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Article

Two-Way Shear Resistance of FRP Reinforced-Concrete Slabs: Data and a Comparative Study

1
Department of civil Engineering, College of Engineering in Al-kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 16278, Saudi Arabia
2
Department of Civil Engineering, College of Engineering, Jouf University, Sakakah 72388, Saudi Arabia
3
Civil Engineering Department, Faculty of Engineering, Al-Azhar University, Cairo 11651, Egypt
4
Department of Structural Engineering, Shoubra Faculty of Engineering, Benha University, Cairo 11629, Egypt
5
Department of Structural Engineering and Construction Management, Future University in Egypt, New Cairo City 11835, Egypt
*
Authors to whom correspondence should be addressed.
On leave from Delta University for Science and Technology, Belkas 35631, Egypt.
Polymers 2022, 14(18), 3799; https://doi.org/10.3390/polym14183799
Submission received: 13 July 2022 / Revised: 10 August 2022 / Accepted: 23 August 2022 / Published: 11 September 2022
(This article belongs to the Special Issue Fibre Reinforced Polymer (FRP) Composites in Structural Applications)

Abstract

:
This study aims to investigate the two-way shear strength of concrete slabs with FRP reinforcements. Twenty-one strength models were briefly outlined and compared. In addition, information on a total of 248 concrete slabs with FRP reinforcements were collected from 50 different research studies. Moreover, behavior trends and correlations between their strength and various parameters were identified and discussed. Strength models were compared to each other with respect to the experimentally measured strength, which were conducted by comparing overall performance versus selected basic variables. Areas of future research were identified. Concluding remarks were outlined and discussed, which could help further the development of future design codes. The ACI is the least consistent model because it does not include the effects of size, dowel action, and depth-to-control perimeter ratio. While the EE-b is the most consistent model with respect to the size effect, concrete compressive strength, depth to control perimeter ratio, and the shear span-to-depth ratio. This is because of it using experimentally observed behavior as well as being based on mechanical bases.

1. Introduction

In 2021, victims of the collapse of a condominium building [1] that is shown in Figure 1(a) totaled 98 people. In addition, a parking garage collapsed suddenly on a playground in Spain [2], as shown in Figure 1(b). Moreover, most of the two-way shear designs of reinforced concrete (RC) slabs are empirical or semi-empirical. Thus, extensive research efforts are direct towards understanding the two-way shear types. However, the mechanism of the two-way shear of the slabs is complicated; thus, it is still open for investigation [3,4,5,6]. The two-way shear resistance of concrete slabs that are without shear reinforcements is composed of several resistance mechanisms, as follows: (1) flexure reinforcements resist shear through using dowel shear; (2) aggregates resist shear across the sides of the diagonal concrete crack through using aggregate interlock and friction; (3) uncracked concrete resists shear through using direct shear [7,8,9].
To avoid corrosion problems, replacing the conventional reinforcement with fiber-reinforced polymers (FRP) reinforcements in concrete slabs is a common solution [10]. In addition, FRP reinforcements are magnetic neutral and have a high strength-to-weight ratio. Thus, they are the best choice to use in buildings that are subjected to severe environmental conditions including, and not limited to, wet-dry cycles, de-icing salts, and freeze-thaw cycles. Many researchers have investigated the behavior of new and existing beams and slabs that are reinforced with FRP bars or fabrics under one-way and two-way shear as well as torsion, mostly through experimental investigations [11,12,13,14,15]. Many research studies have tackled the two-way shear of concrete FRP reinforcements, while very few mechanical models were developed for this case [8]. The FRP’s failure is brittle; thus, before failure, the FRP-reinforced concrete cracks are wider when compared to those in conventional RC [16,17,18]. Wider cracks significantly affect the various mechanisms of the two-way shear strength.
The traditional two-way shear design equations for RC slabs are based on theories that were developed in the early 1960s. These models were based on studies of that period’s tested specimens; however, over the last few decades, much more testing was conducted which show several drawbacks of these methods including, and not limited to, size effect and those models being severely unconservative in many situations. Hence, there is a room for improvements to the two-way shear design models, which could help design code developments [19,20].
This study aims to assess the available methods for study of the two-way shear strength of FRP-reinforced concrete slabs. A state-of-the-art review of design codes, guides, and models for the study of the two-way shear strength of FRP-reinforced concrete slabs was outlined. An extensive review of the experimental testing of the FRP-reinforced concrete slabs that were tested under two-way loads was compiled. The studies that used to extract the models and their experimental testing were collected through various engineering search engines including, and not limited to: Google Scholar, Science Direct, MDPI Hub, and Engineering Village. The strengths calculated using all models were compared with those that were measured by testing. Concluding remarks were outlined and discussed.

2. Research Significance

Many researchers have proposed design models that address the two-way shear strength of RC slabs with FRP. Although safety is the main goal for the design purposes, evaluating these design models is a necessity. The accuracy of these models was assessed based on data from a limited experimental database. Thus, this study provides the community with an extensive collection of models and tested specimens as well as a comparison between the accuracy of each of these models. These results can help to improve the code developments.

3. Simplified Strength Models

For the study of the two-way shear strength of FRP-RC slabs, several simplified strength models have been proposed, either by modifications for conventional concrete slabs or empirically based on limited test data. The two-way shear design provisions of the North American design codes have neglected the effect of flexure reinforcement on strength. They focused on the direct shear resistance of the compression zone. This could be reasonable for conventional steel reinforcements with relatively high stiffness when compared to the FRP ones. Thus, the direct shear component governs the two-way shear strength. However, due to the relatively lower stiffness of the FRP when compared to the steel one, a dowel action could be a more significant contributor to its strength. Details and the background of various models are outlined in this section. V is the two-way shear failure load. E is the Young’s modulus of the FRP. d is the effective depth. f c is the concrete compressive strength. ρ is the flexure reinforcement ratio. b and c are the column dimensions. A and B are the slab dimensions. E s is the Young’s modulus of the steel. b 0.5 d is the control perimeter at 0. 5 d , which is taken as 2 b + c + 2 d . b 1.5 d is the control perimeter at 1. 5 d , which is taken as 2 b + c + 6 d . b 2.0 d is the control perimeter at 2.0 d , which is taken as 2 b + c + 8 d .

