Flexural behavior and serviceability of concrete beams hybrid-reinforced with GFRP bars and steel bars

Journal Pre-proofs Flexural behavior and serviceability of concrete beams hybrid-reinforced with GFRP bars and steel bars Xiangjie Ruan, Chunhua Lu, Ke Xu, Guangyu Xuan, Mingzhi Ni PII: DOI: Reference:

S0263-8223(19)31702-7 https://doi.org/10.1016/j.compstruct.2019.111772 COST 111772

To appear in:

Composite Structures

Received Date: Revised Date: Accepted Date:

8 May 2019 10 October 2019 3 December 2019

Please cite this article as: Ruan, X., Lu, C., Xu, K., Xuan, G., Ni, M., Flexural behavior and serviceability of concrete beams hybrid-reinforced with GFRP bars and steel bars, Composite Structures (2019), doi: https://doi.org/10.1016/ j.compstruct.2019.111772

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Flexural behavior and serviceability of concrete beams hybrid-reinforced with GFRP bars and steel bars

Xiangjie Ruana, Chunhua Lua1, Ke Xua, Guangyu Xuana, Mingzhi Nia a Department

of Civil Engineering, Jiangsu University, Zhenjiang 212013, P. R. China

Abstract In this paper, six concrete beams reinforced with a combination of GFRP (glass fiber reinforced polymer) bars and steel bars, and three concrete beams reinforced only with steel bars were designed and tested. Several flexural behaviors of the tested beams were analyzed and compared with theoretical models. The experimental and analytical results showed that under the designed service loads, the crack width and deflection that appeared in the GFRP-steel reinforced concrete beams developed faster than those shown by the steel-reinforced concrete beams. With the same total reinforcement amount of GFRP and steel bars, the ultimate flexural capacity of GFRP-steel reinforced concrete beams was nearly 91-97% of that of steel-reinforced concrete beams, but the deflection and maximum crack width were obviously larger than those of steel-reinforced concrete beams under the same service load levels. The beam deformability

coefficient

approximately

decreased

with

increasing

nominal

reinforcement ratio ρnom,F. The area ratio of GFRP bars to steel bars Af/As had a great 1

Corresponding author. E-mails: [email protected] (C.H. Lu). 1

influence on the flexural behaviors of GFRP-steel reinforced concrete beams. Comparisons showed that the data obtained for flexural capacity, deflection, deformability and crack width of GFRP-steel reinforced concrete beams were consistent with the predictions calculated by the proposed models. Keywords: GFRP bar; Hybrid-reinforced concrete beam; Flexural behavior; Serviceability; Analytical modelling.

1. Introduction Corrosion of steel reinforcement in concrete has become a major cause of performance deterioration in concrete structures [1-3]. Reduction of the useful service life of reinforced concrete (RC) structures is often due to reinforcement corrosion [4]. Much research work has been conducted in attempts to reduce the costs of repairing corroded RC structures. In recent years, fiber reinforced polymer (FRP) bars have been widely used in the civil engineering field and are considered an ideal alternative to reinforcing bars [5, 6] due to their advantages of high strength, superior manufacturability and corrosion resistance [7-9]. Four typical types of FRP bars are glass, carbon, basalt and aramid FRP bars. Among 2

these, glass-FRP (GFRP) bars have relatively low tensile strength and cost, and therefore, they are often used to replace ordinary steel bars in concrete structures [10]. However, compared with steel bars, FRP bars usually have a low elastic modulus, and their stress-strain behavior is linear without a yield stage, meaning that concrete beams reinforced only with FRP bars exhibit larger crack width and deflection [11]. To overcome these problems, a hybrid-reinforced concrete beam designed with a combination of FRP bars and steel bars has been proposed. Several test results showed that steel yielding could ensure the beam’s ductility and that the high tensile strength of the FRP bars can increase the flexural capacity after steel yielding [12]. In addition, from the viewpoint of steel corrosion, replacement of the steel bars with FRP bars in the corners or near the outer surface of the tensile zone could be effective in improving the durability of the hybrid-reinforced concrete beam [13-16]. Thus, it is imperative that the structural performance of hybrid-reinforced concrete beams be properly investigated and characterized prior to their extensive engineering applications. In recent decades, great efforts have been made to explore the suitability of FRP bars used in concrete beams. Previous studies [17-20] indicated that the durability of RC structures can be improved with the used of FRP bars as a substitute for steel bars in concrete. However, the differences in mechanical properties between the FRP bar and steel bar also pose new challenges to the design of FRP reinforced concrete structures. Safan [21] reported that hybrid-reinforced concrete beams with GFRP bars and steel bars could effectively improve the ductility and reduce the crack widths and spacing 3

compared with pure FRP-reinforced concrete (FRP RC) beams. Lau and Pam [22] and Qin et al. [23] indicated that the hybrid reinforcement area ratio between FRP and steel bars, i.e., Af/As, had a great influence on the flexural behavior of hybrid-reinforced concrete beam because it affected the strength and ductility balance in the flexural design. Experimental observations conducted by Refai et al. [24] showed that the bonding coefficient also had a great influence on calculation of the crack width of the hybrid-reinforced concrete beams. For FRP reinforced concrete structures, many countries have issued various standards and guidelines such as the Recommendations from Japan Society of Civil Engineers (JSCE) 1997 [25], China National Standard GB 50608-2010 [26], Canadian Standards Association’s CSA-S806-12 [27] and American Concrete Institute (ACI) Committee 440.1R-15 [28]. However, most of these standards and guidelines are only suitable for pure FRP-reinforced concrete beams. Theoretical calculations for hybrid-reinforced concrete beams have not been stated in these guides and it was suggested that this work could be done based on the theories of the direct application of steel-reinforced concrete beams or pure FRP-reinforced concrete beams. As mentioned above, the area ratio of GFRP bars to steel bars Af/As has a great influence on the performance of hybrid-reinforced concrete beams. The mechanical properties and the bonding properties of GFRP bars and steel bars are obviously different, and therefore, it is necessary to further explore the flexural performance of hybrid-reinforced concrete beams. 4

This paper investigated the flexural performance of GFRP-steel reinforced concrete beams, which were designed to reduce steel corrosion, and the behaviors examined included flexural carrying capacity, deflection, crack width and deformability. A total of six hybrid-reinforced concrete beams and three reference concrete beams reinforced only with steel bars were prepared and tested. Based on the experimental results, the related calculation methods for hybrid-reinforced concrete beams were revised and improved. Finally, a comparison of the experimental results and the calculations was completed.

2. Theoretical Investigation 2.1. Reinforcement ratio

Due to the difference in mechanical properties between FRP bars and steel bars, it is necessary to consider the coordination ability of the two types of materials used in hybrid-reinforced concrete beams. Therefore, the reinforcement ratio ρ and the area ratio of the FRP bars to steel bars Af/As are two important indices used to evaluate the flexural performance of hybrid concrete beams. Clearly, the practical reinforcement ratio is the sum of the steel reinforcement ratio ρs and the FRP reinforcement ratio ρf, i.e., ρ=ρs + ρf. However, considering the diversity for both materials, the nominal reinforcement ratio ρnom is usually suggested to account for combinations of the elastic modulus or the tensile strength [29], as shown in Eq. (1) and Eq. (2), respectively. It should be noted that no direct relationship exists between Eq. (1) and Eq. (2), and they 5

are only two proposed methods used to define the nominal reinforcement ratio. Additionally, based on the material properties of FRP bars and steel bars, it is expected that the reinforcement ratio of FRP bars can be reduced based on Eq. (1), and in contrast, it can be enhanced as calculated by Eq. (2):

 nom,E  s 

Ef f Es

(1)

 nom,F  s 

f fd f fy

(2)

where ρnom,E and ρnom,F are two types of nominal reinforcement ratio, which are converted by the modulus of elasticity and tensile strength, respectively; Es and Ef are the elastic moduli of the steel and FRP bar, respectively; fy is the yield strength of the steel bars; and ffd is the design tensile strength of the FRP bars. Here, for GFRP bars used in this study, ffd=0.7ffu [28], where ffu is the ultimate tensile strength of the GFRP bars. For concrete beams in flexure, the failure modes of the section can be determined based on the limit conditions of concrete crushing in the compression zone and bar rupture (or yielding) in the tensile zone. If these two conditions occur synchronously, this reinforcement ratio is known as the balanced reinforcement ratio ρb. Therefore, for hybrid-reinforced concrete beams, the balanced reinforcement ratio can be predicted from two possible failure modes [29], namely (1) steel bar yielding and concrete crushing occur synchronously, and (2) FRP bar rupture and concrete crushing occur at same time. Fig. 1 shows the strain and stress distribution of a hybrid-reinforced concrete 6

