Machine learning models for cracking torque and pre-cracking stiffness of RC beams

• Published in: Archives of Civil and Mechanical Engineering 2022-10, Vol.23 (1), p.6, Article 6
• Main Authors: Shenggang, Chen, Quanquan, Guo, Yingying, Zhang, Hexiang, Hu, Bei, Shen
• Format: Article
• Language: English
• Subjects: Algorithms; Artificial neural networks; Bending theory; Civil Engineering; Compressive properties; Compressive strength; Concrete; Cross-sections; Decision trees; Design parameters; Engineering; Hollow sections; Machine learning; Mathematical models; Mechanical Engineering; Modulus of elasticity; Neural networks; Original Article; Performance prediction; Precracking; Root-mean-square errors; Shear strength; Stiffness; Structural Materials; Torque; Torsion; Variables
• ISSN: 1644-9665; 2083-3318; 1644-9665
• DOI: 10.1007/s43452-022-00541-2

The torsional behavior of RC beams is a complex work involving interactions of different design parameters and mechanisms. Considering the limitations and lower accuracy of traditional calculation theories, two machine learning models, including artificial neural network (ANN) model and random forest (RF) model, were applied for the first time to predict the cracking torque and initial or pre-cracking torsional stiffness of RC beams. A comprehensive database consisting 159 experimental results of RC beams with solid or hollow sections was compiled, with input variables including dimension parameters of cross-section, compressive stress of concrete, elastic modulus and strength ratio of reinforcements. The performance of the models was appraised by various statistical estimators and safety ratio, and compared with different theories for cracking torque and initial stiffness. Among all the calculation models, RF model achieved the best overall prediction performance with the highest coefficient of determination ( R 2  = 0.985 for cracking torque and R 2  = 0.978 for initial stiffness) and lowest root-mean-square error (RMSE = 5.867 for cracking torque and RMSE = 3.994 for initial stiffness). However, theories for cracking torque, i.e., plastic theory, Bredt thin-tube theory and skew-bending theory, gave huge underestimation, whereas greatly exaggerated initial stiffness was obtained by elastic theory and simplified soften membrane model for torsion theory. Besides, input variable importance analysis was conducted, revealing that dimension parameters of cross-section were the most critical features to decide prediction performance for pre-cracking torsional performance of RC beams. The achievements of this paper may provide references to the establishment of new predicting model for pre-cracking torsional response of RC beams.