PSI - Issue 17

Danial J. Armaghani et al. / Procedia Structural Integrity 17 (2019) 924–933 Danial J. Armaghaniet al. / Structural Integrity Procedia 00 (2019) 000 – 000

930

7

Table 3.Statistical indexes for the optimum ANN architectures for each one the four cases

Statistical Indices

Case

BPNN model

a20-index

R

RMSE

MAPE

VAF

DataSet

A

9-30-4-1 7-19-28-1 5-28-24-1 4-24-12-1 9-30-4-1 7-19-28-1 5-28-24-1 4-24-12-1

0.9667 0.9300 0.9200 0.7867 0.9333 0.9167 0.8500 0.6500

0.9944 0.9914 0.9925 0.9632 0.9884 0.9863 0.9878 0.9446

0.2397 0.3001 0.2783 0.6671 0.3340 0.3774 0.3451 0.7746

0.0519 0.0715 0.0765 0.1665 0.0792 0.1041 0.1071 0.3207

98.8798 98.2528 98.5135 91.5461 97.6924 97.0797 97.5726 87.7638

B

C D A

All

B

C D

Test

Table 4.Ranking of the optimum NN model with others available in literature proposals based on all datasets Ranking Based on Model Statistical Indices a20-index R RMSE a20-index R RMSE MAPE VAF 1 1 1 9-30-4-1 0.9667 0.9944 0.2397 0.0519 98.8798 2 3 3 7-19-28-1 0.9300 0.9914 0.3001 0.0715 98.2528 3 2 2 5-28-24-1 0.9200 0.9925 0.2783 0.0765 98.5135 4 4 4 4-24-12-1 0.7867 0.9632 0.6671 0.1665 91.5461 5 7 5 EC2 0.4933 0.6824 1.8384 0.6259 42.9313 6 6 6 Canadian Code 0.3500 0.6832 1.9753 0.8064 43.8300 7 9 9 Gandomi et al. 2017 0.3000 0.5799 2.6227 0.9071 -31.9055 8 5 7 NZS 0.2833 0.6931 2.0795 0.8612 47.9592 9 8 8 ACI 0.1900 0.5862 2.3534 0.9600 15.1939 In this work presented herein, soft computing techniques such as feed-forward artificial neural networks have been used for the modeling of the shear strength of reinforced concrete beams. The obtained results show that ANNs can be successfully applied to predict the value of the shear strength of reinforced concrete beams with or without transversal reinforcement (stirrups). Furthermore, the preliminary results presented in this work are clearly shown that the proposed shear strength can be estimated using only four parameters. Namely, the most crucial parameters are i) the product of the longitudinal reinforcement and the associated reinforcement ratio, ii) the product of the transversal reinforcement and the associated reinforcement ratio, iii) the shear span to the effective depth ratio of beam (a/d), iv) the effective span to the effective depth ratio of beam (L/d) and v) the concrete compressive strength. 4. Conclusions

Acknowledgements

The authors would like to thank Dr. Andreas Stavridis, Professor at the Department of Civil, Structural and Environmental Engineering, University at Buffalo, NY, USA, and Dr. Ghassan K. Al-Chaar, Researcher at US Army Construction Engineering Research Lab, Des Plaines, USA, for their valuable contributions to the