Mechanical safety assessment for reinforced concrete columns based on ultimate limit surfaces

It is proposed to assess the mechanical safety of key structural elements under accidental conditions using an ultimate limit surface formed by the joint consideration of local strength criteria for each type of ultimate internal force, without analyzing a single critical cross-section. Such a surface is constructed for vertical loadbearing elements (columns and pylons) of rectangular cross-section subjected to combined loading. Specifically, cases of eccentric compression with bending moments in the two principal planes are con-sidered, as well as the combined action of axial compressive force, bending moment, and torque induced by the specific features of load application. The calculations are performed in a dynamic formulation accounting for both physical and geometric nonlinearities. A plasticity-based damage model is adopted for concrete, while an elastoplastic model with a bilinear stress–strain diagram and no hardening are used for the reinforcement. The dynamic additional loading is modeled by an impulsive load, the magnitude and duration of which are determined approximately based on the law of conservation of momentum. Such a load simulates an accidental action, for example, the impact of a falling body on a deformable slab at the joint interface with the element. Based on the constructed dynamic ultimate limit surface, an assessment of mechanical safety is performed, which includes not only ensuring the absence of total failure but also accounting for the risk of material losses under various accidental scenarios. Practical aspects of the assessment and the risk calculation algorithm are demonstrated using examples of elements made of normal-weight concrete reinforced with welded frames.

1. Lu X., Zhang L., Lin K., Li Y. Improvement to composite frame systems for seismic and progressive collapse resistance. Engineering Structures. 2019. Vol. 186. Pp. 227–242. DOI: 10.1016/J.ENGSTRUCT.2019.02.006.

2. Kiakojouri F., De Biagi V., Chiaia B., Sheidaii M.R. Strengthening and retrofitting techniques to mitigate progressive collapse: A critical review and future research agenda. Engineering Structures. 2022. Vol. 262. DOI: 10.1016/j.engstruct.2022.114274. EDN: NAXIZX

3. Tamrazyan A., Alekseytsev A. Evolutionary optimization of reinforced concrete beams, taking into account design reliability, safety and risks during the emergency loss of supports. E3S Web of Conferences. Vol. 97. 2019. DOI: 10.1051/e3sconf/20199704005. EDN: IYKSXO

4. Alekseytsev A.V. Mechanical safety of reinforced concrete frames under complex emergency actions. Magazine of Civil Engineering. 2021. Vol. 103. DOI: 10.34910/MCE.103.6. EDN: ILMMNH

5. Hassanzadeh A., Gholizadeh S. Collapse-performance-aided design optimization of steel concentrically braced frames. Engineering Structures. 2019. Vol. 197. Article no. 109411. DOI: 10.1016/j.engstruct.2019.109411

6. Jaiswal D.K., Murty C.V.R. Lateral deformation capacity of cantilever RC hollow columns using physics- based concrete confinement model. Structures. 2025. Vol. 75. Article no. 108662. DOI: 10.1016/J.ISTRUC.2025.108662. EDN: EKJANA

7. Serpik I., Alekseytsev A. Optimization of steel frame building systems in terms of parameters and reliability requirements. IOP Conf. Series: Materials Science and Engineering. Vol. 365. 2018. DOI: 10.1088/1757-899X/365/5/052003. EDN: VBIPJF

8. Alekseytsev A.V., Kurchenko N.S., Mohamad A.A. Risk-Based Optimization of RC Beams Under Different Local Damage Scenarios. Advances in Transdisciplinary Engineering. Vol. 43. 2023. DOI: 10.3233/ATDE230697.

9. Lin K., Zheng J., Wu Z., Lu X., Li Y. Risk-based life cycle cost–benefit analysis for progressive collapse design of RC frame structures. Structures. 2024. Vol. 63. Article no. 106468. DOI: 10.1016/J.ISTRUC.2024.106468. EDN: SFPNJF

10. Jiang L., Ye J. Risk-based overall seismic robustness assessment of cold-formed steel structures considering vulnerability and fragility. Bulletin of Earthquake Engineering. 2022. Vol. 20. DOI: 10.1007/s10518-022-01435-7. EDN: IYCBIO

11. Klueva N., Emelyanov S., Kolchunov V., Gubanova M. Criterion of Crack Resistance of Corrosion Damaged Concrete in Plane Stress State. Procedia Engineering. 2015. Vol. 117. Pp. 179–185. DOI: 10.1016/J.PROENG.2015.08.144. EDN: UZYOAB

12. Chen Y., He Q., Chen Z., Liang X. Bending restoring force model of angle-steel reinforced concrete columns under combined torsion. Structures. 2023. Vol. 55. Pp. 2186–2198. DOI: 10.1016/J.ISTRUC.2023.07.008. EDN: NMRBLT

13. Kolchunov V.I., Moskovtseva V.S. Robustness of reinforced concrete frames with elements experiencing bending with torsion. Engineering Structures. 2024. Vol. 314. Article no. 118309. DOI: 10.1016/J.ENGSTRUCT.2024.118309. EDN: PNBEQJ

14. Savin S.Y., Kolchunov V.I. Dynamic behavior of reinforced concrete column under accidental impact. International Journal for Computational Civil and Structural Engineering. 2021. Vol. 17. No. 3. Pp. 120–131. DOI: 10.22337/2587-9618-2021-17-3-120-131. EDN: PMDHWD

15. Alekseytsev A. Local Fracture of a Reinforced Concrete Beam Under High-Velocity Impact on Biaxial Bending and Torsion Deformation. Buildings. 2025. Vol. 15. DOI: 10.3390/buildings15224153. EDN: UMRASV