Fixed cracked membrane model considering crack rotation–fixation hybrid modes and refined biaxial tension stiffening model for the analysis of shear panels

Abstract The rotation‐fixation hybrid mode of smeared cracks is closely related to the behavior of reinforced concrete (RC) panels under in‐plane stresses. To address model limitations in prevailing models, this paper proposes a refined fixed cracked membrane model (RF‐CMM) based on the framework of existing cracked membrane model (CMM). In the developed RF‐CMM, equilibrium is established at the crack, and the crack coordinate system is updated based on re‐cracking phenomena assessments. Strain decomposition formulations are introduced for crack rotation‐fixation hybrid modes. Subsequently, a refined tension stiffening model (TSM) with fewer mechanical simplifications is developed for rebars. Differences between the TSM and existing tension chord model (TCM) are evaluated. The TSM is then extended to biaxial conditions, and a corresponding diagonal crack spacing calculation method is formulated. For concrete behaviors at the crack, three aggregate interlock models are reported and discussed, leading to a recommended model. The concrete crack bridging effect at the crack is also considered. Re‐cracking criteria and methods for updating the crack coordinate system are then proposed. Finally, the numerical algorithm of the RF‐CMM is developed through a Python script. The proposed RF‐CMM is validated using a database of 195 RC panel tests and compared with existing models. The RF‐CMM demonstrates higher accuracy and lower scatter than existing models. For panels with significant crack rotation–fixation hybrid behaviors, for example, unidirectionally reinforced panels subjected to tension and shear stresses, the RF‐CMM can accurately predict the panel behavior, while fixed crack models tend to overestimate its strength by 30%–50%. Additionally, the concrete crack bridging effect can effectively mitigate crack rotational behavior and enhance corresponding panel strength. The impact of different crack kinematic paths on the panel behavior is minimal and is recommended to disregard this discrepancy. Overall, the proposed RF‐CMM can be utilized in the shear analysis of panels with significant crack rotation–fixation hybrid behaviors (e.g., non‐proportional loading panel) and can be further extended to FRC or UHPFRC panels, with limited complex panel experimental research required.