Prediction about Effect of Span-to-Depth Ratio on Shear Capacity for FRP Bar Reinforced Concrete Beams without Web Reinforcement

Gao, Danying; Wang, Tao; Zhang, Changhui; Li, Cong

doi:https://doi.org/10.1155/2022/6546412

Advances in Civil Engineering

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Volume 2022 | Article ID 6546412 | https://doi.org/10.1155/2022/6546412

Prediction about Effect of Span-to-Depth Ratio on Shear Capacity for FRP Bar Reinforced Concrete Beams without Web Reinforcement

Danying Gao,¹Tao Wang,¹Changhui Zhang,²and Cong Li¹

Academic Editor: Wei Liu

Received12 Aug 2021

Revised21 Sept 2021

Accepted14 Mar 2022

Published29 Mar 2022

Abstract

Most of the prediction models for the shear capacity of FRP bar reinforced concrete beams without web reinforcement in current codes are reported to be conservative and do not consider the effect of span-to-depth ratio. Grey relational analysis (GRA) method was used in this paper to investigate the relevance of span-to-depth ratio with the shear capacity, and the results shown that the span-to-depth ratio greatly affects the shear capacity of FRP bar reinforced concrete beams without web reinforcement. A prediction model which considers the effect of span-to-depth ratio was proposed for the shear capacity of FRP bar reinforced concrete beams without web reinforcement by regression analysis, which is more accurate and reasonable in comparison with the current models.

1. Introduction

For the concrete structures exposed to severe environments, the corrosion of steel bars has always been one of the main reasons for structural damage, and it will bring relatively expensive repair and reinforcement costs. To solve this problem, several different types of steel reinforcements have been used, such as stainless, epoxy coated, and galvanized steel, but none of them can fundamentally solve the problem. At the same time, comparing with traditional steel reinforcement, fiber reinforced polymer (FRP) bars have better specific strength, corrosion resistance, and weak electromagnetic properties [1, 2]. Due to the aforementioned advantages, the FRP bars are considered to be an effective substitute for traditional reinforcement, and the application of FRP bars in reinforced concrete beams has been rapidly developed over the last few decades.

As the FRP bars have several differences in the mechanical properties from steel bars, such as lower elastic modulus, brittleness and lower transverse shear strength, a large number of experiments on the shear behavior of FRP bar reinforced concrete beams and one-way slabs have been carried out. In general, the reinforced concrete (RC) beams without web reinforcement resist the shear stresses by means of five possible mechanisms, including shear resistance of the uncracked concrete compression zone, aggregate interlock, residual tensile stresses across cracks, dowel action of the longitudinal reinforcement and arch action [3]. The previous studies showed that the FRP bar reinforced concrete beam typically has a smaller neutral axis depth in comparison with the steel bar reinforced concrete beam with equal areas of longitudinal reinforcement [4, 5]. As a result, the shear capacity generated by FRP bar reinforced concrete beams through the shear resistance of the uncracked concrete compression zone is weaker than that generated by traditional steel bar reinforced concrete beams. Moreover, because of the lower elastic modulus of FRP bars, the axial stiffness of FRP bar reinforced concrete beams is relatively low, which makes the width and depth of the diagonal cracks in the beams increase accordingly, thereby leading to the lower shear capacity generated by the aggregate interlock and residual tensile stresses across cracks [6]. Additionally, owing to the lower transverse shear strength of FRP bars, the dowel action of the longitudinal reinforcement contribution to shear resistance of FRP bar reinforced concrete beams is smaller than that of steel bar reinforced concrete beams [7]. In addition, due to the differences in mechanical properties between FRP bars and steel bars, the failure mode of FRP bar reinforced concrete beams is different from that of traditional steel bar reinforced concrete beams. Therefore, the prediction models of the shear capacity of steel bar reinforced concrete beams are not suitable for FRP bar reinforced concrete beams.

