Theoretical Prediction Model for the Cracking Moment of RC Beams with Openings Based on the Plane Section Assumption

Accurate prediction of the cracking moment in RC beams with openings is crucial for structural safety assessment. This study systematically establishes, for the first time, theoretical prediction models for the cracking moment of six categories of beams with openings and their corresponding applicability criteria. The reliability of the models was validated via ABAQUS finite element analysis, comparing GB 50010-2010 and ACI 318-19 codes. The results indicate that the theoretical model predictions align well with numerical simulation results, exhibiting low dispersion (central openings: Mean = 0.9903, CV = 0.0295; eccentric openings: Mean = 1.0078, CV = 0.032). Model predictions also show high consistency with calculations from the GB 50010-2010 code formulas (central openings: Mean = 1.0157, CV = 0.0471; eccentric openings: Mean = 1.0026, CV = 0.0563). However, agreement with ACI 318-19 code formula calculations is lower and dispersion is greater (central openings: Mean = 1.1858, CV = 0.1068; eccentric openings: Mean = 1.174, CV = 0.1009), primarily attributable to the conservative nature of the ACI 318-19 code. The study reveals that the theoretical models for the cracking moment of beams with central and eccentric openings are not unique and dynamically switch based on changes in material parameters and opening parameters. For beams with central openings, the opening ratio threshold was identified as 30%, and a maximum opening ratio not exceeding 48% is recommended. For beams with eccentric openings, the optimal eccentricity for different opening ratios was determined to be 8%. This research provides a theoretical basis and technical support for the universal prediction of cracking performance in beams with openings.