Shear Strength Prediction Model of FRP Bar-Reinforced Concrete Beams without Stirrups

Gao, Danying; Zhang, Changhui

doi:https://doi.org/10.1155/2020/7516502

Mathematical Problems in Engineering

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Abstract Introduction Experimental Results Conclusions Data Availability Conflicts of Interest Acknowledgments References Copyright Related Articles

Research Article | Open Access

Volume 2020 | Article ID 7516502 | https://doi.org/10.1155/2020/7516502

Shear Strength Prediction Model of FRP Bar-Reinforced Concrete Beams without Stirrups

Danying Gao^1,2and Changhui Zhang^1,3

Academic Editor: A. M. Bastos Pereira

Received25 Jan 2020

Revised29 Feb 2020

Accepted10 Mar 2020

Published09 Apr 2020

Abstract

The shear strength prediction model for fiber-reinforced polymer (FRP) bar-reinforced concrete beams without stirrups in ACI440.1R-2015 does not consider the “size effect” and the effect of shear span-to-depth ratio and predicts the zero-shear strength for concrete members without longitudinal reinforcement. A modified shear strength prediction model for FRP bar-reinforced concrete beams without stirrups was presented in this paper. The proposed model takes into account the effect of concrete strength, size of the beam, shear span-to-depth ratio, reinforcement ratio, and modulus of elasticity of the longitudinal reinforcement and the “size effect.” The superiority of the proposed model has been evaluated by comparing the calculated shear strength of FRP bar-reinforced concrete beams without stirrups by the proposed model with the experimental results and calculated values by the models in design codes, respectively. It confirmed that the shear strength of FRP bar-reinforced concrete beams without stirrups by the proposed model was in better agreement with the experimental results.

1. Introduction

Fiber-reinforced polymer (FRP) bars have gained the acceptance as an alternative to conventional steel bars for concrete structures due to their corrosion resistance, high strength-to-weight ratio, and magnetic neutrality. It has been recognized that the flexural capacity of FRP bar-reinforced concrete beams can be predicted by the traditional assumptions used in steel bar-reinforced concrete beams. However, while FRP bars have two drawbacks including brittle failure and low modulus of elasticity compared with the steel bars, the shear behavior (including shear strength, deformation, and crack width) of concrete beams reinforced with the FRP bar is different from those reinforced with similar amount of steel reinforcement [1–4]. For example, the stiffness [3] and dowel action [4] of FRP bar-reinforced beams are smaller compared to the concrete beams with steel bars, subsequently resulting in the larger deformation and lower shear strength. Therefore, the existing shear strength prediction models for steel bar-reinforced beams cannot be directly applied to FRP bar-reinforced beams.

The shear strength prediction model of FRP bar-reinforced concrete beams in ACI440.1R-2015 [5] was based on the research by Tureyen and Frosch [6]. The ACI440.1R-2015 model was a function of the width () and effective depth () of the beam, concrete compressive strength (), reinforcement ratio (), and modulus of elasticity () of FRP bars, and the shear span-to-depth ratio () was not included [7, 8]. Several investigations confirmed that shear strength of FRP bar-reinforced concrete beams decreases as the increases [7, 9–13]. Some investigators [7] revealed that decreases almost linearly with , while the others [10] reported that it decreases linearly with . In addition, the ACI440.1R-2015 model did not take into account the effect of concrete in the tensile zone of the beam on the shear strength for FRP bar-reinforced concrete beams without longitudinal reinforcement and predicted the zero-shear strength for concrete beams without longitudinal reinforcement [8]. Thirdly, the ACI440.1R-15 model did not take into account the “size effect” [14–17] which explains the phenomenon that the normalized shear strength of FRP bar-reinforced concrete beams decreases with the increasing of beam depth.

It has been recognized that , , , , , and are the important parameters affecting the shear strength of FRP bar-reinforced concrete beams without stirrups. An equation that cannot predict the effects of known parameters would lack generality, and its applicability to general design situations would be uncertain [18]. Thus, there is a need to develop a modified shear strength prediction model for properly reflecting the effects of important parameters, which are known to affect the shear strength of FRP bar-reinforced beams without stirrups.

