Prediction of FRP Contribution to the Shear Resistance of RC Beams Using Artificial Neural Networks

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1 Prediction o FRP Contribution to the Shear Resistance o RC Beams Using Artiicial Neural Networks H. Naderpour 1, A. Kheyroddin 2, M. K. Sharbatdar 1, G. Ghodrati Amiri 3, S. R. Hoseini Vaez 4 1- Assistant Proessor, Department o Civil Engineering, Semnan University 2- Proessor, Department o Civil Engineering, Semnan University 3- Proessor, School o Civil Engineering, Iran University o Science and Technology 4- Ph.D. Student, Department o Civil Engineering, Semnan University naderpour@semnan.ac.ir Abstract Shear strengthening o reinorced concrete (RC) beams using iber-reinorced polymers (FRPs) has been studied intensively in the last decade, even i shear or simple RC beams is not actually ully understood. Three main conigurations o FRP strengthening including side bonding, U-wrapping, and complete wrapping may be used or externally bonded reinorcement o RC beams. In the present study, the FRP contribution to the shear resistance o RC beams is predicted using available experimental data by applying artiicial neural networks (ANNs). With known combinations o input and output data, the neural network can be trained to extract the underlying characteristics and relationships rom the data. Then, when a separate set o input data is ed to the trained network, it will produce an approximate but reasonable output. Neural networks are highly nonlinear and can capture complex interactions among input/output variables in a system without any prior knowledge about the nature o these interactions. A database containing the results rom more than 200 tests perormed in dierent research institutions across the world was collected. Having parameters used as input nodes in ANN modeling such as beam dimensions, compressive strength o concrete, type o FRP iber, ultimate tensile strength o FRP, angle o inclination o FRP ibers with respect to the horizontal axis and thickness o FRP, the target/output nodes was shear contribution o FRP. The transer unctions were assumed to be Tan-sigmoid and Logsigmoid or hidden layers. The comparison o the new approaches with existing experimental data and available empirical models shows that the ANN model can accurately predict the shear contribution o FRP. Keywords: FRP, Artiicial Neural Network, Shear Resistance, RC Beam 1. INTRODUCTION FRP systems have been shown to increase the shear strength o existing concrete beams and columns by wrapping or partially wrapping the members. Orienting FRP ibers transverse to the axis o the member or perpendicular to potential shear cracks is eective in providing additional shear strength. Increasing the shear strength can also result in lexural ailures, which are relatively more ductile in nature compared with shear ailures [1-5]. Shear strengthening o reinorced concrete beams using iber-reinorced polymers has been studied intensively in the last decade, even i shear or simple RC beams is not ully understood. The design equations or RC beams used in the main current design guidelines are based on semi-empirical approaches. The shear capacity o the beams is computed by adding the contribution o the concrete and the steel stirrups. In many cases, using the same procedure, the shear strength o the RC beams strengthened with composite materials is computed by adding the contribution o the FRP. While the empirical design equations or RC beams were validated with extensive experimental results, the equations or predicting the shear resistance o FRP strengthened RC beams are oten compared with a small number o experiments and using test series. The near surace mounted reinorcement has been also used or shear strengthening [6] but the application is limited to side bonding technique. The development o theoretical models began using the assumption that FRP materials behave like internal stirrups. Later, studies were ocused on developing new theories based on the real strain ield distribution. Even i a large eort has been ocused on theoretical studies, the shear strength models are almost as many as the research studies perormed. Chaallal et al. (1998) proposed the