The current researches [8, 9] have confirmed that the shear capacity of FRP bar reinforced concrete beams without web reinforcement, as shown in Figure 1, is influenced by several factors, such as concrete compressive strength , shear span-to-depth ratio , elastic modulus of FRP bars , reinforcement ratio of longitudinal FRP bars , width of the beam and effective depth of the beam . However, the influence of span-to-depth ratio on the shear capacity of FRP bar reinforced concrete beams without web reinforcement is rarely involved, which represents the ratio of two sizes of the specimen, including effective span and effective depth of the beam , respectively. Existing experimental studies showed that the ultimate shear capacity of steel bar reinforced concrete beams without web reinforcement under uniformly distributed loads will gradually decrease as the increases [10, 11]. Because the uniform load can be equivalent to two concentrated loads, and shear span is , where is the effective span of the beam [12, 13], the affects the shear capacity of the steel bar reinforced concrete beams. Furthermore, the effect of on the shear capacity of the reinforced concrete beams is also reflected in the calculation models in codes. The GB50010-2010 in China stipulates that the beams with of less than 5 are collectively called the deep flexural member [14]. At the same time, GB50010-2010 provides a different calculation model for the calculation of the shear capacity of deep flexural members in comparison with the beams with of more than 5, which considers the effect of . The ACI318R-19 stipulates that the beams that satisfy the following two criteria are called deep beams: the effective span does not exceed four times the overall member depth and the concentrated loads exist within a distance from the face of the support [15]. The Eurocode 2 stipulates that the span of a beam is not less than 3 times the overall section depth, otherwise it should be considered as a deep beam [16]. Both ACI318R-19 and Eurocode 2 deem that the deep beams are designed with strut and tie models, which is different from the design model for slender beams. In recent years, Uday Naik has proved that the change of has an effect on the shear capacity of steel bar reinforced concrete beams by the artificial neural network technology [17], which has been widely used in civil engineering because of its excellent performance in the development of accurate and reliable prediction models for the shear capacity of reinforced concrete beams without web reinforcement [18–23]. The previous experimental study indicated that although FRP bars and steel bars have the great differences in elastic modulus and some mechanical properties, FRP bar reinforced concrete beams and steel bar reinforced concrete beams are still similar in shear-carrying mechanism [1, 9, 24]. Thus, the also plays a certain role in the structural analysis of shear capacity of FRP bar reinforced concrete beams.

The calculation models of the shear capacity of FRP bar reinforced concrete beams without web reinforcement in codes, such as CSA/CAN-S806-12, ACI440.1R-15, CNR-DT203–2006, GB50608-2020, and a modified model by Gao and Zhang are summarized in Table 1 [9, 25–28]. The factors that have been considered are listed in Table 2. Obviously, some of the factors which affect the shear capacity, such as and , have not been considered by the codes listed. Previous research results have confirmed that the current shear capacity calculation models of FRP bar reinforced concrete beams without web reinforcement in codes are conservative [9, 29]. This may be due to the lack of the proper consideration of and . The CSA/CAN-S806-12 model and the Gao and Zhang model consider the effect of on shear capacity and are proven to be more accurate in comparing with other models [29]. In spite of this, the effect of on the shear capacity is not fully embodied. The models that are unable to accurately predict the shear capacity will lead to excessive shear design, which results in high costs. Therefore, establishing a more comprehensive and accurate prediction model, which can correctly reflect the relevance of and other parameters on the shear capacity of FRP bar reinforced concrete beams without web reinforcement, is essential at present.

In the present investigation, a database which contains the experimental results of 314 FRP bar reinforced concrete beams without web reinforcement was compiled to propose a more accurate calculation model for the shear capacity of FRP bar reinforced concrete beams. The method of grey relational analysis was used to analyze the relevance of and other parameters with the shear capacity of FRP bar reinforced concrete beams without web reinforcement. On this basis, a new model was proposed based on the CAN/CSA-S806-12 model, which considered the influence of .

2. Database

2.1. Test Data

This study collected 314 the experimental data of FRP bar reinforced concrete beams without web reinforcement failed in shear from the literature. The effects of , , , , , and on the shear capacity of FRP bar reinforced concrete beams are considered. In addition, all test specimens in the database are simply supported and subjected to concentrated loads, and the shape of the cross section is rectangular. The details of the database and the minimum, maximum, average and range of each parameter are shown in Table 3.

