**4.2 Case study 2**

In this part the PBNN and ANFIS models are developed to predict the shear strength of concrete beams reinforced with FRP bars. A database from tests on concrete beams reinforced with FRP bars obtained from the review of literature is used in this study. The structure of ANN and ANFIS models and the results of this study will be described below.

#### **4.2.1 Review on shear strength of concrete beams reinforced with FRP bars**

An FRP bar is made from filaments or fibers held in a polymeric resin matrix binder. The FRP Bar can be made from various types of fibers such as Glass (GFRP) or Carbon (CFRP). FRP bars have a surface treatment that facilitates a bond between the finished bar and the structural element into which they are placed (Bank, 2006).

During the last two decades, fiber reinforced polymer (FRP) materials have been used in a variety of configurations as an alternative reinforcement for new and strengthening civil engineering structures and bridges. The attractiveness of the material lies mainly in their high corrosion resistance, high strength and fatigue resistance. In some cases, the nonmagnetic characteristics became more important for some special structures. An important application of FRP, which is becoming more popular (Tan, 2003, as cited in Al-Sayed et at.,

BPNN ANFIS

empirical expression 100% agreement line

Fig. 14. Comparison experimental and predicted values for testing data Set

Table 4. Comparison summary of correlation R

0

3

6

9

Vu (Predicted) kN

12

15

structural element into which they are placed (Bank, 2006).

**4.2 Case study 2** 

Type Correlation R

0 3 6 9 12 15

Vu (Target) kN

BPNN 0.9981 0.9983 ANFIS 0.9980 0.9976 Empirical Method 0.9500 0.9600

In this part the PBNN and ANFIS models are developed to predict the shear strength of concrete beams reinforced with FRP bars. A database from tests on concrete beams reinforced with FRP bars obtained from the review of literature is used in this study. The structure of ANN and ANFIS models and the results of this study will be described below.

An FRP bar is made from filaments or fibers held in a polymeric resin matrix binder. The FRP Bar can be made from various types of fibers such as Glass (GFRP) or Carbon (CFRP). FRP bars have a surface treatment that facilitates a bond between the finished bar and the

During the last two decades, fiber reinforced polymer (FRP) materials have been used in a variety of configurations as an alternative reinforcement for new and strengthening civil engineering structures and bridges. The attractiveness of the material lies mainly in their high corrosion resistance, high strength and fatigue resistance. In some cases, the nonmagnetic characteristics became more important for some special structures. An important application of FRP, which is becoming more popular (Tan, 2003, as cited in Al-Sayed et at.,

**4.2.1 Review on shear strength of concrete beams reinforced with FRP bars** 

Training Testing

2005a) is the use of FRP for reinforcement in concrete structures. The use of FRP in concrete structures include: (a) the internal reinforcing (rod or bar) which is used instead of the steel wire (rod) equivalent; and (b) the external bonded reinforcement, which is typically used to repair/strengthen the structure by plating or wrapping FRP tape, sheet or fabric around the member (Wu & Bailey, 2005).

There are fundamental differences between the steel and FRP reinforcements: the latter has a lower modulus of elasticity, the modulus of elasticity for commercially available glass and aramid FRP bars is 20 to 25 % that of steel compared to 60 to 75 % for carbon FRP bars (Bank, 2006) linear stress–strain diagram up to rupture with no discernible yield point and different bond strength according to the type of FRP product. These characteristics affect the shear capacity of FRP reinforced concrete members. Due to the relatively low modulus of elasticity of FRP bars, concrete members reinforced longitudinally with FRP bars experience reduced shear strength compared to the shear strength of those reinforced with the same amounts of steel reinforcement.

Some of empirical equations have been developed to estimate shear strength of concrete beams reinforced with FRP. Most of the shear design provisions incorporated in these codes and guides are based on the design formulas of members reinforced with conventional steel considering some modifications to account for the substantial differences between FRP and steel reinforcement. These provisions use the well-known Vc + Vs method of shear design, which is based on the truss analogy. This section reviews the concrete shear strength of members longitudinally reinforced with FRP bars, ���, as recommended by the American Concrete Institute (ACI 440.1R-03, 2003), Tureyen and Frosch Equation (2003), and the proposed equation by El-Sayed et al. (2005a).