3.1. Gardner (1990)

In 1990, Gardner developed a strength model, which will be referred to herein as G [21]. It is based on an experimental database for two-way shear, and the existing design codes were assessed. Gardner concluded that considering the size effect and the flexure reinforcement ratio provides a more reliable design model; thus, when fitting it to the experimental database of that time, the two-way shear is calculated such that:
V = 1.36   100 ρ f c 1 3 1 d 1 4 b 1.5 d d

3.2. Japanese Approaches (1997), JSCE

In 1997, the JSCE [22] used a similar approach to the conventional North American design codes, and they implemented the assumption that the strength was proportional to the square root of the concrete compressive strength. Thus, they implemented the strain approach on the British Standard of that time and proposed that the two-way shear was calculated such that:
V = β d β ρ β r f P c d 1 α b 0.5 d d
where β d = 1000 d 1 4 1.5 , β ρ 100 ρ E E s 3 = 1.5 , β r = 1 + 1 1 + 0.25 b 0.5 d d , f Pcd = 0.2 f c   1.2 , α = 1 + 1.5 e x + e y AB , and e x and e y are the loading eccentricity in the x and y direction of the slabs, respectively.

3.3. Elghandour (2000), EG [23]

In 2000, Elghandour developed a strength model, which will be referred to as EG [23]. The model was developed using the strain and stress approaches to determine the steel area equivalent to the FRP area, and it can be used in the conventional two-way shear models. Thus, they implemented the strain approach, with a limit of the value of 0.0045 for the strain and the British Standard of the time, and proposed that the two-way shear was calculated such that:
V = 0.79 f c 20 1 3 100 ρ E E s 1.8 1 3 400 d 1 4 b 1.5 d d

3.4. Mattys and Taerwe (2000), MT

In 2000, Mattys and Taerwe, developed a strength model, which will be referred to herein as MT [24]. It was developed based on the observed behavior of the experimental testing of FRP-reinforced concrete slabs; their stiffness is less than that of conventional reinforced slabs. In addition, the depth and axial stiffness of FRP reinforcements have a significant effect on their strength; thus, they modified the British design code to be as follows:
V = 1.36 100 ρ f c E E s 1 3 1 d 1 4 b 1.5 d d

3.5. Ospina (2003), O

In 2003, Ospina [25] developed a model (O), which is based on their experimental observations, and it was found that the strength is affected by the axial stiffness of the FRP reinforcements and the bond they have with the concrete. Thus, when it is modified, the MT model is expressed as follows:
V = 2.77 ρ f c 1 3   E E s b 1.5 d d

3.6. Zaghloul (2003), Z

Zaghloul [26] has adapted the one-way shear design of the FRP-reinforced concrete of the Canadian design codes and multiplied it by a factor of two and introduced a perimeter size effect factor, such that:
V = 0.07 E ρ f c 1 3 0.44 + 5.16 α s d b 0.5 d   b 0.5 d d
α s = 4, 3, and 2 for an inner connection, an edge connection, and a corner connection, respectively.

3.7. Jacbson (2005), Jb [27]

This is an empirical model which was developed through experimental testing.
V = 4.5   ρ f c 1 2 1 d 1 4 b 1.5 d d  

3.8. ACI (2005), ACI [28]

This ACI model accounts for the effect of the direct shear of the compression zone of the concrete, where the ACI equation for the conventionally reinforced concrete slabs ( 0.3 f c d b 0.5 d ) is multiplied by the factor (2.5 k). Thus, the shear strength is calculated such that:
V = 0.8 f c k d b 0.5 d
where k = 2 ρ n + ρ n 2 ρ n , modular ratio ( n ) = E E c , concrete young’s modulus, and E c = 4750 f c .

3.9. Elgamal (2005), E [29]

Elgamal developed a model, which was based on the experimentally observed fact that the two-way shear is affected by the FRP axial stiffness, and the slab end conditions are in terms of their continuity or them having an edge beam. Thus, the strength was proposed, such that:
V = 0.33 f c 2 0.62 E ρ 1 3 1 + 8 d b 0.5 d 1.2 N b 0.5 d d
where n = 0, 1, and 2 represents a simple slab, a continuous, one-sided slab, and a continuous, two-sided slab, respectively.

3.10. Zhang (2006), Zg [30,31]

Zhang developed a design model which included the following assumptions: (1) that two-way shear failure occurs after the critical diagonal shear crack passes through the compression zone; (2) that failure is related to concrete tensile strength; (3) that dowel action contributes to the strength. In addition, the model was calibrated using the experimental database that was available at that time, such that:
V = 0.25 + 1.10   100 ρ E E s 1 2 1 d 1 / 5 f c 1 3 b 1.5 d d

3.11. Theodorkopoulos and Swamy (2008), TS [32]

The proposed model was based on moment–shear interaction, which determined the compression zone depth using the tensile elastic stiffness of the FRP reinforcements and the bond between FRP reinforcements and the concrete.
V = 0.117 f c 0.8 2 3 100 d 1 6 2 α f λ f 1 + α f λ f b 0.5 d d
where λ f = 0.55 6 1 + 1 + 48 α f 1 , α f = 0.058 ρ E f c 0.33 .

3.12. CSA-S806-12 (2012), CSA [33]

The design model was developed, based on the conventional concrete design code, however, it was modified for FRP reinforcements instead of steel ones.
V = b 0.5 d d 0.028 1 + 2 β c E ρ f c 1 3 0.147 E ρ f c 1 3 0.19 + α s d b 0.5 d 0.056 E ρ f c 1 3
β c = ratio between the long and short side of the loading area; α s = 4, 3, and 2 for an inner connection, an edge connection, and a corner connection, respectively. b 0.5 d = 4 c + d .

3.13. Nguyen and Rovnak (2013), NR [34]

A fracture mechanics-based semi-empirical model was developed, which considered the effects of the following: (1) span-to-depth ratio; (2) the effective depth; (3) the dowel action.
V = 400 d 0.8 d a ρ / 100 0.33 E 0.33 f c 0.3 b 0.5 d
where a is the slab’s shear span.