2.2. Data Processing Principles

If the cubic compression strength of concrete corresponding to the beams is only provided in the original paper, it can be converted to the cylinder compression strength of concrete according to the following formula [30].

If the elastic modulus and tensile strength of concrete corresponding to the beams are not provided in the original paper, they can be obtained according to the following formula [15].

3. Relevance Analysis of Experimental Parameters with Shear Capacity

3.1. Grey Relational Analysis (GRA) Method

Grey relational analysis (GRA) method [57, 58], as one of multi-factor statistical analysis methods, is mainly used to investigate the relevance between the reference sequence and comparison sequences by calculating the grey relational grade. The purpose of GRA method is to determine the main factors that affect the target value. The advantage of GRA method is that it does not require high sample size, and the workload is relatively small. The grey correlation degree can be calculated as following.

Step 1. Determining the reference sequence and the comparison sequences.
The data sequence that reflects the characteristics of the system behavior is called reference sequence and expressed as follows.The data sequence composed of the factors affecting system behavior is called comparison sequence and expressed as follows.where and .

Step 2. Making the reference sequence and comparison sequences being dimensionless as follows.

Step 3. Calculating the grey correlation coefficient of the reference sequence and the comparison sequences as follows.where is the grey resolution coefficient, and generally .

Step 4. Calculating the grey relational grade as follows.

Step 5. Evaluating the relevance as follows.
The grey relational grade is a manifestation of the degree of the relevance between the reference sequence and comparison sequences. Basically, the greater the grey relational grade, the higher the degree of the influence factors affecting the characteristics of the system behavior. It can be considered that the characteristics of the system behavior is greatly influenced by the influence factor while or , not influenced by the influence factor while [59]. In this paper, to further illustrate the function of the factors, especially the on the shear capacity of FRP bar reinforced concrete beams without web reinforcement, the GRA method will be used.

3.2. Grey Relational Grade for Each Experimental Parameter

As a systematic analysis method, GRA can overcome the shortcomings of conventional analysis methods in analyzing the correlation relationship of factor sequences. In this paper, the GRA method is used to analyze the sensitivity factors of shear capacity. Based on the database newly collected in Table 3, the is taken as the reference sequence ; the experimental parameters including , , , , , and are taken as the comparison sequences, respectively. Then, the new dimensionless sequences were obtained according to equation (5), and the grey relational coefficient and grey relational grade were calculated by equations (6) and (7), respectively. The calculated values of the grey relational grade are shown in Table 4.

From the data in Table 4, the grey relational grade values of seven experimental parameters are all above 0.8, which means that the seven experimental parameters are well correlated with shear capacity of FRP bar reinforced concrete beams without web reinforcement. Among them, the grey relational grade values of , , and are greater than those of , and , which shows that the effect of , , and on is greater than , and . Besides, the grey relational grade between and is 0.88, which is equal to the grey relational grade values of and . It shows that the influence of on the shear capacity of FRP bar reinforced concrete beams without web reinforcement is similar to that of and respectively.

4. Prediction Model of Shear Capacity

4.1. Prediction Model

Considering the effect of , a calculation model for the shear capacity of FRP bar reinforced concrete beams without web reinforcement can be proposed by modifying the model in CAN/CSA-S806-12. Based on the regression analysis for the database newly collected, the model for the shear capacity of FRP bar reinforced concrete beams without web reinforcement has been obtained as follows.where the coefficients of , , , and are given as follows, of which represents the effect of on the shear capacity.

Considering the shear capacity of plain concrete members or members with extremely low reinforcement ratios, equation (10) needs to be used as the lower limit of the shear capacity for the proposed model as follows [5].

4.2. Evaluation of the Models

To evaluate whether the models in Table 1 and equation (8) capture the effect of on the shear capacity, the relationship between the ratios of experimental results to the calculated values and is shown in Figure 2. Meanwhile, a line () which represents that the calculated value is equal to the experimental value is also plotted. When the data is located above the line, the experimental value is greater than the calculated value; when the data is located below the line, it means that the experimental value is less than the calculated value.