#### **4.2.1.1 American Concrete Institute (ACI 440.1R-03)**

The equation for shear strength proposed by the American Concrete Institute (ACI 440.1R-03), can be expressed as follows:

$$V\_{cf} = \frac{\rho\_f E\_f}{^{90}\rho\_1 f\_c'} (\frac{\sqrt{f\_c'}}{^6} b\_W d \ ) \le \frac{\sqrt{f\_c'}}{^6} b\_W d \tag{16}$$

#### **4.2.1.2 Tureyen and Frosch equation (2003)**

This equation was developed by Tureyen and Frosch, 2003. It was developed from a model that calculates the concrete contribution to shear strength of reinforced concrete beams. The equation was simplified to provide a design formula applicable FRP reinforced beams as follows:

$$V\_{cf} = \frac{2}{5} \zeta \frac{\sqrt{f\_c'}}{6} b\_{\text{w}} c \tag{17}$$

where: � = ��= cracked transformed section neutral axis depth ( mm).

$$k = \sqrt{2\rho\_f n\_f + (\rho\_f n\_f)^2 - \rho\_f n\_f} \tag{18}$$

#### **4.2.1.3 El-Sayed et al. equation (2005a)**

They applied the same procedure in ACI 440.1R-03 to derive Eq. 1 above, with some modification for proposing the Eq. below:

Neural Network and Adaptive Neuro-Fuzzy

diverge.

Inference System Applied to Civil Engineering Problems 491

are minimized, the model with all the parameters including the connection weights is tested

The network has trained continually through updating of the weights until error goal of 15.1\*10-4 is achieved. Fig. 15 shows the performance for training and generalization (testing). A resilient back propagation training algorithm is used to train the network, for 800 epochs to check if the performance (MSE) for either training or testing sets might

The network performance with resilient back propagation training algorithm have been tested for training and testing patterns, as shown in Fig. 16 (a) and (b). A good agreement has been

Based on the same idea used to study the effect of the parameters on shear strength of ferrocement members, the effect of each parameter used in the input layer on shear strength of concrete beams reinforced with FRP bars is investigated. Table 6 lists the relative importance of the input variables in BPNN model. It can be observed that for shear strength

important factor among the input variables. This result is very match with the experimental

d� ) is also the most

with a separate set of "testing" data that is not used in the training phase.

noted in the predicting values compared with the actual (targets) values.

of concrete beams reinforced with FRP, the shear span to depth ratio(a

Fig. 15. Convergence of the BPNN for training and testing sets

*d*  (mm)

��′ (MPa)

RI (%) 24.76 18.26 11.11 5.23 37.50 3.19

�� (MPa)

�

�� ��

(%)

*bw*  (mm)

Table 6. Relative importance (RI) (%) of BPNN model

Input variables

results of many papers published in this field.

$$W\_{cf} = 0.037 \left( \frac{\rho\_f E\_f \sqrt{f\_c'}}{\rho\_1} \right)^{1/3} b\_w d \le \frac{\sqrt{f\_c'}}{6} b\_w d \tag{19}$$

According to ACI 440.1R-03, the factor �� in the denominator of Eq. 3 is a function of the concrete compressive strength. It can be simply expressed by the following equation:

$$0.085 \ge \beta\_1 = 0.85 - 0.007(f\_c' - 28) \ge 0.65\tag{20}$$

#### **4.2.2 Shear strength database**

From the review of literature ( Deitz, et al., 1999; El-Sayed et al. , 2005b, 2006a, 2006b, 2006c; Gross et al., 2003, 2004; Omeman et al., 2008; Razaqpur et al., 2004; Tariq & Newhook, 2003; Tureyen & Frosch, 2002, 2003; Wegian & Abdalla , 2005; Yost et al., 2001), a number (74) of shear strength tests are used for developing the ANN and ANFIS as shown in Table B in appendix. All specimens were simply supported and were tested in threepoint loading. The main reinforcement of all specimens is FRP. All specimens had no transverse reinforcement and failed in shear. These data are divided into two sets: a training set containing 64 members, and testing set comprised of 10 members. Six input variables are selected to build the ANN and ANFIS models. These variables are width (��), and depth (�) of the beams, modulus of elasticity of FRP (��), compressive strength of concrete (�� � ), reinforcement ratio of FRP (��) and the shear span to depth ratio (� �� ). The output value is the shear strength of concrete beams reinforced with FRP bars. Table 5 summarizes the ranges of each different variable.