3.14. Hassan, et al. (2017), H [35]

The model is a modification of the CSA which combines the three equations into a single formula. Then, it used a multi-linear regression technique to fit the 69 specimens in the experimental database using a power equation, such that:
V = 0.065 0.65 + 4 d b 0.5 d E ρ f c 1 3 125 d 1 6 b 0.5 d d

3.15. Kara and Sinani (2017), KS [36]

The KS model is a modification of the MT model that replaces the coefficient with 0.46 instead of 1.36 and removes the d parameter, such that:
V = 0.46 100 ρ f c E E s 1 3 b 1.5 d d

3.16. Oller, et al. (2018), CCCM [37]

The CCCM model was developed, based on the model by Mari and co-workers [38], and it is a unified model for two-way shear; thus, it applies the following assumptions: (1) the strains are higher due to the lower modulus of elasticity of the FRP bars; (2) the cracks are wider; (3) the basic perimeter at the point of failure is lower in an FRP-reinforced concrete (RC) slab than it is in a conventional RC slab. Thus, the shear capacity is calculated such that:
V = ξ X d 2.5 f c t β b 0.5 d d 0.25 f c 2 3 1.8 ξ K c + 20 d o b 0.5 d d
where ξ = 2 1 + d 200 d a   0.2 0.45 , X d = 0.75 α e ρ 1 3 , f c t = 0.3 f c 2 3 4.60   M P a , d o = d   100   m m , α e = E E c , K c = X d 0.2 , E c = 22000 f c 10 0.3 39   G P a .

3.17. Hemzah, et al. (2019), Hz [39]

Using numerical modeling and an experimental database, a two-way shear formula which considers the flexure reinforcement ratio and type, the compressive strength of concrete, and the shape of the column was developed, such that:
V = 1 3 f c 1 2 k 90 f c 0.33 5 ρ 0.39 E E s 0.3 b 0.5 d d
k = 0.77   a n d   0.55   for circular and rectangular columns, respectively.

3.18. Elgendy and Elsalakawy (2020), EE [40]

Considering the eccentricity of the slab-column joint, the H model and the EG model were modified, such that:
V = 0.33 f c 1 2 0.62 E ρ 1 3 1 + 2 α s d b 0.5 d 1.2 N b 0.5 d d
V = 0.065 0.65 + α s d b 0.5 d E ρ f c 1 3 125 d 1 6 b 0.5 d d
α s = 4, 3, and 2 for an inner connection, an edge connection, and a corner connection, respectively. N = 1, 2, and 3 for a simple slab, a continuous, one-sided slab, and a continuous, two-sided slab, respectively.

3.19. Ju, et al. (2021), Ju [41]

To guarantee the lowest probability of failure, the design strength was calculated with the probabilistic method with 95% confidence; thus, the Monte Carlo Simulation (MCS) was used to develop the probability distribution with key uncertain factors, such that:
V = 2.3   100 ρ E E s f c 1 2 d b 0.5 d 1 2 b 0.5 d d

3.20. Alrudaini (2022), A [42]

A rational model is developed, which considers the following: (1) concrete compressive strength, elastic properties of reinforcement, reinforcement ratio, and slab depth to the effective perimeter. Each parameter was fitted to the measured strength, such that:
V = 0.41   ρ E f c 1 3 d b 0.5 d 1 5 b 0.5 d d
Table 1 shows a comparison between the various design models, where it is clear that there is a lack of agreement among researchers regarding the considered parameters and methodology used to account for it. All design methods included the effect of concrete compressive strength in terms of f c 1 3 or f c 1 2 . Most of the methods included the dowel action in terms of the flexure reinforcement, which was taken as ρ 1 3 or ρ 1 2 . More than half of the methods included the FRP type in terms of Young’s modulus, which was taken as E 1 3 ., or E 1 2 . About half of the methods included the size effect in terms of 1 d 1 4 , 1 d 1 5 , 1 d 1 2 , or 2 1 + d 200 and included the ratio between the critical perimeter and the depth in terms of 0.44 + 20.8 d b 0.5 d , 1 + 8 d b 0.5 d , 0.19 + 4 d b 0.5 d , 0.65 + 4 d b 0.5 d , 1 + 8 d b 0.5 d , 0.65 + 4 d b 0.5 d , d b 0.5 d 1 2 , or d b 0.5 d 1 5 . On the other hand, very few models included the compression zone and the shear span-to-depth ratio.

4. Experimental Database Profile

Over the last 30 years, a significant number of experimentally tested specimens failed due to the effect of two-way shear. The most comprehensive experimental database, when compared to those of previous studies [2,39,41,43], was produced with a total of 248 slabs with FRP reinforcements that were collected from 50 different research studies. All the gathered slabs were subjected to two-way shear loading and failed, suddenly, under the application of two-way shear, as shown in Figure 2.
Table 2 shows a detailed description of the experimental database, where E is the Young’s modulus of FRP, d is the effective depth, f c is the concrete compressive strength, ρ is the flexure reinforcement ratio, b and c are the column dimensions, A and B are the slab dimensions, and FRP type including carbon FRP (CFRP), glass FRP (GFRP), and Basalt FRP (BFRP) are listed. Although FRP reinforcements could have several shapes and configurations, these variations were considered in terms of ρ and E . Figure 3 shows the frequency and the range of each variable. All variables cover a wide range of values, while also being normally distributed.

5. Behavior Patterns

Based on the existing models and previous studies of slabs, the relationship between the shear stress (V/bod) and the effective parameters including d, E, ρ, fc’, d/bo, and a/d is a power relationship. Thus, Figure 4 shows the scatter plots for the pattern of the log of the shear stress versus the log of the effective parameters. The scatter plots do not allow a straightforward interpretation of the data because of the significant dispersion and poor distribution of the test parameters; thus, the best regression fit line and the Pearson correlation coefficients (r) are shown in Figure 4. The inclination of the best fit lines between the stress and basic variables d, E, ρ, fc’, d/bo, and a/d were the values of −0.19, 0.19, 0.05, 0.34, 0.33, and 0.41, respectively. Comparing these values to those that were used in selected models, as shown in Table 1, it can be shown that variables ρ and fc’ have quite similar power coefficients, while E, d/bo, and a/d are significantly different, and d is only like that of one selected model.

6. Pearson Correlation

The correlation coefficients between the shear stress and the basic variables d, E, ρ, fc’, d/bo, and a/d were calculated, as shown in Figure 4, where their values are −0.19, 0.21, 0.07, 0.23, −0.34, and −0.43, respectively. Therefore, the evidence is sufficient to say that the shear strength is correlated to the basic variables in a reasonable manner, except for the flexure reinforcement ratio. This could be because the effect of the flexure reinforcement varies significantly based on its value [83]. Since the experimental database covered a wide range of flexure reinforcement ratio values, it provided a misleading value for the correlation coefficient.