As shown in Figure 2, it is clear to find out that there is a declining trend for calculated by the CAN/CSA-S806-12, ACI440.1R-15, CNR-DT203–2006,GB50608-2020, Gao and Zhang models with the increasing of , respectively, when is smaller than 10. Obviously, the smaller the , the larger the conservative degree of the predicted shear capacity of FRP bar reinforced concrete beams without web reinforcement by the CAN/CSA-S806-12, ACI440.1R-15, CNR-DT203–2006, GB50608-2020, Gao and Zhang models. The majority of values for the proposed model are scattered around the line , which indicates that the proposed model can well capture the influence of on the shear capacity of FRP bar reinforced concrete beams without web reinforcement. Moreover, the values of CAN/CSA-S806-12, ACI440.1R-15, CNR-DT203–2006, GB50608-2020, Gao and Zhang model and proposed model are scattered in a range of 0.242–4.582, 0.819–17.379, 0.157–4.703, 0.612–12.975, 0.405–2.815, 0.242–1.989, respectively, and the scatter range of values of the proposed model is smaller than that of other models. It is apparent that the results of the proposed model for the shear capacity is more consistent with the experimental value compared with the four calculation models in codes and the Gao and Zhang model.

4.3. Performance Checking and Sensitive Analysis

To check the performance of the proposed model, the calculation values by the models are compared with the experimental values. As shown in Figure 3, the proposed model in this study has a better prediction function on the shear capacity of FRP bar reinforced concrete beams without web reinforcement than the CAN/CSA-S806-12, ACI440.1R-15, CNR-DT203–2006, GB50608-2020 and Gao and Zhang models.

Figure 4 shows the histogram of the frequency distribution of the values calculated by proposed model. The horizontal axis of the figure shows the values calculated by proposed model, and the vertical axis represents the number of the specimens for a certain value of calculated by proposed model. It can be seen that the values of calculated by proposed model follow a normal distribution, and most of the values appear in a narrow range between 0.6 and 1.2, which takes up 231 results of test beams in the database (73.6%).

To further investigate the superiority of the proposed model, the mean (MEAN), standard deviation (SD), and coefficient of variation (COV) were employed as the evaluation indicators, which can be calculated by the following formula. Mean: Standard deviation: Coefficient of variation:

The MEAN, SD and COV of are listed in Table 5.

It is obvious that the proposed model of equation (8) can well predict the shear capacity with MEAN, SD and COV of 1.000, 0.273 and 27.3%. Meanwhile, the MEAN of the proposed model is closer to 1, and the SD and COV of the proposed model are smaller than CAN/CSA-S806-12, ACI440.1R-15, CNR-DT203–2006, GB50608-2020 and Gao and Zhang models, respectively. Thus, the proposed model yields more scientific and accurate results for predicting the shear capacity in comparison with the CAN/CSA-S806-12, ACI440.1R-15, CNR-DT203–2006, GB50608-2020 and Gao and Zhang models, which did not consider the effect of . This may be due to the effect of is considered properly by the proposed model.

To analyze the sensitivity of every parameter for the proposed model, a set of data corresponding to the averages in Table 3 is selected as the starting data. When each parameter increases by 20%, the change rate of the calculated shear capacity is considered as the sensitivity index. The calculating results of sensitivity index are shown in Figure 5. It can be seen from the figure that the most important parameter impacting the shear capacity is . The has less effect on the shear capacity than the other six parameters. Under the fixed values of other parameter, the value of varied from the minimum to maximum, the sensitivity index is 12.08%, which indicates the cannot be ignored for predicting the shear capacity for FRP bar reinforced concrete beams without web reinforcement.

