) Strain of longitudinal steel bar in column, (b) Strain of longitudinal steel bar in the connection between column and joint, (c) Strain of longitudinal steel bar in joint.

The increase of $ρ$ or $α$ the decrease of $h$ will alleviate the joint longitudinal steel bars strain development, as demonstrated in Figure 9(b)–(c), Figure 10(b)–(c), and Figure 11(b)–(c). With the decrease of $s_{f}^{'}$ , the joint longitudinal steel bars ultimate strain increases, as illustrated in Figures 12(b)–(c). For instance, the ultimate strain of specimen A11 with a CFRP strips spacing of 40 mm is 1.34 times larger than that of specimen A2 with a CFRP strips spacing of 60 mm. This is because, with the decrease of $s_{f}^{'}$ , the confining effect of PVC-CFRP tube on concrete core increases, and the ultimate load capacity of the specimens increases, which correspondingly enhances the joint longitudinal steel bars ultimate stress.

Stirrups strain

Because the joint variable parameters (i.e., $l$ , $α$ , $h$ , and $ρ$ ) are not very related to the load capacity of the PFCC columns, the effect of these four studied variables on the PFCC column stirrups strain is not remarkable, as illustrated in Figure13(a)–(d). The PFCC column stirrups strain development accelerates with the increase of $s_{f}^{'}$ , as depicted in Figure 13(e). As shown in Figure 14(a), it can be seen that $l$ has no obvious influence on the joint stirrups strain. With the decrease of $h$ or the increase of $ρ$ or $α$ , the joint stirrups strain development slows down, as depicted in Figure 14(b)–(d). This may come from that increasing the $ρ$ , $α$ or decreasing the $h$ improves the confining effect on concrete core and lowers the joint concrete transverse strain development. The decrease of $s_{f}^{'}$ enhances the ultimate strain of joint stirrups, as depicted in Figure 14(e). The reason is that the ultimate stress of the specimens raises as $s_{f}^{'}$ decreases, thereby correspondingly enhances the joint stirrups stress.

Figure 13.

Effects of various parameters on the strain of stirrup in column. (a) Length of CST, (b) Joint height, (c) Stirrup ratio of joint, (d) Steel ratio of CST, (e) CFRP strips spacing.

Figure 14.

Effects of various parameters on the strain of stirrup in the joint. (a) Length of CST, (b) Joint height, (c) Stirrup ratio of joint, (d) Steel ratio of CST, (e) CFRP strips spacing.

Core steel tube strain

The influence of the studied variables on the CST strain is shown in Figure 15. In this figure, $ε_{a}$ and $ε_{c}$ represent the axial strain and circumferential strain of CST, respectively. Clearly, $l$ has no obvious influence on the CST strain, as shown in Figure 15(a). The confinement effect on joint concrete increases with the increase of $ρ$ or $α$ , and the CST strain development decreases, as demonstrated in Figure 15(c)–(d). It can be seen from Figure 15(b) that the improvement of $h$ leads to the enhancement of the CST ultimate strain. The reason is that the confinement effect of the PFCC columns on the joint decreases as $h$ increases, resulting in the reduction of the stress of joint. As depicted in Figure 15(e), the strain development rate and the ultimate strain of CST increase as $s_{f}^{'}$ decreases. This may be because with the decrease of $s_{f}^{'}$ , the confining effect of the PVC-CFRP tube on concrete core increases. Thus, the ultimate stress increases, and the CST ultimate strain correspondingly improves.

Figure 15.

Effects of various parameters on the strain of CST. (a) Length of CST, (b) Joint height, (c) Stirrup ratio of joint, (d) Steel ratio of CST, (e) CFRP strips spacing.