In this paper, a database of published test results on shear strength of 369 beams reinforced with FRP bars without stirrups was compiled. Considering the effects of on the shear strength of FRP bar-reinforced concrete beams without stirrups and the “size effect” and the contribution of the concrete to the shear strength for concrete beams without longitudinal reinforcement, a more accurate and rational-modified prediction model was proposed based on the ACI440.1R-2015 model. The efficiencies of the proposed model and ACI440.1R-2015, CAN/CSA-S806-2012 [19], JSCE-1997 [20], AASHTO LRFD-2017 [21], and CNR-DT203-2006 [22] models were evaluated by comparing the calculated values with the experimental values in the database and the test data which are not contained in the database.

2. Experimental Database

To present a new shear strength prediction model of FRP bar-reinforced concrete beams without stirrups, a relatively large database including 369 beams reinforced with FRP bars without stirrups from 42 different investigations was established. The criteria for collecting the data of beam specimens were as follows: (1) rectangular cross sections; (2) simply supported; (3) tested under one- or two-point loading; (4) statically loaded; and (5) failed in shear. This database included various parameters which are known to affect the shear strength of FRP bar-reinforced concrete beams without stirrups, such as , , , , , and . The variation range of each parameter and the corresponding shear strength of the beam used in this study are given in Table 1, which is collected from the original source.

3. Review of Shear Strength Prediction Models in Design Codes

The shear strength prediction models of FRP bar-reinforced concrete beams without stirrups were highly valued by many countries, such as America, Japan, Canada, and Italy. The “size effect” and effects of , , and on the shear strength of FRP bar-reinforced concrete beams without stirrups were mainly considered in the shear strength prediction models of different design codes.

3.1. ACI440.1R-2015 Guidelines [5]

The shear strength calculating model of FRP bar-reinforced concrete beams without stirrups recommended by ACI Committee 440 is as follows:where , .

It can be clearly seen that equation (1) of the ACI440.1R-2015 model predicts zero-shear strength for concrete beams without longitudinal reinforcement and does not consider the effect of on the shear strength of FRP bar-reinforced concrete beams without stirrups and the “size effect.”

3.2. JSCE-1997 Design Recommendations [20]

The shear strength calculating model of FRP bar-reinforced concrete beams without stirrups recommended by Japan Society of Civil Engineering (JSCE-1997) is as follows:where , , and

It is the same as equation (1) of the ACI440.1R-15 model that equation (2) of the JSCE-1997 model predicts zero-shear strength for concrete beams without longitudinal reinforcement and does not consider the effect of on the shear strength of FRP bar-reinforced concrete beams without stirrups although it takes into account the “size effect” through .

3.3. CAN/CSA-S806-2012 Design Provisions [19]

The shear strength calculating model of FRP bar-reinforced concrete beams without stirrups recommended by the Technical Committee on Design and Construction of Building Structures with Fibre-Reinforced Polymers of Canadian Standards Association (CAN/CSA-S806) is as follows:where , , , and .

Equation (3) of the CAN/CSA-S806-2012 model considers the effects of nearly all parameters on the shear strength of FRP bar-reinforced concrete beams without stirrups.

3.4. AASHTO LRFD-2017 Design Guide Specifications [21]

The shear strength calculating model of FRP bar-reinforced concrete beams without stirrups recommended by the American Association of State Highway and Transportation Officials is as follows:

Equation (5) of the AASHTO LRFD-2017 model considers the effects of and on the shear strength of FRP bar-reinforced concrete beams without stirrups while the effect of and the “size effect” are not included.

3.5. CNR-DT203-2006 [22]

The shear strength of FRP bar-reinforced concrete beams without stirrups recommended by Advisory Committee Technical Recommendations Construction of Italian National Research Council is as follows:where , , , and .

Equation (6) of the CNR-DT203-2006 model considers the “size effect” through and does not consider the effect of on the shear strength of FRP bar-reinforced concrete beams without stirrups.