beam under the limit states in which FRP and steel bars were placed in a single layer. In this work, x is the depth of the equivalent rectangular stress block, cb is the distance from the extreme compression fiber to the neutral axis at the balanced strain condition, εcu is the extreme concrete strain in compression, εy is the yielding strain of the steel bars, and εfd is the design rupture strain of the FRP bars. Considering the equilibria of forces and strain compatibility, the two balanced reinforcement ratios of hybrid-reinforced concrete beams with FRP and steel bars in one layer can be obtained as follows. Case 1: εc=εcu and 0<εs=εy=εf<εfd This failure mode expresses the condition in which steel bar yielding and concrete crushing occur synchronously before rupture of the FRP bars. As shown in Fig. 1b and c, the horizontal force equilibrium of the beam cross-section can be expressed as Eq. (3):

f y As  f f Af  11 f c,bcb1

(3)

where ff is the tensile stress of FRP bars, which is less than its design tensile strength, ffd; As and Af are the areas of the steel and FRP bars, respectively; α1 is the ratio of the average stress of the equivalent rectangular stress block to the cylinder compressive strength of concrete fc’; β1 is the ratio of the depth of the equivalent rectangular stress block to the depth of the neutral axis; b is the section width; and cb1 is the distance from the extreme compression fiber of concrete to the neutral axis. With the assumptions that the strains of the FRP bars and steel bars at the same depth 7

are equal and the relationship between stress and strain of the FRP bar is linear, Eq. (3) can be rewritten as follows: f y As 

fy Es

Ef Af  11 f c,bcb1

(4)

Based on the plane cross-section assumption, the relationship between the strains of the concrete and steel bar can be expressed as (see Fig. 1c): cb1  d

 cu

 cu   y

(5)

where d is the distance from the extreme fiber in compression to the center of reinforcement. Combining Eqs. (4) and (5), the following equation can be obtained:

 cu f c, Ef As  Af  11 bd fy  cu   y Es

(6)

Dividing by the term bd on both sides of Eq. (6), for the hybrid-reinforced concrete beam, the balanced reinforcement ratio ρb,E expressed by elastic modulus can be determined as follows:

 b,E  s 

f ,  cu Ef f  11 c f y  cu   y Es

(7)

where ρs=As/(bd) and ρf=Af/(bd). Case 2: εc=εcu, and εy<εs=εf =εfd This failure mode means that the steel bars yield first, and after that, the rupture of the FRP bars (ff=ffd) and concrete crushing occur synchronously. Under this condition, the horizontal force equilibrium of the beam cross-section can be expressed as Eq. (8) (see 8

Fig. 1b and d):

f y As  f fd Af  11 f c,bcb2

(8)

where cb2 is the distance from the extreme compression fiber of concrete to the neutral axis. Based on the plane cross-section assumption, the relationship between the strains of the concrete and steel bar can be determined as (see Fig. 1d): cb2  d

 cu

(9)

 cu   fd

Substituting the expression given in Eq. (9) into Eq. (8) and using the term fybd as the divisor, the balanced reinforcement ratio calculated by the steel bar strength ρb,F can be obtained as shown:

 b,F  s 

f ,  cu f fd f  11 c f y  cu   fd fy

(10)

If the modified Eq. (8) is divided by term ffdbd, another balanced reinforcement ratio defined by the FRP bar strength ρb,Ff can be obtained, as shown in Eq. (11). The guidelines of ACI 440.1R-15 [28] adopted this method and proposed Eq. (12) to calculate the balanced reinforcement ratio for pure FRP-reinforced concrete beams. Comparing Eq. (11) and Eq. (12), it can be observed that these two expressions are equal with the conditions of α1=0.85 and εfd=ffd/Ef.

 b,Ff 

fy f fd

s  f  11

fb  0.851

f c,  cu f fd  cu   fd

f c' Ef  cu f fd Ef  cu  f fd 9

(11)

(12)

Here, based on the definitions of the nominal reinforcement ratio shown in Eqs. (1) and (2), the balanced reinforcement ratios given in Eqs. (7) and (10) were used in this paper. Therefore, for hybrid-reinforced concrete beams, the designed failure mode should be described as follows: the steel bars yield first and the strain of FRP bars is less than or equal to the designed strain; subsequently, the concrete in compression is crushed and the beam finally fails. The nominal reinforcement ratios should meet the requirements of Eqs. (13a) and (13b) at the same time. If ρnom,E > ρb,E, the beam is believed to be over-reinforced, and flexural failure is expected to occur directly due to concrete crushing. However, if ρnom,F <ρb,F, the beam seems to be under-reinforced, and the steel and FRP bars are expected to rupture prior to concrete crushing. Of course, for structural safety, Case 2 is not expected in engineering practice, and therefore, Eq. (13b) is the basic requirement for FRP-reinforced concrete beams [28]:

nom,E  b,E

(13a)

nom,F  b,F

(13b)

It should be noted that the above analytical results are obtained from the hybrid-reinforced concrete beam with FRP and steel bars placed in a single layer. However, in this study, a double-layer hybrid-reinforced concrete beam is proposed in which FRP bars are placed at the bottom and steel bars are set over the FRP bars. If the sectional size and reinforcement areas are the same for the two types of the above mentioned hybrid-reinforced concrete beams, it can be confirmed that the strain of the FRP bars is still less than their design rupture strain εfd when the strain of the steel bars 10

in the double-layer hybrid beam reaches the yielding strain εy because the value of εfd is approximately 5-6 times the value of εy (see Fig.3). Therefore, the failure conditions described for Case 1 can still be satisfied by the double-layer hybrid beams. For Case 2, the failure mode is related to the FRP bar strain εfd, and it is certain that the steel bars will yield before the FRP bars rupture. It can be concluded that this mode does not change when the steel bars in the single-layer hybrid beam move upwards within a limited height to form the double-layer hybrid beam. In conclusion, for two types of hybrid-reinforced concrete beams with the same sectional size and reinforcement areas of FRP bars and steel bars, the requirements for the nominal reinforcement ratios shown in Eq. (13) are still applicable to the double-layer hybrid-reinforced concrete beams investigated in this study.

2.2. First cracking moment

Usually, the cracking load and the beam’s stiffness before cracking are controlled by the sectional dimension and the concrete strength. The guideline of ACI440.1R-15 [28] gives an expression for the cracking moment Mcr of FRP-reinforced concrete beams, as shown in Eq. (14). Similarly, the standard of CSA-S806-12 [27] recommends using Eq. (15) to calculate the first cracking moment of concrete beams: M cr 

M cr 

0.62 f c, I g yt 0.6 f c, I g yt 11

(14)

(15)

where λ is the modification factor reflecting the reduced mechanical properties of light weight concrete, and λ=1.0 for normal density concrete used in this study; Ig is the moment of inertia of the gross section; and Ig=(bh3)/12, where h is the height of the beam; and yt is the distance from the centroidal axis of the gross section.

2.3. Flexural strength

For the hybrid-reinforced concrete beams in flexure, Ge et al [29] proposed a model for predicting the ultimate flexural capacity Mu, which is expressed with parameter ξ, i.e., the ratio of depth x to distance d (see Fig. 1a and b). In this work, based on the definition of parameter ξ, the beam’s ultimate flexural capacity Mu can also be equivalently expressed with the depth x, as shown in Eq. (16).

x M u  1 f c,bx(d  ) 2

(16)

In Eq. (16), the depth of the equivalent rectangular stress block x could be determined based on the sectional internal force equilibrium and the plane cross-section assumption, which can be determined as shown [29]: x

f y As  Ef  cu Af  ( f y As  Ef  cu Af ) 2  411 f c, cu Ef Af bd 21 f c,b

(17)

It should be noted that the Eqs. (16) and (17) are suitable for rectangular sectional beams with single reinforcement, similar to the beams tested in this study, in which the reinforcing bars placed in the compressive upper concrete are ignored. Besides, the above models can be applied to evaluate the ultimate flexural capacity of both the

12

single- and double-layer hybrid-reinforced concrete beams tested in this work.