5. Conclusions

Based on the collected experimental data of 314 FRP bar reinforced concrete beams without web reinforcement, the GRA method was used to analyze the relevance of experimental parameters with the shear capacity, and a new shear capacity prediction model was proposed for FRP bar reinforced concrete beams without web reinforcement. The main conclusions can be drawn as follows.(1)The GRA method can be used to analyze the relevance of experimental parameters on the shear capacity of FRP bar reinforced concrete beams without web reinforcement. The span-to-depth ratio affects the shear capacity as the same as the shear span-to-depth ratio , elastic modulus of FRP bars , reinforcement ratio of longitudinal FRP bars , concrete compressive strength , the width and effective depth of the beam.(2)The number of the ratios of the experimental results for the shear capacity of FRP bar reinforced concrete beams without web reinforcement to the calculated values by the proposed model follows a normal distribution, and 73.6% of the ratio values distributes in a narrow range of 0.6–1.2.(3)The proposed model can well capture the influence of span-to-depth ratio on the shear capacity of FRP bar reinforced concrete beams without web reinforcement, and the calculation values by the proposed model are more consistent with the experimental values than those by the existing models.

Notation

:	Cylinder compressive strength of concrete, MPa.
:	Cubic compressive strength of concrete, MPa.
:	Reinforcement ratio of longitudinal FRP bars.
:	Elastic modulus of FRP bars, MPa.
:	Elastic modulus of steel bars, MPa.
:	Tensile strength of concrete, MPa.
:	Effective span of beam, mm.
:	Span-to-depth ratio.
:	Effective depth of beam, mm.
:	Overall member depth, mm.
:	Width of beam, mm.
:	Shear span of beam, mm.
:	Shear span-to-depth ratio.
:	Elastic modulus of concrete, MPa.
:	Experimental value of shear capacity, N.
:	Calculated value of shear capacity, N.

Data Availability

The data used to support the findings of this study are included within the article.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

The authors gratefully acknowledge the financial support of National Natural Science Foundation of China (No. U1704254), Key Scientific Research Project in Colleges and Universities of Henan Province, China (No. 22A570003), and Science and Technology Research Project of Henan Province, China (No. 222102230066).