Joint concrete strain

The influences of five studied variables on the joint concrete strain are depicted in Figure 16, in which $ε_{ja}$ and $ε_{jc}$ represent the measured axial and circumferential strains of joint concrete, respectively. As can be seen from Figure 16(b), as $h$ decreases, the confining effect of PFCC column on joint improves, and the joint concrete axial strain development slows down. The increase of $ρ$ or $α$ will enhance the confining effect on joint concrete and correspondingly reduce the joint concrete ultimate axial strain, as demonstrated in Figure 16(c)–(d). The joint concrete ultimate strain increases as $s_{f}^{'}$ decreases, as shown in Figure 16(e). For instance, the ultimate axial and circumferential strains of specimen A11 with a CFRP strips spacing of 40 mm are 1.32 and 2.82 times larger than those of specimen A2 with a CFRP strips spacing of 60 mm. This is mainly because the decrease of $s_{f}^{'}$ enhances the ultimate load capacity of specimens and correspondingly improves the joint stress. The effect of $l$ on the joint strain of joint concrete is not distinct, as demonstrated in Figure 16(a).

Figure 16.

Effects of various parameters on the strain of concrete in joint. (a) Length of CST, (b) Joint height, (c) Stirrup ratio of joint, (d) Steel ratio of CST, (e) CFRP strips spacing.

Stress–strain relationship analysis

Stress–strain relationship of PVC-FRP Confined Concrete column

The effects of five studied variables on the stress–strain relationship of PFCC column are depicted in Figure 17. In these figures, $σ_{cz}$ , $ε_{ca}$ , and $ε_{cc}$ indicate the compressive stress, measured axial strain, and circumferential strain of PFCC columns.

Figure 17.

Effects of various parameters on stress–strain relationship of column. (a) Length of CST, (b) Joint height, (c) Stirrup ratio of joint, (d) Steel ratio of CST, (e) CFRP strips spacing.

The stress–strain curves of all PFCC columns approximately consist of two sections, that is, parabola and straight line stages. Apparently, during the entire loading process, $l$ , $ρ$ , $α$ , and $h$ have little effect on the stress–strain curves of PFCC columns, as shown in Figure 17(a)–(d). The slope of the stress–strain curves of PFCC columns increases with the decrease of $s_{f}^{'}$ , as depicted in Figure 17(e). With the improvement of $s_{f}^{'}$ , the ultimate axial and circumferential strain of PFCC columns decrease, as depicted in Figure 18. This is because the confining force of CFRP strips is transmitted to the core concrete through PVC tube, and the core concrete is in a three-dimensional compressive state. As $s_{f}^{'}$ increases, the confining effect of the outer PVC-CFRP tube on core concrete decreases, the ultimate load capacity of PFCC columns decreases, the transverse deformation of core concrete increases, and the ultimate axial and circumferential strains of PFCC columns decrease. The effects of $l$ , $ρ$ , $α$ , and $h$ on the ultimate axial and circumferential strains of PFCC columns are not remarkable, as depicted in Figure 18.

Figure 18.

Effects of various parameters on ultimate strain of column. (a) Ultimate axial strain(b) Ultimate circumferential strain.

Stress–strain relationship of joint

Figure 19 depicts the impacts of five studied variables on the stress–strain curves of the joint, in which $σ_{cj}$ , $ε_{ja}$ , and $ε_{jc}$ represent the compressive stress, measured axial strain, and circumferential strain of the joint. Initially, the compressive stress and strain of joint basically increase linearly because the joint is in elastic stage. As the load increases, the axial and circumferential strains deviate from linearity, and the joint enters cracking development stage. $l$ has no obvious influence on the stress–strain relationship of joint, as shown in Figure 19(a). The increase of $ρ$ or $α$ the decrease of $h$ or $s_{f}^{'}$ will increase the slope of stress–strain curves of the joints, as demonstrated in Figure 19(b)–(e). The ultimate axial and circumferential strains of the joint decrease as $ρ$ or $α$ increases, as shown in Figure 20. This may be because of the confining effect on joint concrete strengthens with the increase of $ρ$ or $α$ . The increase of $h$ or $s_{f}^{'}$ decreases the ultimate axial and circumferential strains of the joints, as shown in Figure 20. The reason is that the increase of $h$ or $s_{f}^{'}$ will reduce the ultimate load capacity of specimens, and decrease the joint stress accordingly. Obviously, $l$ has little influence on the ultimate axial and circumferential strains of the joint, as illustrated in Figure 20.

Figure 19.