2.4. Deflection at mid-span

Because the FRP bars have a lower modulus of elasticity than the steel bars, the design of the hybrid-reinforced concrete beams is usually controlled by the serviceability limit state. Therefore, it is necessary to calculate and verify the deflection of the hybrid-reinforced concrete beams. The method used to predict the deflection of FRP-reinforced concrete beams proposed by the guidelines of ACI440.1R-15 [28] was built based on the effective moment of inertia, which can be expressed by Eq. (18):

Ie 

I cr 2

M   I 1    cr  1- cr   M a   Ig

  

 Ig

(18)

where Ie is the effective moment of inertia; Icr is the moment of inertia of the cracked section; γ is the parameter that considers the variation in stiffness along the length of the member, γ=1.72-0.72(Mcr/Ma), and in this situation, Mcr is the cracking moment and Ma is the applied moment. According to the code of ACI318-14 [30], the effective moment of inertia of steel-reinforced concrete beams Ie can also be given by Eq. (19): 3   M 3   M cr  cr Ie    I g  1     I cr  I g   M a    Ma 

(19)

For the four-point bending beam, the maximum deflection at mid-span Δm after concrete cracking can be calculated by Eq. (20) [28]:

13

m 

Pa  3L2  4a 2  48 Ec I e

(20)

where P is the applied load, a is the shear span of the beam, and L is the span of the beam. The standard of CSA-S806-12 [27] suggests that the formula for calculating the maximum deflection of a four-point bending beam is Eq. (21): 3  I PL3   a   a  m  3    4    8 1  cr  48 Ec I cr   L   L   Ig 

3   Lg         L  

(21)

where Lg  a

M cr Ma

(22)

The moment of inertia of the cracked section Icr can be estimated by Eqs. (23) and (24) [24]:

I cr 

bd 3 3 2 k   ns As  nf Af  d 2 1  k  3

k  2(nf f  ns s )   nf f  ns s   (nf f  ns s ) 2

(23) (24)

where ns=Es/Ec, and nf =Ef/Ec.

2.5. Crack width

The guide of ACI440.1R-06 [31] gives a formula for predicting the maximum crack width of FRP-reinforced concrete beams, as shown in Eqs. (25) and (26). w=2 f  kb

s d   2 2 c

14

2

(25)

f 

Ma  Af Ef  As Es  d (1  k 3)

(26)

where w is the maximum crack width at the height of the center of the bars; εf is the tensile strain at the centroid of the reinforcing zone; β is the ratio of the distance from the neutral axis to the extreme tension fiber to the distance from the neutral axis to the center of the tensile reinforcement, and β=(h-kd)/[d/(1-k)], where k can be calculated by Eq. (24); dc is the thickness of the cover from the tension surface to the center of the closest bar; s is the longitudinal reinforcement spacing; kb is the bond coefficient, and kb=1.0 for the steel bar and 1.4 for the FRP bar [31]. Refai et al. [24] reported that the bond coefficient could be obtained in the form of Eq. (27): A  kb  1.4  f   As 

1 5

(27)

where the parameter α is taken as 1.0 and 1.2 for GFRP bars of diameters 12 mm and 16 mm, respectively.

2.6. Deformability

The definition of traditional ductility of the concrete beams refers to the ability to absorb energy without severe damage, usually related to the yield of steel or the ability to deform before the concrete is crushed. Because the FRP bars have no yield point, the ductility of the hybrid-reinforced concrete beams is not the same as those of the steel-reinforced or pure FRP-reinforced concrete beams. Therefore, the term ‘deformability’ is adopted instead of ‘ductility’ in this study [27]. 15

Jeager el al. [32] conducted an experimental study on the deformability of pure FRP-reinforced concrete beams and steel-reinforced concrete beams and proposed that the deformability of these two types of beam can be evaluated using a deformation-based approach in which the deformability index μE,Δ can be described by Eq. (28):

E, 

u M u 0.001 M 0.001

(28)

where Mu and u are the moment and curvature at the ultimate state, respectively; and M0.001 and 0.001 are the moment and curvature at a service limit state with the corresponding concrete strain εc=0.001. Based on an energy-based approach, Naaman and Jeong [33] proposed a model for calculating the deformability index μE,A of pure FRP-reinforced concrete beams, as follows:

E,A  0.5  ET Eel  1

(29)

where ET is the total energy computed with the area under the load-deflection curve up to the failure load, and Eel is the elastic energy released at the failure. Obviously, the deformability indices defined by Eqs. (28) and (29) are quite different. However, it should be noted that both deformability indices can effectively indicate the ability to absorb inelastic energy without loss of the load capacity [34]. Therefore, these two methods were used to evaluate the effect of the nominal reinforcement ratio on the deformability of the hybrid-reinforced concrete beams in this paper. 16

3. Experimental programmes 3.1. Materials

The coarse aggregate was made of crushed stone with a particle size of 2.5-16mm. The fine aggregate was made of river sand with a fineness modulus of 2.4. Grade 42.5 ordinary Portland cement (OPC), which can be approximately classified as Type I cement based on the ASTM C150 standard [35], was used as the cementitious material. Based on the strength grade of 35 MPa and the Specification for Mix Proportion Design of Ordinary Concrete used in China, the concrete used in this study was designed with water-to-cement (W/C) ratio of 0.49. The detailed mixture contents of the concrete and its 28-day compressive strength fcu, as determined on standard 150 mm concrete cubes based on Chinese code, are listed in Table 1. In addition, it should be noted that in this study the cylinder compressive strength of concrete fc’ was adopted in the analysis of the beam flexural behaviors based on ACI codes and guidelines [28, 30], and that the value of fc’ was assumed with the expression of fc’=0.8fcu [36]. Two types of GFRP bars with nominal diameters of 12 mm and 16 mm were adopted in this investigation, and both were manufactured by Nanjing Fenghui Composite Material Co. Ltd. (Jiangsu, China), as shown in Fig. 2. The GFRP bars were made from continuous longitudinal E-glass fibers impregnated in a vinyl ester resin using the pultrusion process, and their fiber volume fraction was approximately 64%. The hot-rolled ribbed steel bars HRB400 with nominal diameters of 12 mm and 16 mm were 17

used as common reinforcing steel bars. The mechanical properties of GFRP and HRB400 bars were tested and are reported in Table 2. Fig. 3 shows the typical tensile stress-strain curves of all bars tested in this study.

3.2. Test specimens

A total of nine rectangular sectioned beams of dimensions 180 × 300 × 1800 mm were prepared (shown in Fig. 4a). To compare the flexural behaviors, three steel-reinforced concrete beams were chosen for testing in this study, and six GFRP-steel reinforced concrete beams were designed. A portion of the steel bars in the steel-reinforced concrete beams was replaced with GFRP bars with consideration of the bar diameter, elastic modulus and tensile strength. From the viewpoint of alleviating steel corrosion in concrete, two types of hybrid reinforcement methods were adopted (shown in Fig. 4b): 1) single-layer form, in which the GFRP bars were placed at the corner of the section; and 2) double-layer form, in which the GFRP bars were placed at the bottom of the section at the tensile zone. It can be observed from Fig. 4b that GFRP bars with equal or similar diameter were selected to replace the steel bars. The net cover between the outside of concrete and the bottom of the outermost bar was 30 mm, and the clear vertical distance between the GFRP and steel bars in the double-layer form was 25 mm. Both the steel bars used in erection and the stirrups were made from HPB300 grade steel bars with a nominal diameter of 8 mm. The spacing of the stirrups was 100mm. Additional details on the tested beams are shown in Fig. 4. 18

To directly compare the two types of hybrid-reinforced beams, the double-layer hybrid-reinforced concrete beams were designed with the same sectional size and reinforcement areas of the GFRP bars and steel bars used in the single-layer beams. The sectional reinforcement ratios of the test beams were calculated by Eqs. (1), (2), (7) and (10) with α1=0.85, β1=0.85 and εcu=0.003 [28], and the results are given in Table 3. It should be noted that the reinforcement ratios of ρnom,E and ρnom,F for the double-layer beams are slightly higher than those of the single-layer beams with the same reinforcement areas because the effective height d becomes slightly smaller in the double-layer beams. The ρnom,E/ρb,E ratios of all hybrid-reinforced concrete beams were in the range of 0.23 (beam 2G12-1S16) to 0.30 (beam 2G16-2S12(D)), and the ρnom,F/ρb,F ratios ranged between 1.33 (beam 2G12-1S16) and 2.19 (beam 2G16-2S12(D)), assuring that no beam fails under the condition of Case 2. It is clear that all test beams simultaneously meet the requirements given by Eq. (13).

