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Fire safety of Reinforced Concrete (RC) columns is an important design aspect to ensure the overall integrity of structures during fire events. Currently, fire ratings of RC sections are achieved using prescriptive methods. As new codes are moving towards performance based design, practitioners are in need of rational design tools to assess the capacity of heated sections. To construct the axial force-moment interaction diagram of a RC section using existing numerical methods, high computation demand and knowledge of heat transfer and stress analysis are required. This paper presents the derivation of a set of formulas that can be used to estimate the average temperature distribution within the concrete section and the corresponding internal forces. The utilization of these formulas to construct interaction diagrams of fire-exposed RC sections is then explained. The proposed formulas are validated by comparing their predictions with experimental and analytical results by others.