Prediction of Shear Capacity of RC Deep Beams Via a Soft Computing Method

Document Type : Original Article

Authors

1 Department of Civil Engineering, Faculty of Engineering, University of Qom, Qom, Iran

2 Department of Civil Engineering, Qom Branch, Islamic Azad University, Qom, Iran

Abstract

It is well known that the shear capacity of RC deep beams is affected by many mechanical and geometric parameters. The accurate prediction of the shear capacity still stands out as one of the major stumbling blocks in structural engineering practice. Traditional prediction methods have often proven less than precise. On the other hand, artificial intelligence-based methods, particularly those represented by SVMs, have presented themselves as a promising alternative. This research employed an enhanced machine learning technique, known as WLS-SVM, to estimate the shear capacity of reinforced concrete deep beams. In assembling a comprehensive dataset, 214 experimental results are obtained from the literature. From selected inputs and outputs, under the supervision of a teaching-learning type approach, a predictive model is derived via WLS-SVM. This model is compared with other AI-based methods and codified design procedures. It presented the best accuracy, with major statistical indicators, including an R² of 0.9804, showing the superiority of the WLS-SVM approach when compared to other methods. Therefore, the study's results reveal WLS-SVM as a very accurate and viable option for the structural calculation and design of reinforced concrete deep beams.