4. Proposed Shear Strength Prediction Model

According to the experimental database mentioned above, the normalized shear strength was plotted against () as shown in Figure 1(a). It can be seen that the relationship between the normalized shear strength and fits into the trendline in Figure 1(a) except some plots. To express this trendline with a reasonable equation, the normalized shear strength was also plotted against () as shown in Figure 1(b), where can be defined as the relative depth of the compressive zone because the depth of compressive zone can be calculated by multiplying by (). From the regression of the results of FRP bar-reinforced concrete beams without stirrups, there is a linear equation between and , which can be written as

(a)

(b)

Equation (7) can take into account the effects of and on the shear strength for FRP bar-reinforced concrete beams without stirrups and the contribution of concrete on shear strength for FRP bar-reinforced concrete beams without longitudinal reinforcement.

4.1. Effect of Shear Span-to-Depth Ratio () on the Shear Strength

In order to eliminate the influence of and on shear strength of FRP bar-reinforced concrete beams without stirrups, the normalized shear strength was taken as on the basis of equation (7), which was plotted against according to the experimental database mentioned above, as shown in Figure 2. Evidently, decreases as increases, and there is a trendline between with . The relationships between and can be obtained by the regressions based on the following three criteria:(1)The regressions can be described in four forms depending upon the value of or determined by the types of failure referred to those for steel bar-reinforced beams [52]. Diagonal compression failure (when ): Shear compression failure (when ): Diagonal tension failure (when ): Bending failure (when ):(2)The regressions remain coordinated on boundary conditions(3)According to Reinforced Concrete Design to Eurocode 2 [53], when and , the shear strength can be calculated by the following equation:

The shear strength of concrete can be expressed by the tension strength of concrete as follows [52]:where is a constant, generally, . Conservatively, here, .

The concrete tension strength can be evaluated with the equation in ACI318-14 [54] as follows:

Substituting the values of in equation (15) into equation (14), the equation for shear strength of concrete can be rewritten as

Substituting the values of in equation (16) into equation (13), when and , the equation for the shear strength of the FRP bar-reinforced concrete beams without stirrups can be rewritten as

Based on the regressions of the database aforementioned, as shown in Figure 2, the functions between and can be obtained as follows:

As there are only two specimens in the database whose shear span-to-depth ratio is below 1.0, no more data can be employed for regression; therefore, the function of could be set up according to the criterions (2) and (3) as follows:

Then, the equation for shear strength of FRP bar-reinforced concrete beams without stirrups, which considers the effect of shear span-to-depth ratio (), can be modified as follows:where

4.2. “Size Effect” on the Shear Strength

According to the experimental database mentioned above and equation (21), the normalized shear strength was plotted against , , , , , and as shown in Figure 3, respectively. It can be seen that does not have the obvious variation with the increase of , , , , , and , respectively, but there is a relation between and . It indicates that the influence of , , , , , and upon the shear strength of FRP bar-reinforced concrete beams without stirrups has been embodied reasonably well by equation (20) except the influence of . This phenomenon demonstrates the “size effect” exists on the shear strength of FRP bar-reinforced concrete beams without stirrups mentioned in the literature review.

(a)

(b)

(c)

(d)

(e)

(f)

Then, referring to Eurocode 2 for the shear capacity of concrete reinforced with the steel bar, the equation for shear strength of FRP bar-reinforced concrete beams without stirrups, which has taken into account the “size effect” by a linear reduction form [15], can be established as follows:where

5. Comparison of Predicted Shear Strength and Experimental Results

Figure 4 presents the correlations of the experimental shear strength of all 369 specimens in the database mentioned above and another 18 test data of specimens from Jumaa and Yousif [55] and Ovitigala [56] with the calculated shear strengths , , , , , and , respectively. A line with tolerance of 0% has been represented in the graph, which indicates that the exact prediction of the shear strength. It can be seen that the ACI440.1R-2015, JSCE-1997, and AASHTO LRFD-2017 models provide conservative predictions of the shear strengths of the most specimens (); the predictions of the CNR-DT203-2006 model are highly unconservative for many specimens; the CAN/CSA-S806-2012 model shows better agreement with the experiment results than other models in the design codes aforementioned; and the predictions of the proposed model by equation (22) fit better with the experiment results than all the models in the design codes aforementioned.