Effects of various parameters on stress–strain relationship of joint. (a) Length of CST, (b) Joint height, (c) Stirrup ratio of joint, (d) Steel ratio of CST, (e) CFRP strips spacing.

Figure 20.

Effects of various parameters on ultimate strain of joint. (a) Ultimate axial strain, (b) Ultimate circumferential strain.

A model for predicting the stress–strain relationship

Previous model

Yu (2007) proposed a model to estimate the stress–strain relationship of axially loaded PFCC columns, as shown in Figure 21, which is composed of a first part with a parabola and a second part with a straight line

σ_{ca} = {\begin{matrix} 0.58 E_{c} ε_{ca} - \frac{{(E_{c} - E_{2})}^{2}}{12 f_{Ro}} ε_{ca}^{2} 0 \leq ε_{ca} \leq ε_{t} \\ f_{Ro} + E_{2} ε_{ca} ε_{t} \leq ε_{ca} \leq ε_{cau} \end{matrix}

(1)

E_{2} = \frac{f_{caR} - f_{Ro}}{ε_{cau}}

(2)

f_{Ro} = f_{o} + k_{a} \frac{N_{s}}{A_{c}}

(3)

ε_{t} = \frac{3 f_{Ro}}{(E_{c} - E_{2})}

(4)

where

σ_{ca}

and

ε_{ca}

denote the axial stress and strain of the reinforced PFCC columns,

E_{2}

represents the slope of intensified segment, and

f_{Ro}

is the intercept of intensified segment (straight line) of the reinforced PFCC columns.

ε_{t}

indicates the intersection of the straight line and parabola, and

ε_{cau}

denotes the ultimate axial strain of the reinforced PFCC columns.

f_{o}

means the straight line intercept of PFCC columns,

A_{c}

is the cross area of concrete, and

N_{s}

is the calculated value of the load capacity of steel bars, where

N_{s} = f_{y}^{'} A_{s}^{'}

f_{y}^{'}

is the steel bars yield strength, and

A_{s}^{'}

is the total cross area of steel bars.

k_{a}

is the enhancement coefficient of the axial strain of the reinforced PFCC columns, and

k_{a} = 1.16

Figure 21.

Stress–strain relationship of PVC-FRP confined concrete (Yu 2007).

In Yu’s model, three key parameters, namely, $f_{caR}$ , $ε_{cau}$ , and $f_{o}$ , are determined by the following formulas

f_{caR} = k_{b} f_{c} (1 + 1.31 ξ_{ef})

(5)

ε_{cau} = k_{a} (0.0111 + 0.0077 ξ_{ef})

(6)

f_{o} = 24.734 ξ_{ef}^{- 0 . 0692}

(7)

in which,

k_{b}

is the enhancement coefficient of the load capacity of PFCC columns, and

k_{b} = 1.24

;

ξ_{ef}

is the equivalent confining effect coefficient, as expressed in equation (8)

ξ_{ef} = \frac{A_{f} f_{f} s_{f}}{A_{c} f_{c} s_{f}^{'}}

(8)

where

A_{f}

and

f_{f}

are the area and tensile strength of CFRP strips and

s_{f}

is the width of CFRP strips. Nevertheless, as depicted in Figure 22, it is obvious that Yu’s model is not suitable for estimating the stress–strain relationship of axially loaded weak PFCC column-strong RC beam joints reinforced with CST because the impact of the joint is not considered. This comparison shows that although the mentioned joint parameters (i.e.,

l

h

, p and a) have little influences on stress and strain of axially loaded weak PFCC column-strong RC beam joints reinforced with CST, the comprehensive influence of joint parameters on the specimens cannot be ignored. Therefore, it is necessary to establish a modified prediction model.

Figure 22.

Comparison between calculated results and experimental data. (a) A1, (b) A2, (c) A3, (d) A4, (e) A5, (f) A6, (g) A7, (h) A8, (i) A9, (j) A11.

A modified model

As mentioned above, three parameters, that is, $f_{caR}$ , $ε_{cau}$ , and $f_{o}$ , must be determined to describe the stress–strain relationship curves. In this study, these three variables are revised to accurately predict the stress–strain relationship of axially loaded weak PFCC column-strong RC beam joints strengthened with CST.