References

F. Peng and W. Xue, “Database evaluation of shear strength of slender fiber-reinforced polymer-reinforced concrete members,” ACI Structural Journal, vol. 117, no. 3, pp. 273–281, 2020.
View at: Google Scholar
M. A. Chowdhury, Z. I. Zahid, and M. M. Islam, “Simplified shear strength prediction model of FRP reinforced concrete beam without web reinforcement,” in Proceedings of the Advances in Civil Infrastructure and Construction Materials, pp. 123–133, Dhaka, Bangladesh, December, 2015.
View at: Google Scholar
M. Nehdi, H. El-Chabib, and Z. Omeman, “Experimental study on shear behavior of carbon-fiber-reinforced polymer reinforced concrete short beams without web reinforcement,” Canadian Journal of Civil Engineering, vol. 35, no. 1, pp. 1–10, 2008.
View at: Google Scholar
A. K. Tureyen and R. J. Frosch, “Shear tests of FRP-reinforced concrete beams without stirrups,” ACI Structural Journal, vol. 99, no. 4, pp. 427–434, 2002.
View at: Google Scholar
A. G. Razaqpur and O. B. Isgor, “Proposed shear design method for FRP-reinforced concrete members without stirrups,” ACI Materials Journal, vol. 103, no. 1, pp. 93–101, 2006.
View at: Google Scholar
M. A. A. Issa, T. Ovitigala, and M. B. Ibrahim, “Shear behavior of basalt fiber reinforced concrete beams with and without basalt FRP stirrups,” Journal of Composites for Construction, vol. 20, no. 4, pp. 1–11, 2016.
View at: Publisher Site | Google Scholar
M. A. Chowdhury, Z. Ibna Zahid, and M. M. Islam, “Development of shear capacity prediction model for FRP-RC beam without web reinforcement,” Advances in Materials Science and Engineering, vol. 2016, Article ID 4356967, 19 pages, 2016.
View at: Publisher Site | Google Scholar
D. Gao and C. Zhang, “Shear strength calculating model of FRP bar reinforced concrete beams without stirrups,” Engineering Structures, vol. 221, pp. 1–8, 2020.
View at: Google Scholar
D. Gao and C. Zhang, “Shear strength prediction model of FRP bar-reinforced concrete beams without stirrups,” Mathematical Problems in Engineering, vol. 2020, no. 2020, Article ID 7516502, 11 pages, 2020.
View at: Publisher Site | Google Scholar
L. Lixin, “An unified calculation method for shear capacity of RC deep beams, short beams and shallow beams,” Journal of Building Structures, vol. 16, no. 04, pp. 13–21+12, 1995.
View at: Google Scholar
Q. Guoliang, “Discussion on unified calculation method of bearing capacity of reinforced concrete beam and deep beam,” Building Structure, vol. 1995, no. 08, pp. 24–29, 1995.
View at: Google Scholar
Kani, “Basic facts concerning shear failure,” ACI Structural Journal, vol. 63, no. 6, pp. 675–692, 1966.
View at: Google Scholar
Zararis, “Shear strength of reinforced concrete beams under uniformly distributed loads,” ACI Structural Journal, vol. 6, no. 105, pp. 711–719, 2008.
View at: Google Scholar
Ministry of housing and urban rural development of the people's Republic of China, Code for Design of concrete Structures, GB50010-2010, China, 2010.
Aci Committee 318, Commentary on building code requirements for structural concretes, ACI318R-19, Farmington Hills, MI, USA, 2019.
European, Design of concrete structures-Part 1-1: general rules and rules for buildings, Technical Committee CEN/TC250, Brussels, Belgium, 2002.
U. Naik, “Span-to-depth ratio effect on shear strength of steel fiber-reinforced high-strength concrete deep beams using ANN model,” International Journal of Advanced Structural Engineering, vol. 29, no. 5, pp. 1–12, 2013.
View at: Publisher Site | Google Scholar
G. B. Jumaa and A. R. Yousif, “Predicting shear capacity of FRP-reinforced concrete beams without stirrups by artificial neural networks, gene expression programming, and regression analysis,” Advances in Civil Engineering, vol. 2018, Article ID 5157824, 16 pages, 2018.
View at: Publisher Site | Google Scholar
M. Mirrashid and H. Naderpour, “Recent trends in prediction of concrete elements behavior using soft computing (2010–2020),” Archives of Computational Methods in Engineering, vol. 28, no. 2021, pp. 3307–3327, 2021.
View at: Publisher Site | Google Scholar
M. Mirrashid and Masoomeh, “Earthquake magnitude prediction by adaptive neuro-fuzzy inference system (ANFIS) based on fuzzy C-means algorithm,” Natural Hazards, vol. 74, no. 3, pp. 1577–1593, 2014.
View at: Publisher Site | Google Scholar