7. Comparison between Selected Models

All collected models were used to calculate the strengths of the slab column connections that were in the experimental database. Three categories of comparison were defined: graphical, central tendency, and statistical goodness-of-fit. The ratio between the measured and calculated strength was taken as the safety ratio (SR). An SR value that is close to unity means that the prediction is accurate. An SR value that is more than the unity indicates that the prediction is conservative. An SR value that is less than the unity mean that the shear strength was overestimated and so, the prediction is conservative. Statistical measures in terms of the coefficient of determination (R2), the root mean square error (RMSE), the mean average error (MAE), the mean, the coefficient of variation (C.O.V.), the lower value with a 95% confidence level (Lower 95%), the maximum value, and minimum value were applied on the SR for each selected model, as shown in Table 3 and Figure 5. Table 3 shows central tendency and statistical goodness-of-fit for all the selected models, which is helpful for the future development of the design models. The JSCE, the ACI, and the H models are over-conservative, with an average value of 2.71, 2.18, and 2.16, respectively. The Zg, the EE-b, the Ju, and the A models are more consistent with respect to other models, where the coefficient of variation values of these were 35%, 35%, 36%, and 36%, respectively.
Figure 5 shows a Box plot for all the selected models. A large dispersion and extreme values are observed in the ACI model. Also, severely un-conservative predictions resulted from the application of the Gd and NR models. The recent models (i.e., Ju, A, Hz, and EE-a) provide accurate predictions for the strength (when the mean is close to the unity), as shown in Figure 6. However, the consistency in these models is still lacking (i.e., C.O.V. is higher than 35%), as shown in Table 3. Models considering basic variables in a power form equation seem to be the most accurate and consistent when they are compared with the mechanically based model (CCCM) or the fracture-based model (NR). In addition, from Figure 5, it is clear that each method was developed or calibrated for a nonsystematic margin of safety which was defined by the judgment and experience of each developer(s). This should be managed by a reliability assessment that includes the resistance and load uncertainty. Although it is an interesting topic, it is not in the scope of this study, but it can be the subject of further studies. Moreover, there is a need for further improved mechanically based models that make physical sense, while being simple in their design.
Figure 5, Figure 6, Figure 7, Figure 8, Figure 9, Figure 10 and Figure 11 shows the SR value, which was calculated using different models, versus the value of the selected effective variable. Although the SR value is affected by the values of the various variables and not only the specific variable in the figure, it is assumed that the presence of the noise, because of the other variables, is insignificant with respect to the specific variable that is in the figure. It is worth noting that this approach was implemented in several pioneering studies as a base for international design codes [11,19,28,33,37,38,42]. In addition, some models do not include that specific variable, however, the experimentally measured strength includes the effect of that variable. Thus, the model’s ability to represent the true value of the strength can be evaluated properly with respect to the effect of that specific variable.

7.1. Depth

Figure 6 shows the SR value that was calculated using the ACI model; the JSCE model; the CSA model; the CCCM model; the Ju model; the EE-b model versus the effective depth. In addition, the best fit line was plotted, whose slope was 0.0011, −0.003, −0.0016, −0.0019, −0.0003, and −0.0025 for the JSCE model, the ACI model, the CSA model, the CCCM model, the EE-b model, and the Ju model, respectively. The safety of the selected models decreases with the increase in the depth, except for the JSCE. The best fit line for the SR value that was calculated using the EE-b model is the lowest, thus, it is the most consistent with respect to the depth. However, using the ACI model resulted in the highest SR value, thus, it is the least consistent one. This could be due to the ACI model not having a size effect factor.

7.2. Concrete Compressive Strength

Figure 7 shows the SR value that was calculated using the ACI model, the JSCE model, the CSA model, the CCCM model, the Ju model, and the EE-b model versus the concrete compressive strength. In addition, the best fit line was plotted, whose slope was 0.0019, 0.0046, 0.0174, −0.0031, −0.0017, and −0.0027 for the JSCE model, the ACI model, the CSA model, the CCCM model, the EE-b model, and the Ju model, respectively. The safety of the CCCM model, the EE-b model, and the Ju model decreases with the increase in the concrete compressive strength. On the other hand, the safety of the JSCE model, the ACI model, and the CSA model increases with the increase in the concrete compressive strength. The best fit line for the SR value that was calculated using the EE-b model is the lowest; thus, it is the most consistent with respect to the concrete compressive strength. However, using the CSA model resulted in the highest SR value; thus, it is the least consistent one.

7.3. Flexure Reinforcment Ratio

Figure 8 shows the SR value that was calculated using the ACI model, the JSCE model, the CSA model, the CCCM model, the Ju model, and the EE-b model versus the flexure reinforcement ratio. In addition, the best fit line was plotted, whose slope was 0.2529, −0.6244, −0.2229, −0.0328, −0.1817, and −0.1844 for the JSCE model, the ACI model, the CSA model, the CCCM model, the EE-b model, and the Ju model, respectively. The safety of the selected models decreases with the increase in flexure reinforcement ratio, except for the JSCE model. The best fit line for the SR value that was calculated using the CCCM model is the lowest; thus, it is the most consistent with respect to the flexure reinforcement ratio. However, using the ACI model resulted in the highest SR value; thus, it is the least consistent one. This could be due to the ACI model not including the flexure reinforcement ratio in the model.

7.4. Young’s Modulus

Figure 9 shows the SR value that was calculated using the ACI model, the JSCE model, the CSA model, the CCCM model, the Ju model, and the EE-b model versus the Young’s modulus. In addition, the best fit line was plotted, whose slope was 0.0075, 0.0012, 0.0013, −0.002, −0.0011, and 0.0002 for the JSCE model, the ACI model, the CSA model, the CCCM model, the EE-b model, and the Ju model, respectively. The safety of selected models increases with the increase in Young’s modulus, except for the CCCM model and the EE-b model. The best fit line for the SR value that was calculated using the Ju model is the lowest; thus, it is the most consistent with respect to the Young’s modulus. However, using the JSCE model resulted in the highest SR value; thus, it is the least consistent one.

7.5. Depth-to-Control Perimeter Ratio

Figure 10 shows the SR value that was calculated using the ACI model, the JSCE model, the CSA model, the CCCM model, the Ju model, and the EE-b model versus the depth-to-control perimeter ratio. In addition, the best fit line was plotted; whose slope was 8.5935, 13.86, 6.8699, −2.4433, −0.8117, and −1.6327 for the JSCE model, the ACI model, the CSA model, the CCCM model, the EE-b model, and the Ju model, respectively. The safety of the CCCM model, the EE-b model, and the Ju model decreases with the increase in the depth-to-control perimeter ratio. On the other hand, the safety of the JSCE model, the ACI model, and the CSA model increases with the increase in the depth-to-control perimeter ratio. The best fit line for the SR value that was calculated using the EE-b model is the lowest; thus, it is the most consistent with respect to the depth-to-control perimeter ratio. However, using the ACI model resulted in the highest SR value; thus, it is the least consistent one. This could be because the ACI model does not include the effect of this parameter.