Modified $f_{caR}$ and $ε_{cau}$

The existing studies have shown that the $h / d$ of joint has obvious influence on the mechanical performances of specimens (Chen et al., 2008; Duan 2020). To simplify the analysis, considering the comprehensive influence of joint dimension on the specimens, the ultimate axial stress $f_{caR}$ and axial strain $ε_{cau}$ of weak PFCC column-strong RC beam joints strengthened with CST are determined by equations (9) and (10)

f_{caR} = [(1 + β_{h}) f_{cc} A_{c} + f_{y}^{'} A_{S}^{'}] / A_{c}

(9)

ε_{cau} = (1 + ς_{h}) ε_{cc}

(10)

where

β_{h}

and

ζ_{h}

mean the comprehensive influence coefficient of joint dimension on ultimate axial stress and strain, respectively, which are fitted by the regression analysis of measured data in this study and test data of Zhu (2018) and Yu (2007), as shown in Figures 23–24 and equations (11), and (12)

β_{h} = 0.001 {(\frac{h}{d})}^{2} - 0.0867 (\frac{h}{d}) + 0.058

(11)

ζ_{h} = - 0.036 {(\frac{h}{d})}^{2} + 0.355 (\frac{h}{d}) - 0.2391

(12)

Figure 23.

Relationship between $β_{h}$ and $h / d$ .

Figure 24.

Relationship between $ζ_{h}$ and $h / d$ .

in which, $h$ and $d$ represent joint height and joint diameter.

The existing studies have shown that the effects of stirrup and FRP wrapping on the axial stress and strain of the FRP confined concrete are significant, and the corresponding theoretical calculation formulas have been proposed (Wang et al., 2012). Considering that the FRP wrapped form proposed in this study is different from that adopted in the previous studies, a modified calculation formula is proposed based on Wang’s model. The multi-parameter regression analysis of test results is conducted, and the ultimate compressive strength $f_{cc}$ and axial strain $ε_{cc}$ of the PFCC can be calculated by the following formulas.

\frac{f_{cc}}{f_{co}} = 1 + 0.644 \times {(\frac{f_{ls}}{f_{co}})}^{0.256} + 0.89 \times {(\frac{f_{lf}}{f_{co}})}^{0.04}

(13)

\frac{ε_{c c}}{ε_{c o}} = 2 + 7.253 \times {(\frac{f_{ls}}{f_{co}})}^{1.269} + 18.677 \times {(\frac{f_{lf}}{f_{co}})}^{0.424}

(14)

where

f_{co}

and

ε_{co}

are the ultimate compressive strength and strain of the unconfined concrete,

f_{ls}

and

f_{lf}

are the lateral confinement pressure provided by the stirrup and CFRP strips, respectively, which can be determined by the following formulas (Wang et al., 2012; Saadatmanes et al., 1994)

f_{ls} = 0.5 k_{es} k_{v} ρ_{st} f_{yt}

(15)

f_{lf} = k_{g} \frac{2 E_{f} ε_{f} t_{f}}{D}

(16)

in which, $k_{es}$ denotes the confinement effectiveness coefficient of stirrup, $k_{es} = 1.0$ , $k_{v}$ is the effectiveness of lateral confinement provided by stirrup and longitudinal steel bar, which can be determined by equation (17). $ρ_{st}$ and $f_{yt}$ represent the volumetric ratio and yield strength of stirrup.

E_f, $ε_{f}$ , and $t_{f}$ are the elastic modulus, tensile strain, and thickness of CFRP strips, respectively. $D$ is the diameter of the circular column. $k_{g}$ is the interval coefficient of CFRP strips, as shown in equation (18).

k_{v} = \frac{{(1 - \frac{s^{'}}{2 d_{s}})}^{2}}{1 - ρ_{cc}}

(17)

k_{g} = \frac{{(1 - \frac{s_{f}^{'}}{2 d_{f}})}^{2}}{1 - ρ_{cc}}

(18)

where

s^{'}

is the net spacing of stirrup.

d_{s}

and

d_{f}

are the diameter of concrete confined by stirrup and CFRP strips.