Keywords

Main Subjects


  1. Cakir, F., Acar, V., Aydin, M. R. Experimental and numerical assessment of intraply hybrid composites strengthened RC deep beams. Mechanics of Advanced Materials and Structures, 2025; 1-24. doi:10.1080/15376494.2025.2476208.
  2. Fathalla, E., Mihaylov, B. Shear behaviour of deep beams strengthened with high-strength fiber reinforced concrete jackets. Engineering Structures, 2025; 325: 119404. doi:10.1016/j.engstruct.2024.119404.
  3. Liu, C., Xu, D., Duanmu, X. Analysis of shear strength influencing factors in reinforced concrete deep beams: A modified calculating model. Journal of Building Engineering, 2024; 95: 110243. doi:10.1016/j.jobe.2024.110243.
  4. Tamimi, M. F., Alshannaq, A. A., Abu Qamar, M. a. I. Enhancing reliability in reinforced concrete deep beams through probabilistic analysis and topology optimized strut-and-tie models. Structures, 2024; 70: 107872. doi:10.1016/j.istruc.2024.107872.
  5. Prayoonwet, W., Koshimizu, R., Ozaki, M., Sato, Y., Jirawattanasomkul, T., Yodsudjai, W. Shear strength prediction for RC beams without shear reinforcement by neural network incorporated with mechanical interpretations. Engineering Structures, 2024; 298: 117065. doi:10.1016/j.engstruct.2023.117065.
  6. AlHamaydeh, M., Markou, G., Bakas, N., Papadrakakis, M. AI-based shear capacity of FRP-reinforced concrete deep beams without stirrups. Engineering Structures, 2022; 264: 114441. doi:10.1016/j.engstruct.2022.114441.
  7. Zhang, G., Ali, Z. H., Aldlemy, M. S., Mussa, M. H., Salih, S. Q., Hameed, M. M., Al-Khafaji, Z. S., Yaseen, Z. M. Reinforced concrete deep beam shear strength capacity modelling using an integrative bio-inspired algorithm with an artificial intelligence model. Engineering with Computers, 2022; 38: 15-28. doi:10.1007/s00366-020-01137-1.
  8. Baghdadi, A., Babovic, N., Kloft, H. Fuzzy Logic, Neural Network, and Adaptive Neuro-Fuzzy Inference System in Delegation of Standard Concrete Beam Calculations. Buildings, 2023; 14: 15. doi:10.3390/buildings14010015.
  9. Feng, D.-C., Wang, W.-J., Mangalathu, S., Hu, G., Wu, T. Implementing ensemble learning methods to predict the shear strength of RC deep beams with/without web reinforcements. Engineering Structures, 2021; 235: 111979. doi:10.1016/j.engstruct.2021.111979.
  10. Chou, J.-S., Pham, A.-D. Enhanced artificial intelligence for ensemble approach to predicting high performance concrete compressive strength. Construction and Building Materials, 2013; 49: 554-563. doi:10.1016/j.conbuildmat.2013.08.078.
  11. Kaloop, M. R., Roy, B., Chaurasia, K., Kim, S.-M., Jang, H.-M., Hu, J.-W., Abdelwahed, B. S. Shear strength estimation of reinforced concrete deep beams using a novel hybrid metaheuristic optimized SVR models. Sustainability, 2022; 14: 5238. doi:10.3390/su14095238.
  12. Vapnik, V. N. The Nature of Statistical Learning Theory. 2nd ed. New York (NY): Springer International Publishing; 1999. doi:10.1007/978-1-4757-3264-1.
  13. Megahed, K. Prediction and reliability analysis of shear strength of RC deep beams. Scientific Reports, 2024; 14: 14590. doi:10.1038/s41598-024-64386-w.
  14. Chen, R., Zhang, P., Wu, H., Wang, Z., Zhong, Z. Prediction of shield tunneling-induced ground settlement using machine learning techniques. Frontiers of Structural and Civil Engineering, 2019; 13: 1363-1378. doi:10.1007/s11709-019-0561-3.
  15. Liu, Z., Wu, D., Liu, Y., Han, Z., Lun, L., Gao, J., Jin, G., Cao, G. Accuracy analyses and model comparison of machine learning adopted in building energy consumption prediction. Energy Exploration & Exploitation, 2019; 37: 1426-1451. doi:10.1177/0144598718822400.
  16. Acar, E., Rais-Rohani, M. Ensemble of metamodels with optimized weight factors. Structural and Multidisciplinary Optimization, 2009; 37: 279-294. doi:10.1007/s00158-008-0230-y.
  17. Chou, J.-S., Yang, K.-H., Lin, J.-Y. Peak shear strength of discrete fiber-reinforced soils computed by machine learning and metaensemble methods. Journal of Computing in Civil Engineering, 2016; 30: 04016036. doi:10.1061/(ASCE)CP.1943-5487.0000595.
  18. Hoang, N.-D., Tran, X.-L., Nguyen, H. Predicting ultimate bond strength of corroded reinforcement and surrounding concrete using a metaheuristic optimized least squares support vector regression model. Neural Computing and Applications, 2020; 32: 7289-7309. doi:10.1007/s00521-019-04258-x.
