Interdisciplinary Journal of Civil Engineering

Interdisciplinary Journal of Civil Engineering

Prediction of the Backbone Curve for Bolted Extended Endplate Moment Connections Using Machine Learning Methods

Document Type : Original Article

Authors
Matin Alizadeh
Mahmoud Reza Shiravand
Amir Saedi Daryan
Faculty of Civil, Water and Environmental Engineering, Shahid Beheshti University, Tehran, Iran
10.48308/ijce.2026.246372.1029
Abstract
This study develops an interpretable artificial intelligence framework for predicting the nonlinear behavior and backbone curve of Bolted Extended End-Plate (BEEP) connections under seismic loading. An analytical-developmental approach based on machine learning was adopted, using an enriched database of BEEP connections to establish relationships between connection parameters and nonlinear moment–rotation responses. Several machine-learning algorithms were investigated, with particular emphasis on ensemble-learning methods, including Random Forest, Extreme Gradient Boosting (XGBoost), and Light Gradient Boosting Machine (LightGBM). The developed models were evaluated using standard statistical performance metrics, including the coefficient of determination (R²), RMSE, and MAE. The results demonstrate that the developed ensemble-learning models achieved high predictive accuracy on unseen test data, with R² values of 0.95 or higher. This indicates that the proposed models can effectively capture the nonlinear characteristics of BEEP connection behavior and accurately reproduce their moment–rotation backbone curves. Furthermore, interpretability techniques were employed to quantify the contribution and relative importance of input variables to the predicted response. The analysis identified the governing connection parameters influencing nonlinear behavior, providing valuable insight into the mechanics of BEEP connections. Overall, the proposed framework provides an accurate, interpretable, and practical data-driven methodology for backbone-curve prediction and seismic performance assessment of BEEP connections.
Keywords
Bolted Endplate Moment Connection
Machine Learning
Ensemble Learning
Backbone Curve
Non-Linear Behavior
Adey, B. T., Grondin, G. Y., & Cheng, J. J. R. (1997). Extended end plate moment connections under cyclic loading (Structural Engineering Report No. 216). Department of Civil and Environmental Engineering, University of Alberta.
Adey, B. T., Grondin, G. Y., & Cheng, J. J. R. (2000). Cyclic loading of end plate moment connections. Canadian Journal of Civil Engineering, 27(4), 683–701.
Astaneh-Asl, A. (1995). Seismic design of bolted steel moment-resisting frames (Steel Tips). Structural Steel Education Council.
Agerskov, H. (1977). Analysis of bolted connections subject to prying. Journal of the Structural Division, 103(11), 2145–2163.
American Institute of Steel Construction. (2022). Specification for structural steel buildings (ANSI/AISC 360-16). American Institute of Steel Construction.
European Committee for Standardization. (2005). Eurocode 3: Design of steel structures—Part 1-8: Design of joints (EN 1993-1-8). European Committee for Standardization.
Sumner, E. A., & Murray, T. M. (2002). Behavior of extended end-plate moment connections subject to cyclic loading. Journal of Structural Engineering, 128(4), 501–508.
Sumner, E. A., III. (2003). Unified design of extended end-plate moment connections subject to cyclic loading [Doctoral dissertation, Virginia Polytechnic Institute and State University].
Guo, B., Gu, Q., & Liu, F. (2006). Experimental behavior of stiffened and unstiffened end-plate connections under cyclic loading. Journal of Structural Engineering, 132(9), 1352–1357.
Ghobarah, A., Korol, R. M., & Osman, A. (1992). Cyclic behavior of extended end-plate joints. Journal of Structural Engineering, 118(5), 1333–1353.
Shi, G., Shi, Y., Wang, Y., & Bijlaard, F. S. K. (2010). Monotonic loading tests on semi-rigid end-plate connections with welded I-shaped columns and beams. Advances in Structural Engineering, 13(2), 215–229.
American Society of Civil Engineers. (2017). Seismic evaluation and retrofit of existing buildings. American Society of Civil Engineers.
Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Blondel, M., Prettenhofer, P., Weiss, R., Dubourg, V., Vanderplas, J., Passos, A., Cournapeau, D., Brucher, M., Perrot, M., & Duchesnay, É. (2011). Scikit-learn: Machine learning in Python. Journal of Machine Learning Research, 12, 2825–2830.
Mohammadnia, M., & Moradi, S. (2022). Artificial neural network–based predictive tool for modeling of self-centering endplate connections with SMA bolts. Journal of Structural Engineering, 148(12), 04022198.
Horton, T. A., Hajirasouliha, I., Davison, B., & Ozdemir, Z. (2021). Accurate prediction of cyclic hysteresis behaviour of RBS connections using deep learning neural networks. Engineering Structures, 247, 113156.
Shah, S. N. R., Sulong, N. H. R., & El-Shafie, A. (2018). New approach for developing soft computational prediction models for moment and rotation of boltless steel connections. Thin-Walled Structures, 133, 206–215.
Wang, K., et al. (2025). Experimental and numerical research on hysteretic behavior of bolted end-plate connections. Structures, 108397.
Stavroulakis, G. E., Avdelas, A. V., Abdalla, K. M., & Panagiotopoulos, P. D. (1997). A neural network approach to the modelling, calculation and identification of semi-rigid connections in steel structures. Journal of Constructional Steel Research, 44(1–2), 91–105.
Interdisciplinary Journal of Civil Engineering
Volume 2, Issue 2 - Serial Number 6
Spring 2026
Pages 159-184