Table 5. Summarizes the ranges of the different variables.

#### **4.2.3 ANN model and results**

ANN is used to investigate the shear strength of concrete beams reinforced with FRP bars. The configuration and training of neural networks is a trail-and-error process due to such undetermined parameters as the number of nodes in the hidden layer, and the number of training patterns. In the developed ANN, there is an input layer, where six parameters are presented to network and an output layer, with one neuron representing shear strength of concrete beams reinforced with FRP bars. One hidden layer as intermediate layer is also included. The network with one hidden layer and four nodes in the hidden layer gave the optimal configuration with minimum mean square error (MSE).

The back-propagation neural network model used for this study is trained by feeding a set of mapping data with input and target variables as explained previously. After the errors

� ��

According to ACI 440.1R-03, the factor �� in the denominator of Eq. 3 is a function of the concrete compressive strength. It can be simply expressed by the following equation:

From the review of literature ( Deitz, et al., 1999; El-Sayed et al. , 2005b, 2006a, 2006b, 2006c; Gross et al., 2003, 2004; Omeman et al., 2008; Razaqpur et al., 2004; Tariq & Newhook, 2003; Tureyen & Frosch, 2002, 2003; Wegian & Abdalla , 2005; Yost et al., 2001), a number (74) of shear strength tests are used for developing the ANN and ANFIS as shown in Table B in appendix. All specimens were simply supported and were tested in threepoint loading. The main reinforcement of all specimens is FRP. All specimens had no transverse reinforcement and failed in shear. These data are divided into two sets: a training set containing 64 members, and testing set comprised of 10 members. Six input variables are selected to build the ANN and ANFIS models. These variables are width (��), and depth (�) of the beams, modulus of elasticity of FRP (��), compressive strength

), reinforcement ratio of FRP (��) and the shear span to depth ratio (�

Parameters Range

�� ) 1.3-6.5

) MPa 24-81

The output value is the shear strength of concrete beams reinforced with FRP bars. Table 5

ANN is used to investigate the shear strength of concrete beams reinforced with FRP bars. The configuration and training of neural networks is a trail-and-error process due to such undetermined parameters as the number of nodes in the hidden layer, and the number of training patterns. In the developed ANN, there is an input layer, where six parameters are presented to network and an output layer, with one neuron representing shear strength of concrete beams reinforced with FRP bars. One hidden layer as intermediate layer is also included. The network with one hidden layer and four nodes in the hidden layer gave the

The back-propagation neural network model used for this study is trained by feeding a set of mapping data with input and target variables as explained previously. After the errors

Width of beams (��) mm 89-1000 Effective depth of beams (�) mm 143-360

Modulus of elasticity of FRP (��) (GPa) 37-145 Reinforcement ratio of FRP (��) 0.25-2.63

*′*

)� �⁄ ��� � ���

� �

��� (19)

�� ).

� − 28) ≥ 0.65 (20)

��� = 0.037 (�������

0.85 ≥ �� = 0.85 − 0.007(��

**4.2.2 Shear strength database** 

of concrete (��

�

Shear span to depth ratio (�

**4.2.3 ANN model and results** 

Compressive strength of concrete (��

summarizes the ranges of each different variable.

Table 5. Summarizes the ranges of the different variables.

optimal configuration with minimum mean square error (MSE).

are minimized, the model with all the parameters including the connection weights is tested with a separate set of "testing" data that is not used in the training phase.

The network has trained continually through updating of the weights until error goal of 15.1\*10-4 is achieved. Fig. 15 shows the performance for training and generalization (testing). A resilient back propagation training algorithm is used to train the network, for 800 epochs to check if the performance (MSE) for either training or testing sets might diverge.

The network performance with resilient back propagation training algorithm have been tested for training and testing patterns, as shown in Fig. 16 (a) and (b). A good agreement has been noted in the predicting values compared with the actual (targets) values.

Based on the same idea used to study the effect of the parameters on shear strength of ferrocement members, the effect of each parameter used in the input layer on shear strength of concrete beams reinforced with FRP bars is investigated. Table 6 lists the relative importance of the input variables in BPNN model. It can be observed that for shear strength of concrete beams reinforced with FRP, the shear span to depth ratio(a d� ) is also the most important factor among the input variables. This result is very match with the experimental results of many papers published in this field.