7.6. Shear Span-to-Depth Ratio

Figure 11 shows the SR value that was calculated using the ACI model, the JSCE model, the CSA model, the CCCM model, the Ju model, and the EE-b model versus the shear span-to-effective depth ratio. In addition, the best fit line was plotted, whose slope was −0.0507, −0.0475, −0.0224, 0.1353, 0.023, and 0.0213 for the JSCE model, the ACI model, the CSA model, the CCCM model, the EE-b model, and the Ju model, respectively. The safety of the JSCE model, the ACI model, the CSA model decreases with the increase in the shear span-to-effective depth ratio. On the other hand, the safety of the CCCM model, the EE-b model, and the Ju model increases with the increase in the shear span-to-effective depth ratio. The best fit line for the SR value that was calculated using the CSA model, the Ju model, and the EE-b model is the lowest; thus, they are the most consistent with respect to the shear span-to-effective depth ratio. However, using the CCCM model resulted in the highest; thus, it is the least consistent one.

8. Future Research

Several areas of potential for future research studies were identified as follows:
  • Experimental testing of high strength slabs with a compressive strength of more than 45 MPa;
  • Experimental testing of ultra-high-performance concrete slabs with a compressive strength of more than 100 MPa;
  • Experimental testing of non-slender concrete slabs with a shear span-to-depth ratio of less than 2.5;
  • Reliability-based analysis for the safety of the design which includes the variability in the loads, the geometry, the material, and the construction;
  • A more reliable and consistent mechanically based model that makes physical sense, while being simple in its design.

9. Conclusions

The accuracy of twenty-one selected methods to predict the two-way shear strength of the concrete slabs was assessed. Each method’s ability to predict the two-way strength of concrete slabs without shear reinforcement was studied by comparing predictions against their measured strength from an extensive experimental database comprising a total of 248 slabs from over 50 research studies. Several statistical measures were applied, and the effect of the various basic variables was discussed. The following conclusions were reached:
  • The JSCE, the ACI, the H models are over-conservative, with an average value of 2.71, 2.18, and 2.16, respectively. The Zg, the EE-b, the Ju, the A models are more consistent with respect to other models, where the coefficient of variation value was 35%, 35%, 36%, and 36%, respectively.
  • The ACI model is the least consistent with respect to the size effect, the dowel action, and the depth-to-control perimeter ratio. This could be due to the fact that the ACI model does not consider these factors in the model.
  • The EE-b model is the most consistent with respect to size effect, concrete compressive strength, depth-to-control perimeter ratio, and the shear span-to-depth ratio. This is because of it using experimentally observed behavior as well as it being based on mechanical bases.

Author Contributions

Conceptualization, F.A.; methodology M.A. (Majed Alzara); software, T.I.; validation, A.M.Y.; formal analysis, M.A. (Mohamed AbdelMongy); investigation, A.F.D. and M.A. (Mohamed AbdelMongy); resources A.F.D. and F.A.; data curation, A.M.Y.; writing—original draft preparation, A.M.Y. and M.A. (Mohamed AbdelMongy); writing—review and editing, A.F.D. and T.I.; visualization, F.A.; supervision, A.F.D. and F.A. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