3.3. Test setup and procedures

All beams were subjected to four-point flexural testing, as shown in Fig. 5. Strain gauges were placed at the top, side and bottom surfaces of the test beams to verify the plane section assumption. Five linear variable differential transducers set at the locations of the supports and bottom surface were placed to measure the deflection. During the flexural test, the loads were applied in a step-by-step manner and all loading and concrete strain data were automatically collected by the instruments. Each step load 19

was hold for more than ten minutes, and the deformations and the crack development of the test beam were subsequently detected and recorded.

4. Test results and analysis 4.1. First cracking moment

Table 4 shows the experimental values of the first cracking moment Mcr-exp of all test beams. Based on the recommended models given in Eqs. (14) and (15) [27, 28], the theoretical results of first cracking moment Mcr-th were predicted with fc’ = 0.8fcu = 30.32N/mm2 [36], and the calculations are also added in Table 4. It can be observed from Table 4 that the measured cracking moments of the hybrid-reinforced beams were an average of 8% and 11% higher than those predicted with Eq. (14) and Eq. (15), respectively. It seems that the ACI440.1R-15 equation [28] gives slightly better predictions than the CSA-S806-12 equation [27] for the cracking moment of hybrid-reinforced beams.

4.2. Flexural capacity

Based on the applied load at failure of the bending beam, the experimental ultimate flexural moment Mu-exp could be obtained. The theoretical ultimate flexural moment Mu-th was predicted using Eq. (16) with α1=0.85 [28] and fc’=0.8fcu=30.32 N/mm2 [36]. Both the experimental and predicted results of the ultimate flexural moment are given in Table 5. It can be observed from Table 5 that when the steel bars were substituted with 20

GFRP bars with the same area, the ultimate flexural capacity of the GFRP-steel reinforced concrete beams was 91-97% of that of steel-reinforced concrete beams. Selected experimental results of the flexural capacity of hybrid concrete beams with GFRP and steel bars published in the literature [15, 24] and their calculations with Eq. (16) are also shown in Table 5. The average value of the ratio Mu-th/Mu-exp is 0.92, and its coefficient of variation is 0.10. This outcome indicates that the data for the beam flexural capacity obtained in our experiment and in other studies have equivalent credibility and can be predicted by Eq. (16).

4.3. Strain Distribution

For several typical flexural beams, Fig. 6 shows the measured strain distribution along the beam depth at the mid-span section under various load levels. It can be found from Fig. 6 that the strain distribution of the hybrid-reinforced concrete beams is similar to that of the steel-reinforced concrete beams, which means that the hybrid-reinforced concrete beam still conforms to the assumption of plan cross-section. In general, these observations are in accordance with the results given in previous experimental studies [15, 37].

4.4. Flexural response

In the form of comparison, the moment-deflection curves of the test beams are shown in Fig. 7. It can be concluded from Fig. 7 that for all beams, the moment-deflection 21

relationship at the initial stage shows a linear characteristic. When the applied moment increases to (0.1-0.15) Mu-exp, the first one or two cracks generally appear at the middle zone of the beam, and at the same time, the cracking moment Mcr can be determined and recorded. After cracking, the beam stiffness begins to decrease, and the deflection begins to increase. When the moment increases to (0.5-0.6) Mu-exp, the maximum crack width of the hybrid-reinforced concrete beam exceeds 0.5 mm, which means that the limit state of serviceability is reached, and the stress of the tensile steel bar is in the range of 330-370 N/mm2. When the applied moment reaches (0.80-0.87) Mu-exp, the steel bar yields first. After yielding, the moment continues to increase due to the action of the GFRP bars. Finally, the concrete at the upper compression zone is crushed, and the beam fails. For steel-reinforced beams, it can be observed from Fig. 7a that under the same load level, the deflection of the 3S16 beam with a higher steel reinforcement ratio (ρs=1.31%) is smaller than that of the 4S12 beam with ρs=0.98%. When the reinforcement area As is equal, the deflection of the 4S12(D) beam with double-layer reinforcement develops faster than that of the single-layer steel-reinforced beam 4S12. For hybrid-reinforced concrete beams, Qin et al. [23] found that the area ratio of FRP and steel bars Af/As had a great influence on the flexural behavior and suggested a limited area ratio Af/As, which varied from 1 to 2.5, to ensure deformability and prevent brittle failure. Based on the bar areas and the area ratio Af/As, the moment-deflection curves of the single-layer hybrid-reinforced concrete beams were divided into two 22

groups and are plotted in Fig. 7b and c, respectively. It can be observed from Fig. 7b and c that when the steel bars were substituted with GFRP bars with the same area, such as beams 4S12 and 2G12-2S12 and beams 3S16 and 2G16-1S16, the deflection of the hybrid-reinforced concrete beam is 1.15 to 2.1 times that of the steel-reinforced beams under the same load level. For hybrid-reinforced concrete beams with the same area of GFRP bars, such as beams 2G12-2S12 and 2G12-1S16 and beams 2G16-2S12 and 2G16-1S16, the deflection increases with the increase of the ratio Af/As. For instance, beam 2G12-1S16 (Af/As=1.12) suffers a larger deflection than beam 2G12-2S12 (Af/As=1.0), and the deflection of beam 2G16-1S16 (Af/As=2.0) is also larger than that of beam 2G16-2S12 (Af/As=1.78). Additionally, it can be found from Fig. 7d that for hybrid-reinforced concrete beams with a slightly larger area of GFRP bars, such as beams 2G16-2S12 and 2G12-2S12, the deflection of beam 2G16-2S12 (Af/As=1.78) is obviously larger than that of beam 2G12-2S12 (Af/As=1.0). It can be proved from the above results that the effect of the Af/As ratio on the flexural behavior of hybrid concrete beams is obvious, and the post-elastic strength of the beam with sufficient deformability and stiffness can be ensured for beams with an Af/As ratio of 1.0-2.0 [23]. For two types of hybrid-reinforced beams with same amount of steel and GFRP bars, such as beams 2G12-2S12 and 2G12-2S12(D) and beams 2G16-2S12 and 2G16-2S12(D), a comparison of their moment-deflection curves is also shown in Fig. 7d. It can be found from Fig. 7d that the deflection of the single-layer hybrid-reinforced concrete beam develops slightly faster than that of the double-layer hybrid-reinforced 23

concrete beam, which means that the speed of the stiffness degradation of the double-layer hybrid-reinforced concrete beam is slightly slower than that of the single-layer hybrid-reinforced concrete beam. For all test beams, with increasing applied moment, the development of crack spacing and crack width was observed and recorded. Fig. 8 shows the average crack spacing of typical test beams. It can be observed from Fig. 8 that under the same load level, the average crack spacing of hybrid concrete beams is larger than that of steel-reinforced beams. It can also be found that the average crack spacing is influenced by the nominal reinforcement ratio ρnom,F. The larger the ratio ρnom,F, such as beam 2G16-2S12(D) with ρnom,F of 1.58%, the smaller the average crack spacing. The failure modes for all test beams were observed and examined in the experiment. The steel-reinforced beams 4S12, 3S16 and 4S12(D) failed in the typical mode appeared in the appropriate reinforced beams in which the steel bars yield first and the beams subsequently fail due to concrete crushing at the compression zone. For all tested hybrid-reinforced concrete beams, the steel bars also yield first, and the upper concrete in compression cracks longitudinally and is gradually crushed with the increasing of moment and deflection. When obvious damage is found in the upper concrete, the hybrid-reinforced beam is considered to have failed in flexure. At the same time, the GFRP bars have not ruptured for all hybrid-reinforced concrete beams. This failure phenomenon is compatible with the designed failure mode in which the steel bars yield first and the strain of the GFRP bars is less than the rupture strain. The concrete in 24

compression is subsequently crushed, and the beam finally fails. It can be concluded from the above results that the nominal reinforcement ratios required by Eq. (13) are valid for the single-layer and double-layer hybrid-reinforced beams tested in this study. For all tested beams, the physical maps of the crack distribution at failure are shown in Fig. 9.

