Civil and Environmental Engineering Publications

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Fire Safety Journal



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Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.


With the recent shift towards performance-based fire design, practical methods to account for natural fire loading when designing concrete structures are needed. Available design methods and analysis approaches are based on standard fire curves. To apply these methods, a natural fire event can be converted to a standard fire with a specific duration (time equivalent). However, existing time equivalents often ignore the influence of internal temperature gradients on the section behaviour, which is unacceptable for concrete structures.

This paper introduces a time equivalent method suitable for reinforced concrete (RC) beams exposed to natural fire. The method is based on the actual temperature gradient within a concrete section. To simplify analysis of RC beams exposed to fire, an average internal temperature profile (AITP) can be utilized, which records the average temperature variation along the height of a section. Two equations are provided such that a standard fire duration can be determined to accurately or conservatively represent the AITP of a beam section exposed to natural fire. Characteristics of the natural fire, as well as the influence of section dimensions are accounted for. The developed AITP time equivalent method is found to be superior to the existing methods and accurate in approximating the moment-curvature response for RC beam sections.


This is an author-accepted manuscript. The final version published by Elsevier can be accessed at

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