ρ_{cc}

is longitudinal reinforcement ratio.

To explore the adaptability of the proposed models, the proposed models for predicting the ultimate compressive strength $f_{cc}$ and axial strain $ε_{cc}$ of the PFCC are validated by test data of Wang et al. (2012), as shown in Figure 25. It can be seen from the comparison results that the PFCC prediction model has better prediction accuracy for FRP confined concrete.

Figure 25.

Comparison between calculated value and experimental value. (a) Ultimate compressive strength, (b) Ultimate axial strain.

Modified $f_{o}$

The regression analysis of test data, including the measured data in this study and collected from Zhu (2018), is conducted, as shown in Figure 26, the modified $f_{o}$ can be expressed as follows.

f_{o} = 23.6 + 19.95 (ξ_{ef}) - 19.44 {(ξ_{ef})}^{2}

(19)

Figure 26.

Relationship between $f_{o}$ and $ξ_{ef}$ .

Model validation

Figure 27 depicts a comparison of the predicted stress–strain curves of the specimens from the proposed model and the measured stress–strain curves. Obviously, the proposed model can well predict the stress–strain relationship of axially loaded weak PFCC column-strong RC beam joints reinforced with CST.

Figure 27.

Comparison of the predicted stress–strain relationship curves of PFCC column with the tested curves. (a) A1, (b) A2, (c) A3, (d) A4, (e) A5, (f) A6, (g) A7, (h) A8, (i) A9, (j) A11.

Conclusions

Eleven weak PFCC column-strong RC beam joints reinforced with CST subjected to axial load are experimentally investigated, and five relevant studied variables are considered as follows:

(1) The failure mode of the axially loaded weak PFCC column - strong RC beam joint reinforced with CST is the cracking of PVC tube, fracture of several CFRP strips, and yielding of longitudinal steel bars, column stirrups, and CST.

(2) The ultimate stress of specimens decreases with the increase CFRP strips spacing. Other studied variables, such as the joint height, CST length, steel ratio, and joint stirrup ratio, have little effect on the ultimate stress of specimen.

(3) The strain development of PVC tube, CFRP strips, column longitudinal steel bars, and column stirrups decreases as the CFRP strips spacing decreases. The slope of the stress–strain curves of PFCC columns decreases as the CFRP strips spacing increases. The ultimate strain of PFCC columns decreases as the CFRP strips spacing increases.

(4) Considering the effect of the joint dimension, the comprehensive influence coefficients of joint dimension are introduced, a modified model for estimating the stress–strain relationship of axially loaded weak PFCC column-strong RC beam joints reinforced with CST is proposed, and it shows good accuracy.

Footnotes

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 study was sponsored by the National Natural Science Foundation of China (No. 51578001, 51878002, 52078001), Outstanding Youth Fund of Anhui Province (No. 2008085J29), University Natural Science Research Project of Anhui Province (No. KJ2020A0234, KJ2020A0261).

Data availability

Some or all data, models, or code generated or used during the study are available from the corresponding author by request ().

ORCID iDs

Feng Yu

Yuan Fang

References

Al-Rousan

(2017) Shear behavior of RC beams externally strengthened and anchored with CFRP composites. Structural Engineering and Mechanics 63(4): 447–456.

Antonopoulos

Triantafillou

(2003) Experimental investigation of FRP-strengthened RC beam-column joints. Journal of Composites for Construction 7(1): 39–49.

Attari

Amziane

Chemrouk

(2012) Flexural strengthening of concrete beams using CFRP, GFRP and hybrid FRP sheets. Construction and Building Materials 37: 746–757.

Carloni

Subramaniam

Savoia

, et al. (2012) Experimental determination of FRP-concrete cohesive interface properties under fatigue loading. Composite Structures 94(4): 1288–1296.

Chen

Cai

, et al. (2008) The Axial Compression Bearing Capacity of the Concrete Filled Steel Tubular Column-Beam Joint with the Column Tube Discontinuous in Joint Zone. Engineering mechanics, 170–175.