4.5. Moment-deflection response

The mid-span deflection of hybrid-reinforced concrete beams with the a M/Mu,exp ratio up to nearly 60% is shown in Fig. 10. The predictions calculated by the ACI440.1R-15 model (Eq. (18) and Eq. (20)), the ACI318-14 model (Eq. (19) and Eq. (20)) and the CSA-S806-12 model (Eq. (21)) are also given in Fig. 10. It can be observed that the calculations given by the ACI440.1R-15 model and ACI318-14 model were nearly equal and that both of them underestimated the deflection measured in all cases at the service moment (up to 0.6 Mu-exp), whereas a great difference in the deflection calculated by the CSA-S806-12 model could be observed for single-layer and double-layer hybrid-reinforced concrete beams. A previous study [39] indicated that the calculation formula of Eq. (18) cannot effectively predict the deflection of hybrid-reinforced concrete beams under the limit state of serviceability, especially if the beam reinforcement is insufficient. Therefore, based on Eq. (18), the effective moment of inertia used in this paper is modified as in Eq. (30).

25

Ie  

I cr 2

M   I  1    cr  1- cr     M a   Ig 

 Ig

(30)

where κ is the reduction factor, and κ=0.64 [40]. In this work, the predictions of mid-span deflection were recalculated based on Eqs. (20) and (30), and the results are also given in Fig. 10. To validate the modified expression of Eq. (30), certain other experimental results from hybrid concrete beams with FRP and steel bars published in the literature [15, 29, 38] were compared with the calculations of Eq. (30), and the results are given in Fig. 11. It can be concluded from Fig. 10 and Fig. 11 that the test results and predictions calculated by Eq. (30) are in good agreement when the reduction factor κ is 0.64.

4.6. Crack width

The relationships between the maximum crack width and the applied moment are plotted in Fig. 12. From Fig. 12, it can be found that under the service load level, the maximum crack width of the hybrid-reinforced concrete beam is 1.3 to 2.2 times that of the steel-reinforced beams, which indicates that the crack-resistant ability of the hybrid-reinforced concrete beam is obviously weaker than that of the steel-reinforced beam. Fig. 12a and b show the comparative results of the moment-maximum crack width curves of single-layer hybrid-reinforced concrete beams. With the same area of GFRP bars Af, the maximum crack width of hybrid-reinforced concrete beams increases with increasing ratio Af/As. From Fig. 12c, it can be found that the maximum crack 26

width of single-layer hybrid-reinforced concrete beams develops faster than that of double-layer hybrid-reinforced concrete beams. Aiello and Ombres [38] investigated the cracking behavior of concrete beams hybrid-reinforced with AFRP (aramid fiber reinforced polymer) bars and steel bars. The same results were observed in that the use of FRP bars in combination with steel bars increased the crack width and crack spacing compared with those of the steel-reinforced beams. Fig. 13 shows a comparison of the measured maximum crack widths and predicted values for all hybrid-reinforced beams. The predictions of the maximum crack width were obtained based on Eqs. (25)-(27). The result shown in Fig. 13 indicates that the bond coefficient kb has a great effect on the predictions. For single-layer hybrid-reinforced concrete beams, the predictions with the value of kb calculated by Eq. (27) can effectively estimate the experimental results of maximum crack width. While, the value of kb=1.0 proposed in ACI-440.1R-06 [31] is more suitable for the double-layer hybrid-reinforced concrete beams.

4.7. Deformability

Table 6 shows the calculations of the deformability index at the ultimate moments. When the area As is equal, the deformability index of the hybrid-reinforced beams with high reinforcement ratio (2G16-2S12 and 2G16-1S16) becomes smaller than that of the beams with low reinforcement ratio (2G12-2S12 and 2G12-1S16). This result indicates that the area ratio of GFRP bars to steel bars Af/As also has a great influence on the 27

deformability of hybrid-reinforced concrete beams. It still can be found from Table 6 that for two types of hybrid-reinforced beams with the same amount of steel and GFRP bars, such as beams 2G16-2S12 and 2G16-2S12(D), the deformability index of the single-layer hybrid-reinforced concrete beam is larger than that of the double-layer hybrid-reinforced concrete beam. Fig. 14 shows the relationship between the deformability index and nominal reinforcement ratio ρnom,F. From Fig. 14, an approximately linear decreasing trend of the deformability index can be found for hybrid-reinforced concrete beams with the increase of nominal reinforcement ratio ρnom,F, especially for the deformability index determined by Eq. (28). A similar phenomenon has also been found in other studies [23, 41, 42].

Conclusions In this paper, the flexural behavior of GFRP-steel reinforced concrete beams was tested and analyzed. With the aim of reducing the risk of steel corrosion in concrete, two types of hybrid reinforcement methods were proposed and used to replace the steel bars with GFRP bars. Based on the existing theoretical models, the experimental results were compared with the predictions and the following conclusions can be drawn from this study. 1. The assumption of plan cross-section is still effective for the tested hybrid-reinforced concrete beams. The flexural performance and crack development of 28

hybrid-reinforced concrete beams are similar to those observed in steel-reinforced beams. 2. No obvious difference was observed in the first cracking moment between hybrid-reinforced beams and steel-reinforced beams, and the model in Eq. (14) proposed by ACI440.1R-15 [28] can effectively predict the first cracking moment of all test beams. 3. For all tested hybrid-reinforced beams, the failure in flexure is compatible with the designed failure mode in which the steel bars yield first, the concrete in compression is subsequently crushed, and the beam finally fails. During this period, the strain of GFRP bars is less than the rupture strain. This observation means that the nominal reinforcement ratios required by Eq. (13) are valid for these hybrid-reinforced beams. 4. For the hybrid-reinforced beam with same area of GFRP bars replacing the steel bars, the ultimate flexural capacity is found to be slightly less (approximately 5% less on average) than that of the referenced steel-reinforced concrete beam. The ultimate flexural capacity of the hybrid-reinforced beams can be effectively evaluated by Eq. (16). 5. With equal section substitution between two bars, the deflection of the hybrid-reinforced concrete beam is 1.15 to 2.1 times that of steel-reinforced beams under the same load level. It was found that the deflection of the hybrid-reinforced beams obviously increases with the increasing of the ratio Af/As. Additionally, with the same reinforcements, the deflection of the single-layer hybrid beam develops faster than 29

that of the double-layer hybrid beam. The deflection calculations with the effective moment of inertia expressed by the modified Eq. (30) are in good agreement with the experimental results. 6. Similar to deflection, the maximum crack width of the hybrid-reinforced concrete beam is larger than that of the steel-reinforced beam, and it increases with increasing ratio Af/As. Besides, the maximum crack width of the single-layer hybrid beam also develops faster than that of the double-layer hybrid beam. Eq. (25) proposed by ACI440.1R-06 can be used to predict the maximum crack width with kb equal to 1.4 and 1.0 for single- and double-layer hybrid-reinforced concrete beams, respectively. 7. The deformability index of the hybrid-reinforced beams with high Af/As ratio becomes smaller than that of the beams with low Af/As ratio. Approximately, the deformability index of the hybrid-reinforced concrete beams decreases linearly with the increase of reinforcement ratio ρnom,F.

Acknowledgements The authors acknowledge financial support from the National Natural Science Foundation of P.R. China (Grant Nos. 51578267 and 51878319) and the ‘six talent peaks’ project in Jiangsu Province (Grant No. 2015-JZ-008).