  19. Luo, H., Paal, S. G. Metaheuristic least squares support vector machine-based lateral strength modelling of reinforced concrete columns subjected to earthquake loads. Structures, 2021; 33: 748-758. doi:10.1016/j.istruc.2021.04.048.
  20. Gharehbaghi, S., Yazdani, H., Khatibinia, M. Estimating inelastic seismic response of reinforced concrete frame structures using a wavelet support vector machine and an artificial neural network. Neural Computing and Applications, 2020; 32: 2975-2988. doi:10.1007/s00521-019-04075-2.
  21. Luo, H., Paal, S. G. A novel outlier-insensitive local support vector machine for robust data-driven forecasting in engineering. Engineering with Computers, 2023; 39: 3671-3689. doi:10.1007/s00366-022-01781-9.
  22. Prayogo, D., Cheng, M.-Y., Wu, Y.-W., Tran, D.-H. Combining machine learning models via adaptive ensemble weighting for prediction of shear capacity of reinforced-concrete deep beams. Engineering with Computers, 2020; 36: 1135-1153. doi:10.1007/s00366-019-00753-w.
  23. American Concrete Institute (ACI). ACI 318-25: Building Code for Structural Concrete—Code Requirements and Commentary. Farmington Hills (MI): ACI; 2025.
  24. Canadian Standards Association (CSA). CSA A23.3:19: Design of Concrete Structures. Longueuil (QC): CSA; 2019.
  25. Clark, A. P. Diagonal Tension in Reinforced Concrete Beams. ACI Journal Proceedings, 1951; 48: 145-156. doi:10.14359/11876.
  26. Kong, F.-K., Robins, P. J., Cole, D. F. Web Reinforcement Effects on Deep Beams. ACI Journal Proceedings, 1970; 67: 1010-1018. doi:10.14359/7336.
  27. Smith, K. N., Vantsiotis, A. S. Shear Strength of Deep Beams. ACI Journal Proceedings, 1982; 79: 201-213.
  28. Anderson, N. S., Ramirez, J. A. Detailing of Stirrup Reinforcement. ACI Structural Journal, 1989; 86: 507-515. doi:10.14359/3005.
  29. Tan, K.-H., Kong, F.-K., Teng, S., Guan, L. High-Strength Concrete Deep Beams With Effective Span and Shear Span Variations. ACI Structural Journal, 1995; 92: 395-405. doi:10.14359/991.
  30. Oh, J.-K., Shin, S.-W. Shear Strength of Reinforced High-Strength Concrete Deep Beams. ACI Structural Journal, 2001; 98: 164-173. doi:10.14359/10184.
  31. Aguilar, G., Matamoros, A. B., Parra-Montesinos, G. J., Ramírez, J. A., Wight, J. K. Experimental Evaluation of Design Procedures for Shear Strength of Deep Reinforced Concrete Beams. ACI Structural Journal, 2002; 99: 539-548. doi:10.14359/12123.
  32. Quintero-Febres, C. G., Parra-Montesinos, G., Wight, J. K. Strength of Struts in Deep Concrete Members Designed Using Strut-and-Tie Method. ACI Structural Journal, 2006; 103: 577-586. doi:10.14359/16434.
  33. Suykens, J. A. K., De Brabanter, J., Lukas, L., Vandewalle, J. Weighted least squares support vector machines: robustness and sparse approximation. Neurocomputing, 2002; 48: 85-105. doi:10.1016/S0925-2312(01)00644-0.
  34. Li, H.-s., Lü, Z.-z., Yue, Z.-f. Support vector machine for structural reliability analysis. Applied Mathematics and Mechanics, 2006; 27: 1295-1303. doi:10.1007/s10483-006-1001-z.
  35. Widodo, A., Yang, B.-S. Wavelet support vector machine for induction machine fault diagnosis based on transient current signal. Expert Systems with Applications, 2008; 35: 307-316. doi:10.1016/j.eswa.2007.06.018.
  36. Faris, H., Hassonah, M. A., Al-Zoubi, A. M., Mirjalili, S., Aljarah, I. A multi-verse optimizer approach for feature selection and optimizing SVM parameters based on a robust system architecture. Neural Computing and Applications, 2018; 30: 2355-2369. doi:10.1007/s00521-016-2818-2.
  37. Hoang, N.-D., Pham, A.-D. Hybrid artificial intelligence approach based on metaheuristic and machine learning for slope stability assessment: A multinational data analysis. Expert Systems with Applications, 2016; 46: 60-68. doi:10.1016/j.eswa.2015.10.020.
  38. Cheng, M.-Y., Prayogo, D., Wu, Y.-W. Prediction of permanent deformation in asphalt pavements using a novel symbiotic organisms search–least squares support vector regression. Neural Computing and Applications, 2019; 31: 6261-6273. doi:10.1007/s00521-018-3426-0.
  39. Prayogo, H. Prediction of Concrete Compressive Strength from Early Age Test Result Using an Advanced Metaheuristic-Based Machine Learning Technique. In: Proceedings of the 34th International Symposium on Automation and Robotics in Construction (ISARC); 2017 July 1-3; Taipei, Taiwan. p. 856-863. doi:10.22260/ISARC2017/0120.
Volume 2, Issue 1
January 2026
Pages 1-11
  • Receive Date: 23 August 2025
  • Revise Date: 12 September 2025
  • Accept Date: 18 September 2025
  • First Publish Date: 19 September 2025