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This chapter addresses design fires in the context of structural fire safety. First, the design fuel load must be derived for the given space, which represents the potential energy that needs to be considered. Once the design fuel load is established, estimation of the fire exposure intensity on the structure is a key next step in the process. Specifically, thermal boundary conditions acting on structural and/or insulative exposed boundaries must be derived so that subsequent heat transfer analyses may be conducted to determine the temperature histories of the given structural system. Structural fire engineering designs typically only consider a subset of design fires, which are those that are uncontrolled (any cooling effects of active fire protection systems and/or manual intervention are neglected). Other design fires (e.g. those used for determining the available safe escape time) would not commonly be used for SFE applications. Accordingly, fire dynamics concepts pertaining to uncontrolled fire exposures are presented in this chapter.

The structural fire engineering community has demonstrated a growing interest in probabilistic methods in recent years. The trend towards consideration of probability is, amongst others, driven by an understanding that further advances in detailed numerical models are potentially offset by the basic uncertainty in the input parameters. Consequently, there has been a call for the development of fragility curves for fire-exposed structural elements, to support the application of probabilistic methods both in design as well as in standardization. State-of-the-art structural fire engineering models are, however, commonly very computationally expensive, even for simple cases such as isolated structural elements. This can be attributed to the requirement of coupling thermal and mechanical analyses, and to the large non-linearity in both the heating of structural elements and the resulting mechanical effects of temperature-induced degradation and strains. This severely hinders the development of fragility curves beyond very specific cases, especially when including a stochastic description of the (natural) fire exposure. In the current contribution the application of regression techniques to structural fire engineering modeling is explored, as a stepping stone towards establishing a methodology for the efficient development of fragility curves for fire-exposed structural members. A simplified model with limited computational expense is applied to allow for validation of the proof-of-concept.

To demonstrate adequate structural fire safety for exceptional designs, the uncertainties of the design input parameters must be explicitly considered. In this contribution, the case study included in ISO/CD TR 24679-8:2020 of a concrete column subject to a standardized heating regime is revisited considering improved uncertainty modelling for the input parameters. Monte Carlo simulations are applied to obtain the distribution of the axial load bearing capacity of the column, \({P}_{\max}\), at 240 min of ISO 834 standard fire exposure. The obtained distribution however does not fit any distribution type commonly assumed for the resistance effect. To get more detailed information on the parameters governing the distribution of \({P}_{\max}\), and to allow for the application of more efficient calculation procedures and the development of design guidance, a detailed analysis of the obtained distribution for the load bearing capacity is conducted. The effect of each of the input parameters’ uncertainty on the column capacity is quantified using three different methods of sensitivity analysis. Furthermore the distribution type describing the concrete load bearing capacity for the considered standard fire exposure is evaluated in detail. It is concluded that the parameter defining the quantile of the concrete strength retention is the main contributor to the variability of the column capacity at 240 min standard fire exposure. Furthermore, it is found that the column capacity can be described by a mixed lognormal distribution, considering constituent lognormal distributions for fixed concrete strength retention parameter values. Based on these findings, improvements for probability of failure calculations of fire-exposed concrete columns are developed. The analysis provides insight for the reliability-based design of concrete columns exposed to fire, achieving a specified target safety level.

Structural fire safety requirements implicitly balance up-front investments in materials (protection or element sizing) with improved performance (loss reductions) in the unlikely event of a fire. For traditional prescriptive fire safety recommendations, the underlying target safety levels are not clear to the designer, nor is the associated balancing of risk and investment costs. While easy to apply, guidance / code-based approaches to the specification of fire protection / resistance have the severe disadvantage that the level of safety investment is not tailored to the specifics of the case, resulting in large overinvestments in some cases, and possibly insufficient structural fire safety in others. This observation is a major driver for the use of performance-based design (PBD) methodologies, where the fire safety design is tailored to the needs of the building. However, it is posited in this chapter that traditional PBD in a structural fire context is deterministic, with the safety foundation premised upon the collective experience of the profession. It is separately noted that building forms are increasingly uncommon in nature, due to material choice, height, failure consequences, etc., and, as such, collective experience is increasingly a weak safety foundation. This is where probabilistic methods add value and provide a quantified / explicit basis for demonstrating the adequacy of a design. This chapter, thus, focusses on uncertainties and uncertainty quantification in the context of structural performance in the event of fire, introducing reliability and risk concepts, with supporting data and applications.

Concrete columns exhibit a loss of both strength and stiffness during fire. The current contribution focusses on the fire performance of concrete columns subjected to biaxial bending in combination with axial loads, as such information is rarely available in literature. First, the second-order effects are quantified using a numerical tool. In Eurocode 2, the most important parameters which influence second-order effects of columns during fire are the slenderness ratio, fire duration as well as the magnitude of the axial loading. The influences of these parameters are investigated using a parametric study. Additionally, from the viewpoint of fire safety and structural reliability, uncertainties should be incorporated in the second-order analysis in order to achieve reliability-based design guidelines. Hence, the numerical tool is further developed in order to take into account uncertainties. Furthermore, the tool is validated using the Eurocode provisions and existing experimental data, while considering an ISO 834 standard fire. Finally, examples are given for the fire resistance design of concrete columns.