Data availability statement All data included in this study are available upon request by contacting the corresponding author. 30

Notations The following symbols were used in this paper: As

areas of steel bars (mm2)

Af

areas of FRP bars (mm2)

a

depth of equivalent rectangular stress block (mm)

b

width of rectangular cross section (mm)

cb

distance from extreme compression fiber to neutral axis at balanced strain condition (mm)

d

distance from extreme fiber in compression to the center of reinforcement (mm)

dc

thickness of the cover from the tension surface to the center of the closest bar (mm)

Es

modulus of elasticity of steel (MPa)

Ef

elastic modulus of FRP bar (MPa)

ET

total energy computed with the area under the load-deflection curve up to the failure load

Eel

elastic energy released at the failure

fy

yield strength of steel bar (MPa)

ff

stress of tensile FRP bar which is less than its design tensile strength (MPa)

f c,

cylinder compressive strength of concrete (MPa)

fcu

150mm cubic compressive strength of concrete (MPa)

h

height of the beam (mm)

Mcr

cracking moment (N-mm)

Ma

applied moment (N-mm)

Mu

moment at ultimate state (N-mm) 31

M0.001

moment at a service limit state with the corresponding concrete strain εc=0.001 (N-mm)

Ie

effective moment of inertia (mm4)

Icr

moment of inertia of the cracked section (mm4)

Ig

moment of inertia of gross section (mm4)

kb

the bond coefficient

yt

the distance from centroidal axis of gross section (mm)

s

longitudinal reinforcement spacing (mm)

w

maximum crack width (mm)

α1

ratio of average stress of equivalent rectangular stress block to f c,

β

ratio of distance from neutral axis to extreme tension fiber to distance from neutral axis to center

of tensile reinforcement β1

ratio of the depth of the equivalent rectangular stress block to the depth of the neutral axis

λ

the modification factor reflecting the reduced mechanical properties of light weight concrete

εc

strain in concrete

εcu

ultimate strain in concrete

εy

strain in steel bar

εfu

design rupture strain of FRP bar

εf

tensile strain at the centroid of the reinforcing zone

γ

parameter to account for the variation in stiffness along the length of the member,

u

the moment and curvature at ultimate state

0.001

curvature at a service limit state with the corresponding concrete strain εc=0.001 32

ρs

steel reinforcement ratio

ρf

FRP reinforcement ratio

ρb,E

balanced reinforcement ratio expressed by elastic modulus

ρb,F

balanced reinforcement ratio calculated by strength of hybrid-reinforced concrete beams

ρnom,F

nominal reinforcement ratio converted by bar’s strength

ρnom,E

nominal reinforcement ratio calculated by elastic modulus



cross section relative to the height of the compression zone

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[26] GB50608. Technical Code for Infrastructure Application of FRP Composites. Beijing, China: China Planning Press; 2010. (In Chinese). [27] CSA-S806-12. Design and construction of building components with fibre-reinforced polymers. Ontario (Canada): Canadian Standards Association; 2012. [28] ACI Committee 440. Guide for the design and structural of concrete reinforced with Fiber-reinforced polymer (FRP) bars (ACI 440.1R-15). American Concrete Institute, Farmington Hills, MI, USA, 2015. [29] Ge W, Zhang J, Gao D, Tu Y. Flexural behaviors of hybrid concrete beams reinforced with BFRP bars and steel bars. Constr Build Mater 2015; 87: 28-37. [30] ACI Committee 318. Building code requirements for structural concrete (ACI 318-14) and commentary (ACI 318R-14). Farmington Hills, MI: American Concrete Institute; 2014. [31] ACI Committee 440. Guide for the design and construction of concrete reinforced with FRP bars (ACI 440.1R-06). American Concrete Institute, Farmington Hills, MI, USA, 2006. [32] Jaeger LG, Mufti AA, Tadros G. The concept of the overall performance factor in rectangular-section reinforced concrete members. Proc. 3rd Int. Symp. Non-Metallic Reinf. Concr. Struct, vol. 2. 1997, 551-9. [33] Naaman A, Jeong S. Structural ductility of concrete beams prestressed with FRP tendons, Non-metallic (FRP) reinforcements for concrete structures. Proc. 2nd Int. Symp. FRPRCS-2. 1995, 379-86. [34] Park Y, Kim YH and Lee SH. Long-term flexural behaviors of GFRP reinforced concrete beams exposed to accelerated aging exposure conditions. Polymers 2014. 6(6): 1773-93. 36

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and

aramid

reinforcement.

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Figure captions Fig. 1. Strain and stress distribution under limit states: (a) cross-section of hybridreinforced concrete beam with FRP and steel bars in one layer; (b) equilibrium of forces; (c) failure at the condition of steel yielding and concrete crushing; (d) failure at the condition of FRP rupture and concrete crushing. Fig. 2. Reinforcements of (a) GFRP with diameter of 16 mm, (b) GFRP with diameter of 12 mm, (c) HRB400 bar with diameter of 16 mm and (d) HRB400 bar with diameter of 12 mm. Fig. 3. Tensile stress-strain curves of two kinds of bars tested in this study. Fig. 4. Schematic diagrams of test beams: (a) details of beam’s reinforcements and (b) details of beams’ section. Fig. 5. Diagram of test setup. Fig. 6. Strain distribution of test beams: (a) beam 4S12, (b) beam 2G12-2S12 and (c) beam 2G12-2S12(D). Fig. 7. Moment-deflection relationships of test beams: (a) the moment-deflection curves of steel reinforced concrete beams, (b) and (c) the moment-deflection curves of single-layer hybrid-reinforced concrete beams, and (d) the moment-deflection curves of two kinds of hybrid-reinforced concrete beams. Fig. 8. Measured average crack spacing versus applied moment. Fig. 9. Crack distribution at failure of all tested beams. Fig. 10. Comparisons of mid-span deflection between experimental and calculated 38

results: (a) beam 2G12-2S12, (b) beam 2G16-2S12, (c) beam 2G12-1S16, (d) beam 2G16-1S16, (e) beam 2G12-2S12(D), and (f) beam 2G16-2S12(D). Fig. 11. Comparison of mid-span deflection between test results got from literatures and predictions with Eq. (30). Fig. 12. Relationships between maximum crack width and applied moment: (a) comparison between beams 4S12, 2G12-2S12 and 2G12-1S16, (b) comparison between beams 3S16, 2G16-2S12 and 2G16-1S16, and (c) comparison between beams with different reinforcement arrangements. Fig. 13. Comparison of measured and predicted maximum crack width: (a) beam 2G12-2S12, (b) beam 2G16-2S12, (c) beam 2G12-1S16, (d) beam 2G16-1S16, (e) beam 2G12-2S12(D), and (f) beam 2G16-2S12(D). Fig. 14. Relationship between deformability index and nominal reinforcement ratio ρnom,F of test beams.

Table captions Table 1 Mix design and strength of concrete. Table 2 Mechanical properties of GFRP bars and steel bars. Table 3 Reinforcement ratios of test beams. Table 4 Results of beams’ cracking moments. Table 5 Results of beams’ ultimate moments. Table 6 Comparison of deformability index. 39

b

εcu

α1fc,bx

εcu cb1

x=β1cb

cb2

d M As+Af (a)

ffAf+fy As (b)

εy

εfd

(c)

(d)

Fig. 1. Strain and stress distribution under limit states: (a) cross-section of hybridreinforced concrete beam with FRP and steel bars in one layer; (b) equilibrium of forces; (c) failure at the condition of steel yielding and concrete crushing; (d) failure at the condition of FRP rupture and concrete crushing.

40

(a)

(b)

(c)

(d)

Fig. 2. Reinforcements of (a) GFRP with diameter of 16 mm, (b) GFRP with diameter of 12 mm, (c) HRB400 bar with diameter of 16 mm and (d) HRB400 bar with diameter of 12 mm.

41

1000

ffu

12mm HRB400 steel bar 16mm HRB400 steel bar 12mm GFRP bar 16mm GFRP bar

Stress (MPa)

800

0.7ffu 600

fy

400 200 0

y

0.01

fd 0.02

0.03

0.04

0.05

0.06

Strain (mm/mm)

Fig. 3. Tensile stress-strain curves of two kinds of bars tested in this study.

42

2 8 8@100

600

8@100

600

600

(a)

2 8 Steel

300

300

2 8 Steel

2 12 Steel 2 12

4 12 Steel

2 12 Steel 2 16 GFRP

GFRP

2G12-2S12

2G16-2S12

180

180

180

1 16 Steel 2 12

2 8 Steel

300

2 8 Steel

300

2 8 Steel

3 16 Steel

1 16 Steel 2 16 GFRP

GFRP

3S16

2G12-1S16

2G16-1S16

180

180

180

4S12(D)

GFRP

2G12-2S12(D)

300

2 12 Steel 2 12

2 8 Steel 25

25

25

2 12 Steel 2 12 Steel

2 8 Steel

300

2 8 Steel

300

Double -layer form

2 8 Steel

4S12

300

Single -layer form

180

300

180

180

2 12 Steel 2 16 GFRP

2G16-2S12(D)

(b)

Fig. 4. Schematic diagrams of test beams: (a) details of beam’s reinforcements and (b) details of beams’ section.

43

Hydraulic jack Load sensor

Distribute beam

LVDT5

300

LVDT1

LVDT2 500

LVDT3

LVDT4

300

300

500

1800

Fig. 5. Diagram of test setup.

