Keywords: steel structure, structural fire design, size optimisation, cost optimisation, temperature surrogate, frame structure.

This paper presents a size optimisation approach for steel structures exposed to fire and designed according to EN 1993-1-2. The main focus is on unprotected steel members, for which the incremental computation of the steel temperature is replaced by an explicit continuous surrogate model. The surrogate is constructed from Eurocode-based heat-transfer calculations and fitted using an L_inf regression formulation. For a prescribed fire-resistance time, it maps the cross-section parameters directly to the steel temperature, thereby avoiding repeated incremental temperature calculations during optimisation while preserving differentiability of the fire-design constraints. The approach is implemented in MATLAB and applied to an elevated steel connecting corridor with a thirty-minute fire-resistance requirement. Three design variants are considered: an ambient-temperature design, an unprotected fire design, and a protected fire design that includes the cost of passive fire protection. The resulting costs are compared and used to discuss the influence of fire-design requirements and passive protection on the optimal design.

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