Fig. 15. Convergence of the BPNN for training and testing sets


Table 6. Relative importance (RI) (%) of BPNN model

Neural Network and Adaptive Neuro-Fuzzy

Inference System Applied to Civil Engineering Problems 493

(a) For training pattern (b) For training pattern

The predictions of shear strength of beams reinforced with FRP as that obtained from BPNN, ANFIS, ACI 440.1R-03, Tureyen and Frosch's equation**,** and the proposed equation by El-Sayed et al. (2005a), are compared with the experimental results and shown for both

In Table 6 the ratios of experimental (Ve) to theoretical (Vi) predictions of the shear strength of beams reinforced with FRP are calculated, the theoretical predictions include those obtained by BPNN (V1), ANFIS (V2), proposed equation by El-Sayed et al. (V3), ACI 440.1R-03 (V4), and Tureyen and Frosch's equation (V5). The average and the standard deviation of the ratios Ve/Vi are also given in this table. It can be seen that the BPNN and ANFIS models give average values for the testing set of Ve/V1 and Ve/V2 of 0.97 and 1.03 and standard deviations of 0.1 and 0.167 respectively which are much better than the values obtained from other methods as shown in table 7. Figs. 19 and 20 confirm the same conclusion that the predictions of the ANN and ANFIS models are better than those of the other methods. Also in Table 8 the correlation coefficient R of predicted shear strength that was evaluated by BPNN, ANFIS and the other methods are summarized. As shown in Table 8, the BPNN and ANFIS produces a higher correlation coefficient R as compared with the other methods. These results indicate that the BPNN and ANFIS is a reliable and simple model for

Fig. 18. Comparison between BPNN results and target results

training and testing sets in Figs. 19 and 20 and Table 7.

**4.2.5 Comparison between experimental and theoretical results** 

predicting the shear strength of beams reinforced with FRP bars.

V� V�

V� V�

Specimens No Average of of Ve / Vi STDEV of Ve / Vi

V� V�

Training set 64 1.01 1.04 2.30 5.32 3.17 0.16 0.23 2.31 3.94 2.98 Testing set 10 0.96 1.03 2.01 3.93 2.73 0.103 0.17 1.72 1.62 2.27 Table 7. Comparison between experimental and Predicted results for training and testing sets

V� V� V� V�

V� V� V� V�

V� V� V� V�

V� V�

Fig. 16. Comparison between BPNN results and target results

#### **4.2.4 ANFIS model and results**

The same technique used to build the ANFIS to predict shear strength of ferrocement members is used to build of ANFIS to predict the shear strength of concrete beams reinforced with FRP bars. Fig. 17 presents the structure of an adaptive neuro-fuzzy inference system developed to predict shear strength of concrete beams reinforced with FRP bars. The membership functions (MFs) of type (Gauss) for all input variables and linear for output present the best prediction in this study. The number of MFs assigned to each input variable is chosen by trial and error. After training and testing the number of MFs was fixed at two MFs for each input variable, when the ANFIS model reaches an acceptable satisfactory level. A comparison between the predictions from ANFIS and target value for both the training and testing data set is presented in Fig. 18(a) and(b) respectively. A good agreement has been noted in the predicting values compared with the experimental (target) values with reasonably high correlation R.

Fig. 17. Structure of the proposed ANFIS model

(a) For training pattern (b) For training pattern

The same technique used to build the ANFIS to predict shear strength of ferrocement members is used to build of ANFIS to predict the shear strength of concrete beams reinforced with FRP bars. Fig. 17 presents the structure of an adaptive neuro-fuzzy inference system developed to predict shear strength of concrete beams reinforced with FRP bars. The membership functions (MFs) of type (Gauss) for all input variables and linear for output present the best prediction in this study. The number of MFs assigned to each input variable is chosen by trial and error. After training and testing the number of MFs was fixed at two MFs for each input variable, when the ANFIS model reaches an acceptable satisfactory level. A comparison between the predictions from ANFIS and target value for both the training and testing data set is presented in Fig. 18(a) and(b) respectively. A good agreement has been noted in the predicting values compared with the experimental (target) values with

Fig. 16. Comparison between BPNN results and target results

**4.2.4 ANFIS model and results** 

reasonably high correlation R.