44

4S12

300

0.1Mu-exp 0.2Mu-exp

250

0.3Mu-exp 0.4Mu-exp

h (mm)

200

0.5Mu-exp 0.6Mu-exp

150

0.7Mu-exp

100 50 0 -1000

-500

0

500

1000

1500

2000

2500

Strain ()

(a) 2G12-2S12

300

0.1Mu-exp 0.2Mu-exp

250

0.3Mu-exp 0.4Mu-exp

h (mm)

200

0.5Mu-exp 0.6Mu-exp

150

0.7Mu-exp

100 50 0 -1000

-500

0

500

1000

1500

2000

2500

Strain ()

(b) 300

2G12-2S12(D)

0.2Mu-exp

250

0.3Mu-exp 0.4Mu-exp

200

h (mm)

0.1Mu-exp

0.5Mu-exp 0.6Mu-exp

150

0.7Mu-exp

100 50 0 -2000-1500-1000-500 0

500 1000 1500 2000 2500 3000 3500

Strain ()

(c)

Fig. 6. Strain distribution of test beams: (a) beam 4S12, (b) beam 2G12-2S12 and (c) beam 2G12-2S12(D).

45

1.2

1.2

1.0

1.0

3S16 As=603

0.8 4S12(D) As=452

0.6

M/Mu-exp

M/Mu-exp

0.8

4S12 As=452

0.4

2G12-2S12 (Af/As=1.0)

0.6

2G12-1S16 (Af/As=1.12)

0.4 0.2

0.2 0.0

4S12 As=452

0.0 0

3

6

9

12

15

18

21

24

27

30

33

0

3

6

9

12

(a)

21

1.2 3S16 As=603

1.0

24

27

30

33

2G16-2S12(D) Af/As=1.78

2G12-2S12(D) Af/As=1.0

1.0 0.8

0.8 2G16-1S16 (Af/As=2.0)

0.6 0.4

M/Mu-exp

M/Mu-exp

18

(b)

1.2

2G16-2S12 (Af/As=1.78)

0.2 0.0

15

Mid-span deflection (mm)

Mid-span deflection (mm)

0

3

6

9

12

15

2G12-2S12 Af/As=1.0

0.6 0.4

2G16-2S12 Af/As=1.78

0.2

18

21

24

27

30

0.0

33

0

3

6

9

12

15

18

21

24

27

30

Mid-span deflection (mm)

Mid-span deflection (mm)

(c)

(d)

Fig. 7. Moment-deflection relationships of test beams: (a) the moment-deflection curves of steel reinforced concrete beams, (b) and (c) the moment-deflection curves of single-layer hybrid-reinforced concrete beams, and (d) the moment-deflection curves of two kinds of hybrid-reinforced concrete beams.

46

33

1.0

4S12 nom,F=0.89%

0.9

2G12-2S12 nom,F=0.97%

0.8

2G16-2S12 nom,F=1.46%

M/Mu-exp

0.7

2G12-1S16 nom,F=0.89%

0.6

2G16-1S16 nom,F=1.37%

0.5

2G12-2S12(D) nom,F=1.04%

0.4

2G16-2S12(D) nom,F=1.58%

0.3 0.2 0.1 0.0

0

50

100

150

200

250

300

350

400

Average crack spacing (mm)

Fig. 8. Measured average crack spacing versus applied moment.

47

Fig. 9. Crack distribution at failure of all tested beams.

48

0.8

0.8 2G12-2S12 nom,F=0.97%

0.6

0.6

0.5

0.5

0.4 0.3

Experimental ACI440.1R-15 (Eqs.18 and 20) ACI318-14 (Eqs.19 and 20) CSA-S806-12 (Eq.21) Eq.(30)

0.2 0.1 0.0

0

1

2

2G16-2S12 nom,F=1.46%

0.7

M/Mu-exp

M/Mu-exp

0.7

3

4

5

6

7

8

9

0.4 0.3

Experimental ACI440.1R-15 (Eqs.18 and 20) ACI318-14 (Eqs.19 and 20) CSA-S806-12 (Eq.21) Eq.(30)

0.2 0.1 0.0

10

0

1

3

2

(a)

0.6

0.6

0.5

0.5

M/Mu-exp

M/Mu-exp

8

9

10

0.4 0.3

Experimental ACI440.1R-15 (Eqs.18 and 20) ACI318-14 (Eqs.19 and 20) CSA-S806-12 (Eq.21) Eq.(30)

0.1 0

1

2

2G16-1S16

0.7

0.2

3

4

5

6

7

8

9

nom,F=1.37%

0.4 0.3

Experimental ACI440.1R-15 (Eqs.18 and 20) ACI318-14 (Eqs.19 and 20) CSA-S806-12 (Eq.21) Eq.(30)

0.2 0.1 0.0

10

0

1

2

3

4

5

6

7

8

9

10

Mid-span deflection (mm)

Mid-span deflection (mm) (c)

(d) 0.8

0.8 2G12-2S12(D) nom,F=1.04%

0.7 0.6

0.6

0.5

0.5

0.4 0.3

Experimental ACI440.1R-15 (Eqs.18 and 20) ACI318-14 (Eqs.19 and 20) CSA-S806-12 (Eq.21) Eq.(30)

0.2 0.1 0

1

2

2G16-2S12(D) nom,F=1.58%

0.7

M/Mu-exp

M/Mu-exp

7

0.8 2G12-1S16 nom,F=0.89%

0.7

0.0

6

(b)

0.8

0.0

5

4

Mid-span deflection (mm)

Mid-span deflection (mm)

3

4

5

6

7

8

9

0.4 0.3

Experimental ACI440.1R-15 (Eqs.18 and 20) ACI318-14 (Eqs.19 and 20) CSA-S806-12 (Eq.21) Eq.(30)

0.2 0.1 0.0

10

0

1

2

3

4

5

6

7

8

9

Mid-span deflection (mm)

Mid-span deflection (mm) (e)

(f)

Fig. 10. Comparisons of mid-span deflection between experimental and calculated results: (a) beam 2G12-2S12, (b) beam 2G16-2S12, (c) beam 2G12-1S16, (d) beam 2G16-1S16, (e) beam 2G12-2S12(D), and (f) beam 2G16-2S12(D).

49

10

0.8 0.7 0.6

M/Mu-exp

0.5 0.4 0.3

B3-Exp. Qu et al. [15] B3-Eq.(30) FS1-Exp. Ge et al [29] FS1-Eq.(30) C1-Exp. Aiello and Ombres [38] C1-Eq.(30)

0.2 0.1 0.0

0

5

10

15

20

25

30

35

40

Mid-span deflection (mm)

Fig. 11. Comparison of mid-span deflection between test results got from literatures and predictions with Eq. (30).

50

1.0 0.9 0.8 0.7

M/Mu-exp

0.6 0.5 0.4 0.3

4S12 2G12-2S12 (Af/As=1.0)

0.2

2G12-1S16 (Af/As=1.12)

0.1 0.0 0.0

0.5

1.0

1.5

2.0

2.5

Maximum crack width (mm)

(a) 1.0 0.9 0.8 0.7

M/Mu-exp

0.6 0.5 0.4 0.3

3S16 2G16-2S12 (Af/As=1.78)

0.2

2G16-1S16 (Af/As=2.0)

0.1 0.0 0.0

0.5

1.0

1.5

2.0

2.5

Maximum crack width (mm)

(b) 1.0 0.9 0.8 0.7

M/Mu-exp

0.6 0.5

4S12 4S12(D) 2G12-2S12 Af/As=1.0

0.4 0.3

2G16-2S12 Af/As=1.78

0.2

2G12-2S12(D) Af/As=1.0

0.1 0.0 0.0

2G16-2S12(D) Af/As=1.78

0.5

1.0

1.5

2.0

2.5

Maximum crack width (mm)

(c)

Fig. 12. Relationships between maximum crack width and applied moment: (a) comparison between beams 4S12, 2G12-2S12 and 2G12-1S16, (b) comparison between beams 3S16, 2G16-2S12 and 2G16-1S16, and (c) comparison between beams with different reinforcement arrangements.

51

0.8

0.8 2G12-2S12

p. Ex

0.4 0.3

Ex p.

kb =1.0

0.6

M/Mu-exp

kb =1.0 kb =1.4

0.5

kb =1 .68

0.5 0.4 0.3

0.2 0.0

0.5

1.0

1.5

0.2 0.0

2.0

0.5

1.0

(a) 0.8 2G16-1S16

2G12-1S16

0.4

1.9 3

Ex p.

