Closed-Form Prediction of the Thermal and Structural Response of a Perimeter Column in a Fire

Spencer E. Quiel1, *, Maria E.M. Garlock2
1 Hinman Consulting Engineers Alexandria, VA, USA
2 Department of Civil and Environmental Engineering, Princeton University, Princeton, NJ, USA

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© Quiel et al.;

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Hinman Consulting Engineers Alexandria, VA, USA. Tel: 703-416-6780; Fax: 703-836-4423; E-mail:;


This paper proposes a simplified closed-form methodology with which to predict the thermal and structural response of steel perimeter columns in high-rise building frames exposed to fire. Due to their orientation in the building compartment, perimeter columns are heated on three sides and will develop a thermal gradient through their crosssectional depth. Restraint of the thermal expansion associated with this gradient will cause these members to experience a combination of axial load (P) and bending moment (M), thus acting as beam-columns. At high temperatures, the thrudepth gradient will alter the plastic capacity and mechanical behavior of the perimeter column, leading to plastic P-M behavior that is not captured under the assumption of uniform cross-sectional temperature. Simplified methodologies are proposed to calculate the following: (1) the thru-depth temperature distribution that develops due to three-sided heating, (2) the gradient-induced changes in plastic capacity, and (3) the gradient-induced changes in demand (i.e. P and M). These methodologies are sufficiently simple for use in code-based design and can be implemented via a spreadsheet because they are closed-form. The individual results of each simple methodology as well as their combination are validated against the results of computational thermal and structural analysis, showing good agreement.