Fig. 17. Structure of the proposed ANFIS model

(a) For training pattern (b) For training pattern

#### **4.2.5 Comparison between experimental and theoretical results**

The predictions of shear strength of beams reinforced with FRP as that obtained from BPNN, ANFIS, ACI 440.1R-03, Tureyen and Frosch's equation**,** and the proposed equation by El-Sayed et al. (2005a), are compared with the experimental results and shown for both training and testing sets in Figs. 19 and 20 and Table 7.

In Table 6 the ratios of experimental (Ve) to theoretical (Vi) predictions of the shear strength of beams reinforced with FRP are calculated, the theoretical predictions include those obtained by BPNN (V1), ANFIS (V2), proposed equation by El-Sayed et al. (V3), ACI 440.1R-03 (V4), and Tureyen and Frosch's equation (V5). The average and the standard deviation of the ratios Ve/Vi are also given in this table. It can be seen that the BPNN and ANFIS models give average values for the testing set of Ve/V1 and Ve/V2 of 0.97 and 1.03 and standard deviations of 0.1 and 0.167 respectively which are much better than the values obtained from other methods as shown in table 7. Figs. 19 and 20 confirm the same conclusion that the predictions of the ANN and ANFIS models are better than those of the other methods.

Also in Table 8 the correlation coefficient R of predicted shear strength that was evaluated by BPNN, ANFIS and the other methods are summarized. As shown in Table 8, the BPNN and ANFIS produces a higher correlation coefficient R as compared with the other methods. These results indicate that the BPNN and ANFIS is a reliable and simple model for predicting the shear strength of beams reinforced with FRP bars.


Table 7. Comparison between experimental and Predicted results for training and testing sets

Neural Network and Adaptive Neuro-Fuzzy

this study, the following conclusions can be stated:

engineering problems as a future research.

ݒ: Volume fraction of the mesh reinforcement (100\*Als/ bd). ܣ௦: Cross sectional area of the longitudinal reinforcing mesh ܾ௪: Width of the concrete specimen reinforced wih FRP

ܧ: Modulus of elasticity of fiber reinforced polymers.

ߚଵ: Is a function of the concrete compressive strength.

: Compressive strength of concrete or mortar. ݂௬: Yield strength of reinforcement (wire mesh or FRP).

**5. Conclusion** 

methods results.

**6. Nomenclature**  ܸ௨: Shear strength.

݂ *′*

ܽ

ܾ: Width of the specimen. ݀: Depth of the specimen.

ߩ: Reinforcement ratio of flexural FRP.

݀ൗ : Shear span to depth ratio.

Inference System Applied to Civil Engineering Problems 495

Two civil engineering applications are preformed using back-propagation neural network (BPNN)and adaptive neuro fuzzy inference system (ANFIS). The models were developed by predicting the shear strength of ferrocement members and the shear strength of concrete beams reinforced with fiber reinforced polymer (FRP) bars using BPNN and ANFIS based on the results of experimental lab work conducted by different authors. From the results of

1. BPNN and ANFIS have the ability to predict the shear strength of ferrocement members and the shear strength of concrete beams reinforced with FRP with a high degree of accuracy when they are compared with experimental and available

2. The relative importance of each input parameter is estimated using ANN. The relative importance study indicated that the predicted shear strength for both ferrocement and concrete beams with FRP by ANN models are in agreement with the underlying

3. The ANN and ANFIS techniques offer an alternative approach to conventional techniques and, from them, some advantages can be obtained. Conventional models are based on the assumption of predefined empirical equations dependent on unknown parameters. However, in problems for which the modeling rules are either not known or extremely difficult to discover, such as in our problem, the conventional methods do not work well as shown in results. By using artificial neural network and the adaptive neuro fuzzy inference system, these difficulties are overcome since they are based on the learning and generalization from experimental data. ANN and ANFIS models can serve as reliable and simple predictive tools for the prediction of shear strength for both ferrocement and concrete beams with FRP of ferrocement members. Therefore, these models can be applied to solve most of civil

ܸ: The shear resistance of members reinforced with FRP bars as flexural reinforcement.

݊: Ratio of the modulus of elasticity of FRP bars to the modulus of elasticity of concrete.

behavior of shear strength prediction based on the prior knowledge.

Fig. 19. Comparison experimental and predicted values for testing data set

Fig. 20. Comparison experimental and predicted values for testing data set


Table 8. Comparison summary of correlation R