All data are available within the manuscript.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Collapsed of (a) condominium building [1] and (b) a parking garage on a playground [2].
Figure 1. Collapsed of (a) condominium building [1] and (b) a parking garage on a playground [2].
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Figure 2. Two-way shear (a) failure isometric view; (b) failure elevation; (c) loading test setup schematic; (d) actual loading test setup [43,44].
Figure 2. Two-way shear (a) failure isometric view; (b) failure elevation; (c) loading test setup schematic; (d) actual loading test setup [43,44].
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Figure 3. Frequencies and ranges of the tested column-slab connections with FRP.
Figure 3. Frequencies and ranges of the tested column-slab connections with FRP.
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Figure 4. Stress versus basic variables.
Figure 4. Stress versus basic variables.
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Figure 5. The performance of selected models.
Figure 5. The performance of selected models.
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Figure 6. The effect of depth on the SR value, calculated using selected models. (a) Design codes; (b) Models.
Figure 6. The effect of depth on the SR value, calculated using selected models. (a) Design codes; (b) Models.
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Figure 7. The effect of the concrete compressive strength on the SR value, calculated using selected models. (a) Design codes; (b) Models.
Figure 7. The effect of the concrete compressive strength on the SR value, calculated using selected models. (a) Design codes; (b) Models.
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Figure 8. The effect of the flexure reinforcement ratio on the SR value, calculated using selected models. (a) Design codes; (b) Models.
Figure 8. The effect of the flexure reinforcement ratio on the SR value, calculated using selected models. (a) Design codes; (b) Models.
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Figure 9. The effect of the Young’s modulus on the SR value, calculated using selected models. (a) Design codes; (b) Models.
Figure 9. The effect of the Young’s modulus on the SR value, calculated using selected models. (a) Design codes; (b) Models.
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Figure 10. The effect of the ratio between the control perimeter and depth on the SR value, calculated using selected models. (a) Design codes; (b) Models.
Figure 10. The effect of the ratio between the control perimeter and depth on the SR value, calculated using selected models. (a) Design codes; (b) Models.
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Figure 11. The effect of the shear span-to-depth ratio on the SR value, calculated using selected models. (a) Design codes; (b) Models.
Figure 11. The effect of the shear span-to-depth ratio on the SR value, calculated using selected models. (a) Design codes; (b) Models.
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Table 1. Comparison between design models.
Table 1. Comparison between design models.
Design ModelCritical Perimeter LocationSize EffectDowel ActionYoung’s ModulusConcrete StrengthControl Perimeter-to-Depth RatioCompression Zone DepthShear Span-to
-Depth Ratio
G1.5 d d 1 4 ρ 1 3 ------ f c 1 3 ------------------
JSCE0.5 d d 1 4 ρ 1 3 E 1 3 f c 1 2 1 + 1 1 + 0.25 b 0.5 d d ------------
Gd1.5 d d 1 4 ρ 1 3 E 1 3 f c 1 3 ------------------
MT1.5 d d 1 4 ρ 1 3 E 1 3 f c 1 3 ------------------
O1.5 d------ ρ 1 3 E 1 2 f c 1 3 ------------------
Z0.5 d------ ρ 1 3 E 1 3 f c 1 3 0.44 + 20.8 d b 0.5 d ------------
Jb1.5 d d 1 4 ρ 1 2 ------ f c 1 2 ------------------
ACI0.5 d------------------ f c 1 2 ------ k ------
EG0.5 d------ ρ 1 3 E 1 3 f c 1 2 1 + 8 d b 0.5 d ------------
Zg1.5 d d 1 5 ρ 1 2 E 1 2 f c 1 3 ------------------
TS0.5 d d 1 6 ------------ f c 2 3 ------------------
CSA0.5 d------ ρ 1 3 E 1 3 f c 1 3 0.19 + 4 d b 0.5 d ------------
NR0.5 d d 1 2 ρ 1 3 E 1 3 f c 1 3 ------------ a d
H0.5 d d 1 6 ρ 1 3 E 1 3 f c 1 3 0.65 + 4 d b 0.5 d ------------
KS1.5 d------ ρ 1 3 E 1 3 f c 1 3 ------------------
CCCM0.5 d 2 / 1 + d 200 ρ 1 3 E 1 3 f c 2 3 ------ X d a d 0.2
Hz0.5 d------ ρ 0.39 E 0 ; 3 f c 1 6 ------------------
EE-(a)0.5 d------ ρ 1 3 E 1 3 f c 1 2 1 + 8 d b 0.5 d ------------
EE-(b)0.5 d d 1 6 ρ 1 3 E 1 3 f c 1 3 0.65 + 4 d b 0.5 d ------------
Ju0.5 d------ ρ 1 2 E 1 2 f c 1 2 d b 0.5 d 1 2 ------------
A0.5 d------ ρ 1 3 E 1 3 f c 1 3 d b 0.5 d 1 5 ------------
Table 2. Experimental database for RC slabs with FRP reinforcements under two-way shear loading.
Table 2. Experimental database for RC slabs with FRP reinforcements under two-way shear loading.
Year of StudySpecimen LabelA (mm)B (mm)b (mm)c (mm)d (mm)fc’ (MPa)FRP Type ρ (%) E (GPa)V (kN)#
1993CFRC-SN169069075756142.4CFRP0.9511393[45]
CFRC-SN269069075756144.6CFRP0.9511378
CFRC-SN36906901001006139CFRP0.9511396
CFRC-SN46906901001006136.6CFRP0.9511399
199516006001001005541CFRP0.3110065[46]
26006001001005552.9CFRP0.3110061
36006001001005541.5CFRP0.3110072
19951180015002502507630CFRP2.05143186[47]
2180015002502507630CFRP2.05143179
3180015002502507630CFRP1.81143199
4180015002502507630CFRP2.05156198
5180015002502507630CFRP1.81156201
6180015002502507630CFRP1.49156190
199913000180057522517543GFRP141.3500[48]
23000180057522517543GFRP141.31050
33000180057522517543GFRP139.3875
43000180057522517543GFRP139.31090
53000180057522517543GFRP139.31180
C13000180057522517555CFRP11001000
C23000180057522517555CFRP11001200
C33000180057522517555CFRP11001328
H23000180057522517545Hybrid11601055
H43000180057522517545Hybrid11601096