F. Alizadeh, H. Naderpour, and M. Mirrashid, “Bond strength prediction of the composite rebars in concrete using innovative bio﹊nspired models,” Engineering Reports, vol. 2, no. 11, pp. 1–21, 2020.
View at: Publisher Site | Google Scholar
H. Naderpour, M. Haji, and M. Mirrashid, “Shear capacity estimation of FRP-reinforced concrete beams using computational intelligence,” Structures, vol. 28, pp. 321–328, 2020.
View at: Publisher Site | Google Scholar
H. Naderpour and M. Mirrashid, “Shear strength prediction of RC beams using adaptive neuro-fuzzy inference system,” Scientia Iranica, vol. 27, no. 2, pp. 657–670, 2018.
View at: Publisher Site | Google Scholar
E. C. Bentz, L. Massam, and M. P. Collins, “Shear strength of large concrete members with FRP reinforcement,” Journal of Composites for Construction, vol. 14, no. 6, pp. 637–646, 2010.
View at: Publisher Site | Google Scholar
Canadian Standards Association, Design and construction of building structures with fibre-reinforced polymers, CSA/CAN-S806-12, Mississauga, Canada, 2012.
Aci Committee 440, Guide for the design and construction of concrete reinforced with Fiber Reinforced Polymers (FRP) bars, ACI 440.1R-15, Farmington Hills, MI, USA, 2015.
Advisory Committee Technical Recommendations Construction, Guide for the design and structural of concrete reinforced with fiber-reinforced, CNR-DT203-06, Rome, Italy, 2006.
China Metallurgical Construction Association, Technical standard for fiber reinforced polymer (FRP) in construction, GB50608-2020, China, 2020.
A. K. El-Sayed and K. Soudki, “Evaluation of shear design equations of concrete beams with FRP reinforcement,” Journal of Composites for Construction, vol. 15, no. 1, pp. 9–20, 2011.
View at: Publisher Site | Google Scholar
A. F. Ashour, “Flexural and shear capacities of concrete beams reinforced with GFRP bars,” Construction and Building Materials, vol. 20, no. 10, pp. 1005–1015, 2006.
View at: Publisher Site | Google Scholar
S. P. Gross, J. R. Yost, and D. W. Dinehart, “Shear strength of normal and high strength concrete beams reinforced with GFRP bars,” in Proceedings of the International Conference on High Performance Materials in Bridges, pp. 426–437, Kona, Hawaii, USA, September, 2001.
View at: Google Scholar
A. G. Razaqpur, B. O. Isgor, S. Greenaway, and A. Selley, “Concrete contribution to the shear resistance of fiber reinforced polymer reinforced concrete members,” Journal of Composites for Construction, vol. 8, no. 5, pp. 452–460, 2004.
View at: Publisher Site | Google Scholar
T. Alkhrdaji, M. Wideman, A. Belarbi, and A. Nanni, “Shear strength of GFRP RC beams and slabs,” in Proceedings of the International Conference, Composites in Construction-CCC, pp. 409–414, Porto, Portugal, 2001.
View at: Google Scholar
M. S. Alam and A. Hussein, “Size effect on shear strength of FRP reinforced concrete beams without stirrups,” Journal of Composites for Construction, vol. 17, no. 4, pp. 507–516, 2013.
View at: Publisher Site | Google Scholar
M. S. Alam, Influence of Different Parameters on Shear Strength of FRP Reinforced concrete Beams without Web Reinforcement, Memorial University of Newfoundland, Canada, 2010.
D. Tomlinson and M. A. Amir Fam, “Performance of concrete beams reinforced with basalt FRP for flexure and shear,” Journal of Composites for Construction, vol. 19, no. 2, pp. 1–10, 2015.
View at: Publisher Site | Google Scholar
F. Abed, H. El-Chabib, and M. AlHamaydeh, “Shear characteristics of GFRP-reinforced concrete deep beams without web reinforcement,” Journal of Reinforced Plastics and Composites, vol. 31, no. 16, pp. 1063–1073, 2012.
View at: Publisher Site | Google Scholar
M. Guadagnini, K. Pilakoutas, and P. Waldron, “Shear resistance of FRP RC beams: experimental study,” Journal of Composites for Construction, vol. 10, no. 6, pp. 464–473, 2006.
View at: Publisher Site | Google Scholar
C. H. Kim and H. S. Jang, “Concrete shear strength of normal and lightweight concrete beams reinforced with FRP bars,” Journal of Composites for Construction, vol. 18, no. 2, Article ID 04013038, 2014.
View at: Publisher Site | Google Scholar
R. S. Olivito and F. A. Zuccarello, “On the shear behaviour of concrete beams reinforced by carbon fibre-reinforced polymer bars: an experimental investigation by means of acoustic emission technique,” Strain, vol. 46, no. 5, pp. 470–481, 2010.
View at: Publisher Site | Google Scholar