2 equation or calculating the shear contribution o FRP based on the assumption that the composite and the stirrups behave similarly [7]. Malek and Saadatmanesh (1998) introduced in their ormulation the anisotropic behavior o the FRP. Studies have revealed that the inclination angle o the critical shear crack is inluenced by the plate thickness, FRP percentage and orientation angle, percentage o existing steel hoops, concrete quality, and percentage and diameter o the tensile longitudinal steel bars [8]. A model, obtained by experimental itting, was derived by Triantaillou (1998), and Triantaillou and Antonopoulos (2000) [9 and 10]. The contribution o the FRP is limited by the eective strain in the composite. Further on, Khalia et al. (1998) modiied the model o Triantaillou introducing strain limitations due to shear crack opening and loss o aggregate interlock [11]. The proposed model was appraised by considering more tests. By combining the strip method and shear riction approach Deniaud and Cheng (2001) stated that the FRP strains are uniormly distributed among the ibers crossing the critical shear crack. A design model was developed based on the ailure mechanism observed on the tested specimens. The evaluation showed a good agreement between model predictions and test results [12]. Continuing the Khalia model, Pellegrino and Modena (2002) suggested a modiied reduction actor or the ratio o the eective strain to ultimate strain in FRP. According to the experimental studies perormed, the stiness ratio between transversal shear reinorcement and FRP shear reinorcement has a signiicant eect on the eectiveness o shear strengthening. Available inormation is restricted to side-bonded beams strengthening conigurations. Aspects regarding lateral concrete peeling ailure under shear loading o FRP were studied later by Pellegrino and Modena. The model o these writers ollows the truss model approach and describes the concrete, steel, and FRP contributions to the shear capacity o RC beams based on the experimental observations [13]. Carolin and Täljsten (2005) proposed an equation to predict the contribution o EBR composites or the shear strengthening, limiting the tensile ailure o the iber. The non-uniorm distribution o the strains in FRP over the cross section was stated [14]. A 55 to 65% o the maximum measured strain value was recommended or engineering design. The equations are used today in the Swedish Design Guideline or FRP strengthening. Chen and Teng (2004) analyzed the shear ailure o the RC beams strengthened with FRP and concluded that the stress distribution in the FRP along the crack plane is non-uniorm. They proposed a model or RC beams strengthened with FRP that takes into account the iber rupture and debonding ailure modes. The model also assumes a non-uniorm stress distribution in the FRP along the shear crack. Stress limitation is introduced by bond length coeicient and strip width coeicient [15]. Using an adapted compression ield theory, ib Bulletin 14 (2001) developed a theoretical model to predict the contribution o FRP sheets or the shear capacity o RC beams [16]. Although the writers have made a coherent derivation, the model has some limitations, since it can be used only or wrapping strengthening schemes; hence it is not prepared to predict debonding ailure mechanism or side bonding and U conigurations. Furthermore, the model does not simulate the strain concentration at the composite-crack intersection, so the potential rupture in the composite at cracking regions cannot be captured. Theoretical predictions were compared with experimental results and, unortunately ound to be incompatible. 2. THEORETICAL ASPECTS Figure 1 shows three dierent types o FRP wrapping schemes used to increase the shear strength o rectangular beams, or columns. Completely wrapping the FRP system around the section on all our sides is the most eicient wrapping scheme and is most commonly used in column applications where access to all our sides o the column is usually available. In beam applications where an integral slab makes it impractical to completely wrap the member, the shear strength can be improved by wrapping the FRP system around three sides o the member (U-wrap) or bonding to two opposite sides o the member. Although all three techniques have been shown to improve the shear strength o a member, completely wrapping the section is the most eicient, ollowed by the three-sided U-wrap. Bonding to two sides o a beam is the least eicient scheme. The design shear strength o a concrete member strengthened with an FRP system should exceed the required shear strength. The required shear strength o an FRP-strengthened concrete member should be computed with the load actors. The design shear strength should be calculated by multiplying the nominal shear strength by the strength reduction actor. 2

3 Fig. 1. Typical wrapping schemes or shear strengthening using FRP laminates The nominal shear strength o an FRP-strengthened concrete member can be determined by adding the contribution o the FRP external shear reinorcement to the contributions rom the reinorcing steel (stirrups, ties, or spirals) and the concrete. An additional reduction actor ψ is applied to the contribution o the FRP system. φ Vn V u (1) n ( V + V ψ V ) φ V φ + (2) c s Figure 2 presents the variables used in shear-strengthening calculations or FRP laminates. The contribution o the FRP system to shear strength o a member is based on the iber orientation and an assumed crack pattern. The shear strength provided by the FRP reinorcement can be determined by calculating the orce resulting rom the tensile stress in the FRP across the assumed crack. V A ( sin α + cosα ) d v e v = (3) s A = 2nt w (4) v The tensile stress in the FRP shear reinorcement at nominal strength is directly proportional to the level o strain that can be developed in the FRP shear reinorcement at nominal strength. e = ε E (5) e Fig. 2. Variables used in shear-strengthening calculations using FRP laminates 3