H53000180057522517545Hybrid11601183
2000C1100010001501509637.3CFRP0.2791.8181[24]
C1’100010002302309535.7CFRP0.2791.8189
C2100010001501509536.3CFRP1.0595255
C2’100010002302309536.3CFRP1.0595273
C31000100015015012633.8CFRP0.5292347
C3’1000100023023012634.3CFRP0.5292343
CS100010001501509532.6CFRP0.19148142
CS’100010002302309533.2CFRP0.19148150
H11000100015015095118HFRP0.6237.3207
H2100010001501508935.8HFRP3.7640.7231
H2’1000100080808935.9HFRP3.7640.7171
H31000100015015012232.1HFRP1.2244.8237
H3’10001000808012232.1HFRP1.2244.8217
200012000250025015016242GFRP0.2885622[49]
22000250025015016242GFRP0.2885698
32000250025015016242GFRP0.2885575
42000250025015016242GFRP0.2885534
52000250025015016242GFRP0.2885584
200011800300057522516559CFRP0.571471000[50]
21800300057522516559CFRP0.571471200
31800300057522516559CFRP0.571471328
200012000400050025013835GFRP2.442756[51]
2003SG12000200020020014233.3GFRP0.2245170[23]
SC12000200020020014234.7CFRP0.18110229
SG22000200020020014246.6GFRP0.4745271
SG32000200020020014230.3GFRP0.4745237
SC22000200020020014229.6CFRP0.43110317
2003GFR-12150215025025012029.5GFRP0.7334217[25]
GFR-22150215025025012028.9GFRP1.4634260
NEF-12150215025025012037.5GFRP0.8728.4206
2003ZJF5176017602502507545CFRP-1100234[26]
2004G-S11830183025025010040GFRP1.1842249[52]
G-S21830183025025010035GFRP1.0542218
G-S31830183025025010029GFRP1.6742240
G-S41830183025025010026GFRP0.9542210
200512300200063525017527.6GFRP0.9833537[27]
22300200063525017527.6GFRP0.9833536
32300200063525017527.6GFRP0.9533531
72000200063525017527.6GFRP0.9833721
82000200063525017527.6GFRP0.9833897
2005G-S13000250060025015949.6GFRP144.6740[29]
G-S23000250060025015944.3GFRP1.9938.5712
G-S33000250060025015949.2GFRP1.2146.5732
C-S13000250060025016549.6CFRP0.35122.5674
C-S23000250060025016544.3CFRP0.69122.5799
2005GS21830183025025010035GFRP1.0542218[31]
GSHS1830183025025010071GFRP1.1842275
2006CS11900190025025010031CFRP0.41120251[30]
CS21900190025025010033CFRP0.54120293
CS31900190025025010025.7CFRP0.75120285
CSHD11900190025025010035.9CFRP0.54120325
CSHD21900190025025010038.6CFRP0.75120360
CSHS11900190025025015085.6CFRP0.36120399
CHSHS21900190025025015098.3CFRP0.5120446
200711900190025025011070GFRP141282[53]
21900190025025011070GFRP1.241319
31900190025025011070GFRP1.541384
41900190025025016070GFRP1.241589
51900190025025014570GFRP1.241487
61900190025025013570GFRP1.241437
2007ZJEF11760100025025012025CFRP1.37100188[54]
ZJEF21760100025025012027CFRP0.94100156
ZJEF31760100025025012055CFRP1.37100211
ZJEF5176010002502508128CFRP1.3710097
ZJEF71760100045025012026CFRP1.37100196
ZJF81760176035025010128CFRP1.48100178
ZJF91760176025025010057.6CFRP1.48100272
2007G-S43000250060025015644.1GFRP1.244.5707[55]
G-S53000250060025015644.1GFRP1.244.5735
2008F1120012002002008237.4GFRP1.146165[56]
F21200120020020011233GFRP0.8146170
F3120012002002008238.2GFRP1.2946210
F4120012002002008239.7GFRP1.5446230
2009GFU12300230022522511036.3GFRP1.1748.2222[57]
GFB22300230022522511036.3GFRP2.1448.2246
GFB32300230022522511036.3GFRP348.2248
GFBF32300230022522511033.8GFRP348.2330
2010S31500150015015013533.5BFRP0.29100145[58]
S41500150015015013535.6BFRP0.55100275
S51500150015015013532.8BFRP0.42100235
S61500150015015013532.5BFRP0.42100225
S71500150015015013522.6BFRP0.42100170
S81500150015015013541.8BFRP0.42100235
S91500150015015013540.6BFRP0.42100200
2010NC-G-4530030025254547.8GFRP0.787644[59]
NC-G-0/9030030025254547.8GFRP0.787645
NC-C-4530030025254547.8CFRP0.2423039
NC-C-0/9030030025254547.8CFRP0.2423045
SFRC-C-4530030025254547.8CFRP0.2423063
UHPC-C-45300300252545179CFRP0.2423097
UHPC-C-0/90300300252545179CFRP0.2423098
2010A1500150015015013022.16GFRP0.4245.6176[60]
B-21500150015015013032.46GFRP0.4245.6209
B-31500150015015013032.4GFRP0.5545.6245
B-41500150015015013032.8GFRP0.2945.6167
B-51500150015015013033.2GFRP0.4245.6217
B-61500150015015013028.32GFRP0.4245.6222
B-71500150015015013046.05GFRP0.4245.6253
2011G200n3000250060025015549.1GFRP1.2043732[61]
G175N3000200060025013535.2GFRP1.2043484
G150N3000200060025011035.2GFRP1.2043362
G175h3000200060025013564.8GFRP1.2043704
G175n0.73000200060025013553.1GFRP0.743549
G175n0.353000200060025013753.1GFRP0.3543506
C175N3000200060025014040.3GFRP0.40122530
2012A1500150015015013022.2GFRP0.4245.6176[62]
B-21500150015015013032.5GFRP0.4245.6209
B-31500150015015013032.4GFRP0.5545.6245
B-41500150015015013032.8GFRP0.2945.6167
C1500150015015013044.4GFRP0.4245.6252
2013GSL-PUNC-0.42200220020020013048.8GFRP0.4848180[34]
GSL-PUNC-0.52200220020020013048.8GFRP0.6848212
GSL-PUNC-0.62200220020020013048.8GFRP0.9248244
2013G (0.7) 30/202500250030030013434.3GFRP0.7148.2329[35]
G (1.6) 30/202500250030030013138.6GFRP1.5648.1431
G (1.6) 30/20-H2500250030030013175.8GFRP1.5657.4547
G (1.2) 30/202500250030030013137.5GFRP1.2164.9438
G (0.3) 30/352500250030030028434.3GFRP0.3448.2825
G (0.7) 30/352500250030030028439.4GFRP0.7348.11071
G (1.6) 30/352500250030030027538.2GFRP1.6156.71492
G (1.6) 30/35-H2500250030030027575.8GFRP1.6156.71600
G(0.7) 30/20-B2500250030030013438.6GFRP0.7148.2386
G(0.7) 45/202500250030030013444.9GFRP0.7148.2400
G (1.6) 45/20-B2500250030030013139.4GFRP1.5648.1511
G (0.3) 30/35-B2500250030030028439.4GFRP0.3448.2781
G (0.7) 30/35-B-22500250030030028146.7GFRP0.7348.11195
G (0.3) 45/352500250030030028448.6GFRP0.3448.2911
G (1.6) 30/20-B2500250030030013132.4GFRP1.5648.1451
G (1.6) 45/202500250030030013132.4GFRP1.5648.1504
G (0.7) 30/35-B-12500250030030018129.6GFRP0.7348.11027
G(0.3) 45/35-B2500250030030028432.4GFRP0.3448.21020
G (0.7) 45/352500250030030028129.6GFRP0.7348.11248
2015GSC-0.9-XX-0.42800150030030016041GFRP0.960.505251[63]
GSC-1.35-XX-0.42800150030030016041GFRP1.3560.505268
GSC-1.8-XX-0.42800150030030016041GFRP1.760.505277
GSC-0.9-XX-0.22800150030030016041GFRP0.8560.505239