Duan

Cai

Tang

, et al. (2020) Axial compressive behaviour of square through-beam joints between CFST columns and RC beams with multi-layers of steel meshes. Materials 13(11): 2482. DOI: 10.3390/ma13112482.

Duran

Tunaboyu

Kaplan

, et al. (2018) Effectiveness of seismic repairing stages with CFRPs on the seismic performance of damaged RC frames. Structural Engineering and Mechanics 67(3): 233–244.

ElGawady

Dawood

(2012) Analysis of segmental piers consisted of concrete filled FRP tubes. Engineering Structures 38: 142–152.

El-Sayed

(2014) Effect of longitudinal CFRP strengthening on the shear resistance of reinforced concrete beams. Composites Part B: Engineering 58: 422–429.

10.

Fakharifar

Chen

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

11.

Fam

Rizkalla

(2001) Behavior of axially loaded concrete-filled circular FRP tubes. ACI Structural Journal 98(3): 280–289.

12.

Fathuldeen

Qissab

(2019) Behavior of RC beams strengthened with NSM CFRP strips under flexural repeated loading. Structural Engineering and Mechanics 70(1): 67–80.

13.

GB/T 228.1 . (2010) Metallic Materials - Tensile Testing - Part 1: Method of Test at Room Temperature. Beijing, China: Ministry of Housing and Urban-Rural Development of the People’s Republic of China.

14.

GB/T 3354-2014 . (2014) Test Method for Tensile Properties of Orientation Fiber Reinforced Polymer Matrix Composite Materials. Beijing, China: Ministry of Housing and Urban-Rural Development of the People’s Republic of China.

15.

GB/T 50081-2002 . (2002) Standard for Test Method of Mechanical Properties on Ordinary the Concrete Strength of the Concrete. Beijing, China: Ministry of Housing and Urban-Rural Development of the People’s Republic of China.

16.

Hollaway

(2010) A review of the present and future utilisation of FRP composites in the civil infrastructure with reference to their important in-service properties. Construction and Building Materials 24(12): 2419–2445.

17.

Isleem

Wang

, et al. (2018) Monotonic and cyclic axial compressive behavior of CFRP-confined rectangular RC columns. Journal of Composites for Construction 22(4): 04018023.

18.

Jiang

Dai

, et al. (2012) Experimental study on concrete columns confined by BFRP-PVC tubes under uniaxial loading. Journal of Shenyang Jianzhu University (Natural Science) 28(1): 23–29.

19.

Jiang

, et al. (2014) Experimental study on reinforced concrete columns confined by FRP-PVC tubes under reversed loading. Journal of Building Structures 35(2): 111–118.

20.

Lim

Ozbakkaloglu

(2013) Confinement model for FRP-confined high-strength concrete. ACI Structural Journal 18(4): 04013058.

21.

Louk Fanggi

Ozbakkaloglu

(2015) Behavior of hollow and concrete-filled FRP-HSC and FRP-HSC-steel composite columns subjected to concentric compression. Advances in Structural Engineering 18(518): 715–738.

22.

Marthong

(2019) Rehabilitation and strengthening of exterior RC beam column connections using epoxy resin injection and FRP sheet wrapping: experimental study. Structural Engineering and Mechanics 72(6): 723–736.

23.

Lin

Jiang

(2012) Experimental study on flexural behavior of circular concrete-filled FRP-PVC tubular members. Journal of Shenyang Jianzhu University (Natural Science) 28(6): 988–996.

24.

Jiang

(2014) Study on behavior of concrete-filled CFRP-PVC tubular slender column under axial compression. China Civil Engineering Journal 47(1): 99–106.

25.

Mirmiran

Shahawy

(1997) Behavior of concrete columns confined by fiber composites. Journal of Structural Engineering 123(5): 583–590.

26.

Mohana

(2019) Reinforced concrete confinement coefficient estimation using soft computing models. Periodicals of Engineering and Natural Sciences 7(4): 1833–1844.

27.

Nordin

Täljsten

(2004) Testing of hybrid FRP composite beams in bending. Composites Part B: Engineering 35(1): 27–33.

28.