4 3. ARTIFICIAL NEURAL NETWORKS From historical point o view, neural networks appear to be a recent development. However, this ield was established beore the advent o computers. An Artiicial Neural Network (ANN) is an inormation processing tool that is inspired by the way biological nervous systems (such as the brain), process the inormation. The key element o this tool is the novel structure o the inormation processing system. It is composed o a large number o highly interconnected processing elements (called neurons) working in unison to solve speciic problems. Similar to human, ANNs learn by examples. An ANN is conigured or a speciic application, such as pattern recognition or data classiication, through a learning process. Learning in biological systems involves adjustments to the synaptic connections that exist between the neurons; the same process happens in ANNs. Artiicial neural networks provide a general practical method or real-valued, discrete-valued, and vector-valued unctions rom examples and so they have been widely used in the various applications o engineering ields. In engineering applications, a neural network can be a vector mapper which maps an input vector to an output one. Network Architectures A single biological neuron is composed o three major parts including the cell body, the axon, and the dendrite. Fig. 3 shows the schematic drawing o representative biological neurons and a simpliied computational neuron. The cell body o a neuron is connected to the dendrite o a neighbouring neuron. These individual biological neurons are interconnected with the other neurons through hair-like dendrites. A group o these neurons can consist o layers o neurons, and a collection o layers can orm nerve systems in the human body. Signal communications between neurons are continuously generated which is delivered rom one neuron to the others by iring an electrical signal generated through a chemical reaction. The other neurons receive the signal through the interaces with the neighbouring neurons, reerred to as a synapse. This system is capable o learning, recalling, and generating output corresponding to external signals. I a system o neurons has a consistent and requent external signal, its output signal will be consistent and thus stored in the system. On the other hand, i it is subjected to an insistent or rare signal, the memory or this type o inormation may vanish ater receiving other signals or patterns. This biological neuron system can work collectively to handle more complicated learning to illustrate how the mathematical operations are used to mimic the major biological unctionalities. The general computational neuron is shown in Fig. 4. Similar to biological neurons, a computational neuron has input, a neuron cell, and output. Each neuron is commonly connected with net-like internal weights in which complex knowledge is embedded. The ANN types can be distinguished by overall structure, neuron type, training data space, and learning rules among others. Each input is weighted with an appropriate w. The sum o the weighted inputs and the bias orms the input to the transer unction. Neurons can use any dierentiable transer unction to generate their output. Backpropagation is the generalization o the Widrow-Ho learning rule to multiple-layer networks and nonlinear dierentiable transer unctions. Since networks with biases, a sigmoid layer, and a linear output layer are capable o approximating any unction with a inite number o discontinuities, input vectors and the corresponding target vectors are used to train a network until it can approximate a unction. Standard backpropagation is a gradient descent algorithm in which the network weights are moved along the negative o the gradient o the perormance unction. The term backpropagation reers to the manner in which the gradient is computed or nonlinear multilayer networks. There are a number o variations on the basic algorithm that are based on other standard optimization techniques, such as conjugate gradient and Newton methods. Properly trained backpropagation networks tend to give reasonable answers when presented with inputs that they have never seen. Typically, a new input leads to an output similar to the correct output or input vectors used in training that are similar to the new input being presented. This generalization property makes it possible to train a network on a representative set o input/target pairs and get good results without training the network on all possible input/output pairs. The most common backpropagation training algorithm is Levenberg-Marquardt which was used in this investigation. 4

5 Fig. 3. Schematic o a biological neuron and its components 4. NEURAL NETWORK MODELLING Fig. 4. Schematic o a computational neuron As the irst step or providing suicient inormation or training, veriying and testing o neural networks, a comprehensive set o test results was collected. All together, the selected database contains more than 200 test results including signiicant test programs o three recent decades. The parameters used as the main input nodes in the ANN modelling were the ollowing: B slab T =width o lange or T section beams b web =beam s cross section width h=height o the beam h slab T =thickness o the lange or T section beams cm =mean value o concrete compressive cylinder strength ck =characteristic compressive cylinder strength o concrete at 28 days ctm =mean value o concrete cylinder tensile strength E c =elastic modulus o concrete E FRP =elastic modulus o ibers ϵ FRP,u =ultimate design strain o the FRP FRP,u =ultimate design stress o the FRP t FRP =thickness o the FRP w FRP =width o the FRP s FRP =spacing o the FRP Having the input nodes as described above, the target node was V FRP =contribution o the FRP to the shear capacity o the beam. One hidden layer was used in this ANN modelling, where the transer unctions were tan-sigmoid. Beore training the selected data, normalization/scaling or the whole data were made. This was done since logsigmoid transer unction was used in the network which recognizes values between 0 and 1. In order to scale the data rom 0.1 to 0.9, minimum and maximum values were taken to use linear relationship between those values. 5