(a)

(b)

(c)

(d)

(e)

(f)

Figure 5 illustrates the relationships among the shear strength ratio of the experimental shear strength to the calculated shear strength and , , and , respectively. As shown in Figure 5, the ratio of decreases as increases, while for all the models in the design codes aforementioned; both ratios of and increase as increases, for the CAN/CSA-S806-2012 model does not well consider the effects of nor , and the AASHTO LRFD-2017 model does not consider the effect of ; and the ratio of does not have obvious variation with the increase of , , or . Moreover, the proposed model has the least scatter range of from 0.39 to 2.63, whilst the scatter range of for ACI440.1R-2015, JSCE-1997, CAN/CSA-S806-2012, AASHTO LRFD-2017, and CNR-DT203-2006 models is from 0.82 to 17.38, 0.44 to 12.88, 0.24 to 4.58, 0.39 to 13.91, and 0.18 to 4.87, respectively. Hence, the effect of , , , and on shear strength normalized by the proposed model of equation (22) is captured reasonably well. It should be mentioned that the predicted values by the proposed model for the two specimens with shear span-to-effective depth less than 1 are in good agreement with the experimental values () though the function of the proposed model () was not obtained by the regression method.

The ratios of are presented graphically using a histogram as shown in Figure 6. The horizontal axis of the figure shows the ratio of , and the vertical axis represents the frequency of the specimens for a certain ratio. It can be seen that the values of follow a normal distribution, and 60% of the values is in a narrow range 0.8 to 1.2.

To further investigate the superiority of the proposed shear strength prediction model of FRP bar-reinforced concrete beams without stirrups, a total of three performance checks were adopted. The mean, standard deviation (SD), and coefficient of variation (COV) of the ratio are given in Table 2. It can be observed that the proposed model, as a whole, predicts the shear strength of FRP bar-reinforced concrete beams without stirrups with smaller SD and COV values than ACI440.1R-2015, JSCE-1997, AASHTO LRFD-2017, CNR-DT203-2006, and CAN/CSA-S806-2012 models.

6. Conclusions

The impacts of shear span-to-depth ratio upon the shear strength of FRP bar-reinforced concrete beams without stirrups and the “size effect” were investigated by analyzing the collected experimental results. A new model for the shear strength prediction of FRP bar-reinforced concrete beams without stirrups was proposed by using the regression method based on the experimental database. The main conclusions of this research are summarized as follows:(1)The proposed model considers the “size effect” and the effect of shear span-to-depth ratio on the shear strength for FRP bar-reinforced concrete beams without stirrups, which decrease as the shear span-to-depth ratio and effective depth increase, respectively.(2)The values of experimental results for the shear strength of FRP bar-reinforced concrete beams without stirrups to calculated values by the proposed model follow a normal distribution, and 60% of the values distribute in a narrow range 0.8 to 1.2.(3)The proposed model has more reasonable and reliable predictions for the shear strength of FRP bar-reinforced concrete beams without stirrups in comparison with the models in design codes mentioned.

Notations

:	Cylinder compressive strength of concrete, MPa
:	Cube compressive strength of concrete, MPa
:	Tension strength of concrete, MPa
:	Shear span, mm
:	Beam width, mm
:	Effective depth, mm
:	Shear span-to-depth ratio
:	Relative depth of the compressive zone
:	Depth of the compressive zone, mm
:	Reinforcement ratio
:	Modular ratio
:	Modulus of elasticity of FRP bars, MPa
:	Modulus of elasticity of concrete, MPa
:	Shear strength of FRP bar-reinforced concrete beams, N
:	Experimental shear strength, N
:	Calculated shear strength, N
:	Calculated shear strength using the proposed model, N
:	Calculated shear strength using the ACI440.1R-15 model, N
:	Calculated shear strength using the JSCE-1997 model, N
:	Calculated shear strength using the CAN/CSA-S806-2012 model, N
:	Calculated shear strength using the AASHTO LRFD-2017 model, N
:	Calculated shear strength using the CNR-DT203-2006 model, N.

Data Availability

All data included in this study are available upon request by contact with the corresponding author.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

This research was financially supported by the National Natural Science Foundation of China (Grant no. U1704254).

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Copyright © 2020 Danying Gao and Changhui Zhang. 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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