Ozbakkaloglu

(2013) Compressive behavior of concrete-filled FRP tube columns: assessment of critical column parameters. Engineering Structures 51: 188–199.

29.

Pantelides

Okahashi

Reaveley

(2008) Seismic rehabilitation of reinforced concrete frame interior beam-column joints with FRP composites. Journal of Composites for Construction 12(4): 435–445.

30.

Pham

Hadi

MNS

(2013) Strain estimation of CFRP confined concrete columns using the energy approach. Journal of Composites for Construction 17(16): 04013001.

31.

Pham

Hadi

MNS

(2014a) Predicting stress and strain of FRP-confined square/rectangular columns using artificial neural networks. Journal of Composites for Construction 18(6): 04014019.

32.

Pham

Hadi

MNS

(2014b) Stress prediction model for FRP confined rectangular concrete columns with rounded corners. Journal of Composites for Construction 18: 04013019.

33.

Saadatmanesh

Ehsani

(1994) Strength and ductility of concrete columns externally reinforced with fiber composite straps. Structural Journal 91(4): 434–447.

34.

Saafi

(2001) Development and Behavior of a New Hybrid Column in Infrastructure systems. PhD Thesis. Tuscaloosa, AL: University of Alabama.

35.

Shit

Roychowdhury

(2019) A numerical study on the behaviour of reinforced concrete slab strengthened with FRP laminates using finite element approach. Advances in Structural Engineering 2: 675–686.

36.

Toutanji

Saafi

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

37.

Wang

Smith

, et al. (2012) Experimental testing and analytical modeling of CFRP-confined large circular RC columns subjected to cyclic axial compression. Engineering Structures 40: 64–74.

38.

Xiao

(2003) Compressive behavior of concrete confined by various types of FRP composite jackets. Journal of Reinforced Plastics and Composites 22(13): 1187–1201.

39.

(2007) Experimental Study and Theoretical Analysis on Mechanical Behavior of PVC-FRP Confined Concrete columnPhD Thesis. Xian, China: Xi´an university of Architecture and Technology.

40.

Niu

(2013) Experimental study on PVC-CFRP confined reinforced concrete short column under axial compression. Journal of Building Structures 34(6): 129–136.

41.

Niu

(2016) Experimental study on axial behavior of PVC-CFRP confined concrete column under alkaline environment. Journal of Basic Science and Engineering 24(3): 573–581.

42.

Niu

(2018) Experimental study on PVC-CFRP confined concrete columns under low cyclic loading. Construction and Building Materials 177(20): 287–302.

43.

Niu

, et al. (2019a) A model for ultimate bearing capacity of PVC-CFRP confined concrete column with reinforced concrete beam joint under axial compression. Construction and Building Materials 214: 668–676.

44.

Zhang

Niu

, et al. (2019b) Strain analysis of PVC-CFRP confined concrete column with ring beam joint under axial compression. Composite Structures 224: 1–14.

45.

Zhu

(2018) Study on Mechanical Behavior of Joint of PVC-FRP Confined Concrete Column and Reinforced Concrete Beam under Axial compression. Master’s Thesis. Maanshan, China: Anhui University of Technology.

Deformation analysis of axially loaded weak PVC-fiber reinforced polymer confined concrete column-strong reinforced concrete beam joints reinforced with core steel tube

Abstract

Keywords

Introduction

Experimental program

Specimen design

Basic properties of test materials

Measurement scheme

Loading scheme

Analysis of test results

Failure mode

Stress analysis

Strain analysis

Carbon fiber reinforced polymer strips tensile strain

PVC tube compressive strain

Longitudinal steel bars strain

Stirrups strain

Core steel tube strain

Joint concrete strain

Stress–strain relationship analysis

Stress–strain relationship of PVC-FRP Confined Concrete column

Stress–strain relationship of joint

A model for predicting the stress–strain relationship

Previous model

A modified model

Modified f caR and ε cau

Modified f o

Model validation

Conclusions

Footnotes

Declaration of conflicting interests

Funding

Data availability

ORCID iDs

References

Modified $f_{caR}$ and $ε_{cau}$

Modified $f_{o}$