6 In the ANN modelling, 60% o whole data was speciied as the training data in which the network would be adjusted according to its error. Similarly 20% o database was considered as the validating data which was used to measure network generalization and to halt training when generalization stops improving. Finally the remaining 20% o whole data was speciied as the testing data which has no eect on training and so provides an independent measure o network perormance during and ater training. The criterion or stopping the training o the networks was Mean Square Error (MSE) which is the average squared dierence between outputs and targets. Lower values mean better perormance o the network (Zero means no error). Regression values (R-values) measure the correlation between outputs and targets in the networks; An R-value o 1 means a close relationship and in contrast, 0 means a random relationship. These two criteria (MSE and R-values) were considered as the basis or selecting the idealised network. The results or training the idealised network are summarized in Figs. 5 to 7. Figure 6 shows the mean squared error o the network starting at a large value and decreasing to a smaller value. In other words, it shows that the network is learning. The plot has three lines, because the input and targets vectors are randomly divided into three sets. Training on the training vectors continues as long the training reduces the network s error on the validation vectors. Ater the network memorizes the training set (at the expense o generalizing more poorly), training is stopped. This technique automatically avoids the problem o over-itting, which plagues many optimization and learning algorithms. Fig. 5. Regressions o training, validation and test data simulated by NN Fig. 6. Training state o NN

7 Fig. 7. Perormance o NN CONCLUSIONS A large collection o experimental data or FRP-shear strengthened RC beams was gathered. Through development o neural networks, the contribution o the FRP to the shear capacity o the beam was related to some input parameters. Ater training the many neural networks with dierent number o hidden neurons, by considering the perormance o the networks (MSE and R), one o the networks was selected or simulation which showed eective perormance through training, testing, and validation. The precision o the ANN approach was veriied by available experimental data and showed good agreement. REFERENCES 1. Malvar, L., Warren, G., and Inaba, C. (1995). Rehabilitation o Navy Pier Beams with Composite Sheets. Second FRP International Symposium on Non-Metallic (FRP) Reinorcement or Concrete Structures, Ghent, Belgium, Aug., pp Chajes, M., Januska, T., Mertz, D., Thomson, T., and Finch, W. (1995). Shear Strengthening o Reinorced Concrete Beams Using Externally Applied Composite Fabrics. ACI Structural Journal, Vol. 92, No. 3, May-June, pp Eshghi, S., and Zanjanizadeh, V. (2008). Retroit o slender square reinorced concrete columns with glass iber-reinorced polymer or seismic resistance. Iranian Journal o Science & Technology, Vol. 32, No. B5, pp Mostoinejad, D. and Talaeitaba, S. B. (2006). Finite element modeling o RC connections strengthened with FRP laminates. Iranian Journal o Science & Technology, Vol. 30, No. B1, pp ACI 440.2R-08. (2008). Guide or the Design and Construction o Externally Bonded FRP Systems or Strengthening Concrete Structures, ACI Committee 440, American Concrete Institute. 6. Dias, S. J. E., and Barros, J. A. O. (2008). Shear strengthening o T cross section reinorced concrete beams by near surace mounted technique. J. Compos. Constr., 12(3), Chaallal, O., Nollet, M.-J., and Perraton, D. (1998). Strengthening o reinorced concrete beams with externally bonded ibre-reinorcedplastic plates: Design guidelines or shear and lexure. Can. J. Civ. Eng., 25, Malek, A. M., and Saadatmanesh, H. (1998). Analytical study o reinorced concrete beams strengthened with web bonded ibre reinorced plastic plates or abrics. ACI Struct. J., 95(3),

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