GSC-0.9-XX-0.32800150030030016041GFRP0.960.505159
GRD-0.9-XX-0.42800150030030016041GFRP0.959.877191
2015G-0.6%-12-125 T&B14255005002511968.1GFRP0.667.4344[64]
G-0.6%-16-300 T&B14255005002511765.7GFRP0.667.4365
B-0.6%-12-125 T&B14255005002511969.3BFRP0.654300
B-0.6%-16-300 T&B14255005002511766.1BFRP0.654295
2016GSC-0.9-XX-0.42600145030030016081GFRP0.8760.505251[65]
GSC-1.35-XX-0.52600145030030016085GFRP1.2860.505272
GSC-1.8-XX-0.42600145030030016080GFRP1.760.505288
2016S2-B3000200060025016048.81BFRP0.869.3548[66]
S3-B3000200060025016042.2BFRP0.7969.3665
S4-B3000200060025016042.2BFRP0.869.3566
S5-B3000200060025016047.9BFRP1.269.3716
S6-B3000200060025016047.9BFRP0.469.3576
S7-B3000200060025016047.9BFRP0.469.3436
2016GN-0.652600260030030016042GFRP0.6569.3363[67]
GN-0.982600260030030016038GFRP0.9868378
GN-1.302600260030030016039GFRP1.368425
GH-0.652600260030030016070GFRP0.6568380
G-00-XX2800280030030016038GFRP0.6568421[68]
2016G-15-XX2800280030030016042GFRP0.6568363
G-30-XX2800280030030016042GFRP0.6568296
R-15-XX2800280030030016040GFRP0.6568320
2017NW5980080025025017659GFRP0.70368719[69]
2017SG1110011001501506229.8GFRP0.2247136[70]
SO1110011001501506237.3GFRP0.134768
SO2110011001501506232.6GFRP0.134785
SO3110011001501506230.5GFRP0.224780
SO4110011001501506235.4GFRP0.2247100
SO5110011001501506230.1GFRP0.2247102
2018GFS13000220020020018036.7GFRP1.5747410[71]
GFS23000220020020018036.7GFRP1.247360
GFS33000220020020018036.7GFRP0.7947370
2018H-1.0-XX2800280030030016080GFRP0.9865461[72]
H-1.5-XX2800280030030016084GFRP1.4665541
H-2.0-XX2800280030030016087GFRP1.9365604
2019C-F-S-10-46006001001008051CFRP0.3144103[39]
C-F-S-10-66006001001008052CFRP0.45144127
S-F-D-10-46006001001008046CFRP0.6144112
S-F-D-10-66006001001008060CFRP0.9144129
S-F-S-10-46006001001008052CFRP0.314479
S-F-S-10-66006001001008048CFRP0.45144107
S-F-S-7.5-46006001001006049CFRP0.4114457
S-F-S-7.5-66006001001006049CFRP0.6114479
2019G2500135030030016041.4GFRP1.5565314[73]
2019G1 (1.06)2500250030030015152GFRP1.0662.6140[74]
G2 (1.51)2500250030030015192GFRP1.5162.6140
G3(1.06)-SL2500250030030015145GFRP1.0662.6180
2020A30-1150015003003008827.4GFRP1.2851.1191[75]
A30-21500150030030010827.3GFRP1.0551.1289
A30-31500150030030013826.2GFRP0.8251.1413
A30-4150015003503508626.8GFRP1.3151.1209
A40-1150015003503508828.2GFRP1.2851.1232
A40-2150015003503508826.4GFRP0.8951.1221
A40-3150015003003008828.6GFRP1.2851.1236
A50-1150015003003008829.2GFRP1.2851.1253
A50-2150015003003009032.2GFRP0.8754.1237
A50-3150015003503508826.7GFRP1.2851.1280
2020S40-1150015003003008832.3GFRP0.9851.1314[76]
S50-1150015003003008643.2GFRP0.754.4187
2020G4(1.06)-H2500250030030015192GFRP1.0662.6134[77]
2020F11600160020020012524.97CFRP0.89123262[78]
2021G-N-0.32500130030030016037.1GFRP1.0465260[79]
G-H-0.33000220020020016085.8GFRP1.0465306
G-N-0.63000220020020016038.8GFRP1.0465178
G-H-0.63000220020020016086GFRP1.0465213
20210F-6052000200025025012538.2GFRP2.8150.6463[80]
0F-80F2000200025025012538.2GFRP2.1150.6486
0F-11052000200025025012538.2GFRP1.5350.6436
1.25F-60S2000200025025012538.2GFRP2.8150.6455
1.25F-80S2000200025025012538.2GFRP2.1150.6506
1.25F-110S2000200025025012538.2GFRP1.5350.6498
2022SA150050055553645BFRP0.845030[81]
SA250050055553645GFRP0.844228
SA450050055553645BFRP0.565026
SA550050055553645GFRP0.564224
SA750050055553665BFRP0.845035
SA050050055553645BFRP0.845028
2022CFRP116701670107510755229.62CFRP0.36140169[82]
CFRP216701670107510755234.59CFRP0.36140178
CFRP316701670107510755234.59CFRP0.36140208
BFRP116701670107510755229.62BFRP0.3655103
BFRP216701670107510755234.59BFRP0.3655120
BFRP316701670107510755234.59BFRP0.3655144
Minimum30030025253622.16 0.1328.424.34
Maximum3000400010751075284179 3.762301600
Mean1915171530323512544 175372
Variation40%39%66%65%40%44% 64%55%82%
Table 3. Statistical measures for all strength models.
Table 3. Statistical measures for all strength models.
Design ModelR2RMSEMAEMeanC.O.V.Lower 95%MaximumMinimum
G0.672051440.820.380.781.850.15
JSCE0.693372382.710.382.588.080.69
Gd0.697766530.360.370.340.780.08
MT0.691831211.180.361.132.920.23
O0.711701101.000.380.953.010.18
Z0.672001260.940.380.902.810.16
Jb0.671821101.150.381.102.590.21
ACI0.692721942.180.452.066.900.36
Eg0.682221370.860.370.822.590.13
Zg0.701661061.000.350.962.430.19
TS0.702551761.780.361.703.960.33
CSA0.721651101.190.401.133.170.21
NR0.563602520.630.450.601.600.14
H0.702902032.160.362.075.560.40
KS0.711631031.070.371.023.070.19
CCCM0.671981261.060.441.003.480.22
Hz0.721641051.000.450.953.540.19
EE-a0.673051950.740.380.702.270.11
EE-b0.702331601.610.351.544.240.30
Ju0.701731171.260.361.203.600.22
A0.711631061.130.361.073.210.20
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Aslam, F.; AbdelMongy, M.; Alzara, M.; Ibrahim, T.; Deifalla, A.F.; Yosri, A.M. Two-Way Shear Resistance of FRP Reinforced-Concrete Slabs: Data and a Comparative Study. Polymers 2022, 14, 3799. https://doi.org/10.3390/polym14183799

AMA Style

Aslam F, AbdelMongy M, Alzara M, Ibrahim T, Deifalla AF, Yosri AM. Two-Way Shear Resistance of FRP Reinforced-Concrete Slabs: Data and a Comparative Study. Polymers. 2022; 14(18):3799. https://doi.org/10.3390/polym14183799

Chicago/Turabian Style

Aslam, Fahid, Mohamed AbdelMongy, Majed Alzara, Taha Ibrahim, Ahmed Farouk Deifalla, and Ahmed M. Yosri. 2022. "Two-Way Shear Resistance of FRP Reinforced-Concrete Slabs: Data and a Comparative Study" Polymers 14, no. 18: 3799. https://doi.org/10.3390/polym14183799

APA Style

Aslam, F., AbdelMongy, M., Alzara, M., Ibrahim, T., Deifalla, A. F., & Yosri, A. M. (2022). Two-Way Shear Resistance of FRP Reinforced-Concrete Slabs: Data and a Comparative Study. Polymers, 14(18), 3799. https://doi.org/10.3390/polym14183799

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