0.5

b

0.5

k=

0.6

kb =1 .0 k= b 1.4

kb =1 .4 k =1 b .72

0.7 p. Ex

M/Mu-exp

0.4 0.3

0.3

0.5

1.0

1.5

0.2 0.0

2.0

0.5

1.0

(c) 0.8

0.4

b

0.5

1.4

M/Mu-exp

=1 .4 b

k

b

k=

k

8 .6 =b 1

b

0.6

k=

0.6 1.0

0.7

Ex p.

M/Mu-exp

0.7

Exp. k= b 1 .0

2G16-2S12(D)

2G12-2S12(D)

0.4 0.3

0.3 0.2 0.0

2.0

(d)

0.8

0.5

1.5

Maximum crack width (mm)

Maximum crack width (mm)

1.8 9

M/Mu-exp

kb =1.0

0.7

0.2 0.0

2.0

(b)

0.8

0.6

1.5

Maximum crack width (mm)

Maximum crack width (mm)

k=

M/Mu-exp

0.6

0.7

kb =1.4 kb =1 .89

2G16-2S12

0.7

0.5

1.0

1.5

0.2 0.0

2.0

0.5

1.0

1.5

2.0

Maximum crack width (mm)

Maximum crack width (mm)

(e)

(f)

Fig. 13. Comparison of measured and predicted maximum crack width: (a) beam 2G12-2S12, (b) beam 2G16-2S12, (c) beam 2G12-1S16, (d) beam 2G16-1S16, (e) beam 2G12-2S12(D), and (f) beam 2G16-2S12(D).

52

7 Calculations with Eq.(28) Calculations with Eq.(29)

Deformability index

6 5 4

y= -1.6788x+6.5603

3 y= -0.4346x+1.8279

2 1 0 0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

nom,F (%)

Fig. 14. Relationship between deformability index and nominal reinforcement ratio ρnom,F of test beams.

Table 1 Mix design and strength of concrete. W/C

Water

Cement

Fine aggregate

Coarse aggregate

28d cubic compressive

ratio

(kg/m3)

(kg/m3)

(kg/m3)

(kg/m3)

strength, fcu (MPa)

0.49

220

449

615

1116

37.9

53

Table 2 Mechanical properties of GFRP bars and steel bars. Bar type GFRP

HRB400

Nominal diameter (mm)

Yield strength (MPa)

Tensile strength (MPa)

Elasticity modulus (GPa)

12

-

868.22

40.06

16

-

958.20

45.69

12

517

631.00

200

16

540

643.00

200

54

Table 3 Reinforcement ratios of test beams. As

Af

(mm2

(mm2

)

)

4S12

452.4

-

-

2G12-2S12

226.2

226.2

1.0

2G16-2S12

226.2

402.1

1.78

3S16

603.2

-

-

2G12-1S16

201.1

226.2

1.12

2G16-1S16

201.1

402.1

2.0

4S12(D)

452.4

-

-

-layer

2G12-2S12(D)

226.2

226.2

1.0

form

2G16-2S12(D)

226.2

402.1

1.78

Type

Singlelayer form

Specimen

Af/As

ρb,E

ρb,F

ρnom,E

ρnom,F

(%)

(%)

(%)

(%)

-

0.89

0.89

2.27

0.70

0.53

0.97

0.23

1.39

2.27

0.72

0.62

1.46

0.27

2.03

-

1.18

1.18

2.13

0.67

0.48

0.89

0.23

1.33

2.13

0.69

0.58

1.37

0.27

1.99

-

0.96

0.96

2.27

0.70

0.57

1.04

0.25

1.49

2.27

0.72

0.67

1.58

0.30

2.19

ρnom,E/ρb,E

ρnom,F/ρb,F -

-

-

Double

Note: 1) The capital letters S and G denote the steel bar and GFRP bar, respectively; and the capital letter D means the bars are placed in the double-layer form. 2) The notation of 2G12-2S12 represents the beam’s reinforcement with 2 GFRP bars in diameter of 12 mm and 2 steel bars in diameter of 12 mm. 3) For beams of 4S12, 3S16 and 4S12(D), the ratios of ρnom,F and ρnom,E are just the steel reinforcement ratio ρs.

55

Table 4 Results of beams’ cracking moments. Specimen

Mcr-exp

Predictions with Eq.(14) [28]

Predictions with Eq.(15) [27]

(kN·m)

Mcr-th

Mcr-th/Mcr-exp

Mcr-th

Mcr-th/Mcr-exp

4S12

10.67

9.22

0.86

8.92

0.84

3S16

10.95

9.22

0.84

8.92

0.82

4S12(D)

9.05

9.22

1.02

8.92

0.99

2G12-2S12

8.55

9.22

1.08

8.92

1.04

2G16-2S12

9.85

9.22

0.94

8.92

0.91

2G12-1S16

9.85

9.22

0.94

8.92

0.91

2G16-1S16

10.33

9.22

0.89

8.92

0.86

2G12-2S12(D)

10.27

9.22

0.90

8.92

0.87

2G16-2S12(D)

9.88

9.22

0.93

8.92

0.90

56

Table 5 Results of beams’ ultimate moments. Widt Reference

Specimen

h (mm)

Height

Span

f c,

Af

As

Mu-th

Mu-exp

(mm2)

(kN·m)

(kN·m)

(mm)

(mm)

(MPa)

(mm2)

Mu-th/Mu-exp

4S12

180

300

1600

30.32

-

452.39

46.71

59.12

0.79

3S16

180

300

1600

30.32

-

603.19

62.97

60.25

1.05

4S12(D)

180

300

1600

30.32

-

452.39

43.22

60.77

0.71

2G12-2S12

180

300

1600

30.32

226.19

226.19

46.98

57.50

0.82

2G16-2S12

180

300

1600

30.32

402.12

226.19

56.56

63.30

0.89

2G12-1S16

180

300

1600

30.32

226.19

201.06

45.08

56.37

0.80

2G16-1S16

180

300

1600

30.32

402.12

201.06

55.78

66.70

0.84

2G12-2S12(D)

180

300

1600

30.32

226.19

226.19

41.61

53.79

0.77

2G16-2S12(D)

180

300

1600

30.32

402.12

226.19

50.69

50.56

1.00

B3

180

250

1800

28.14

253.23

226.08

33.97

38.28

0.89

Qu et al.

B4

180

250

1800

28.14

396.91

200.96

36.84

39.66

0.93

[15]

B5

180

250

1800

29.24

141.69

401.92

33.50

36.36

0.92

B6

180

250

1800

29.24

253.23

401.92

39.50

42.57

0.93

2G12-2S10

230

300

3700

40.00

226.19

157.08

58.61

53.55

1.10

2G12-2S12

230

300

3700

40.00

226.19

226.19

56.60

58.94

0.96

2G16-2S10

230

300

3700

40.00

402.12

157.08

65.39

68.30

0.96

2G16-2S12

230

300

3700

40.00

402.12

226.19

68.53

64.71

1.06

2G16-2S16

230

300

3700

40.00

402.12

402.12

77.78

83.53

0.93

This study

Refai et al. [24]

57

Table 6 Comparison of deformability index. Specimen

ρnom,F

Mu,exp

u

M0.001

0.001

ET

Eel

(%)

(kN·m)

(10-5/mm)

(kN·m)

(10-5/mm)

(kN•m)

(kN•m)

Deformability Index Eq.(28)

Eq.(29)

[32]

[33]

4S12

0.89

59.12

5.96

28.94

2.34

1.50

0.87

5.01

1.36

2G12-2S12

0.97

57.50

5.71

28.40

2.53

1.78

1.01

4.57

1.38

2G16-2S12

1.46

63.30

4.63

27.41

2.43

2.32

1.68

4.40

1.19

2G12-1S16

0.89

56.37

5.99

26.23

2.58

2.49

1.40

4.99

1.39

2G16-1S16

1.37

66.70

4.76

29.15

2.47

2.54

1.67

4.41

1.26

2G12-2S12(D)

1.04

53.79

6.10

24.70

2.59

1.63

1.57

5.13

1.02

2G16-2S12(D)

1.58

50.56

5.63

29.76

2.71

1.42

1.09

3.53

1.15

Conflict of Interest

The authors declare that there is no conflict of interest regarding the publication of this paper. Authors: Xiangjie Ruan, Chunhua Lu, Ke Xu, Guangyu Xuan and Mingzhi Ni Oct. 10, 2019

58