F. Matta, “Size effect on concrete shear strength in beams reinforced with fiber-reinforced polymer bars,” ACI Structural Journal, vol. 110, no. 4, pp. 617–628, 2013.
View at: Google Scholar
J. Thomas and S. Ramadass, “Parametric study of shear strength of concrete beams reinforced with FRP bars,” Journal of the Institution of Engineers: Series A, vol. 97, no. 3, pp. 273–284, 2016.
View at: Publisher Site | Google Scholar
F. M. Wegian and H. A. Abdalla, “Shear capacity of concrete beams reinforced with fiber reinforced polymers,” Composite Structures, vol. 71, no. 1, pp. 130–138, 2005.
View at: Publisher Site | Google Scholar
M. F. Andermatt and A. S. Lubell, “Behavior of concrete deep beams reinforced with internal fiber-reinforced polymer-experimental study,” ACI Structural Journal, vol. 110, no. 4, pp. 585–594, 2013.
View at: Google Scholar
A. F. Ashour and I. F. Kara, “Size effect on shear strength of FRP reinforced concrete beams,” Composites Part B: Engineering, vol. 60, pp. 612–620, 2014.
View at: Publisher Site | Google Scholar
L. Huaxin, “Shear capacity of basalt fiber reinforced polymer reinforced recycled concrete deep beam without web reinforcement,” Journal of Sichuan University (Medical Science Edition), vol. 47, no. 5, pp. 17–22, 2015.
View at: Google Scholar
Z. Xiaoliang and Q. Wenjun, “Shear behavior test of GFRP-reinforced concrete beams without stirrups,” China Journal of Highway and Transport, vol. 23, no. 05, pp. 51–57, 2010.
View at: Google Scholar
A. E. Refai and M. A. Farid Abed, “Concrete contribution to shear strength of beams reinforced with basalt fiber-reinforced bars,” Journal of Composites for Construction, vol. 20, no. 4, pp. 1–13, 2016.
View at: Publisher Site | Google Scholar
K. Chang and D. Seo, “Behavior of one-way concrete slabs reinforced with GFRP bars,” Journal of Asian Architecture and Building Engineering, vol. 11, no. 2, pp. 351–358, 2012.
View at: Publisher Site | Google Scholar
B. Abdul-Salam, A. S. Farghaly, and B. Benmokrane, “Mechanisms of shear resistance of one-way concrete slabs reinforced with FRP bars,” Construction and Building Materials, vol. 127, pp. 959–970, 2016.
View at: Publisher Site | Google Scholar
A. El-Sayed, E. El-Salakawy, and B. Benmokrane, “Shear strength of one-way concrete slabs reinforced with fiber-reinforced polymer composite bars,” Journal of Composites for Construction, vol. 9, no. 2, pp. 147–157, 2005.
View at: Publisher Site | Google Scholar
A. K. El-Sayed, E. F. El-Salakawy, and B. Benmokrane, “Shear strength of FRP-reinforced concrete beams without transverse reinforcement,” ACI Structural Journal, vol. 103, no. 2, pp. 235–243, 2006.
View at: Google Scholar
A. K. El-Sayed, E. F. El-Salakawy, and B. Benmokrane, “Shear capacity of high-strength concrete beams reinforced with FRP bars,” ACI Structural Journal, vol. 103, no. 3, pp. 383–389, 2006.
View at: Google Scholar
A. S. Farghaly and B. Benmokrane, “Shear behavior of FRP-reinforced concrete deep beams without web reinforcement,” Journal of Composites for Construction, vol. 17, no. 6, pp. 1–11, 2013.
View at: Publisher Site | Google Scholar
I. Ali, “Diagonal shear cracks and size effect in concrete beams reinforced with glass fiber reinforced polymer (GFRP) bars,” Applied Mechanics and Materials, vol. 621, pp. 113–119, 2014.
View at: Google Scholar
G. B. Jumaa and A. R. Yousif, “Numerical modeling of size effect in shear strength of FRP-reinforced concrete beams,” Structures, vol. 20, pp. 237–254, 2019.
View at: Publisher Site | Google Scholar
L. Zhang and X. Y. Bao, “Evaluation of green degree of concrete based on the gray relation,” Applied Mechanics and Materials, vol. 507, pp. 410–414, 2014.
View at: Publisher Site | Google Scholar
C. Y. Liang, C. X. Qian, W. C. Kang, and H. C. Chen, “The evolution analysis of mechanical properties of marine submerged concrete based on GRA,” Key Engineering Materials, vol. 748, pp. 316–322, 2017.
View at: Publisher Site | Google Scholar
Z. Yongshuai and W. Xiaoyong, “Grey correlation analysis of factors affecting bonding performance of FRP rebar,” China Concrete and Cement Products, vol. 2019, no. 04, pp. 46–48+100, 2019.
View at: Google Scholar

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Copyright © 2022 Danying Gao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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