Performance Based Design is increasingly applied in structural fire engineering, sometimes entailing the use of deflection-based criteria to demonstrate adequate performance. Since no ...deflection-based design format currently exists which takes into account the many uncertainties associated with structural performance during fire, the attainment of an ‘adequate safety level’ is not necessarily ensured. Building on earlier studies, the feasibility of a deflection-based design format with a single global safety factor is explored for concrete floors exposed to fire. Considering the common assumption of lognormality for slab deflections, safety factors can be defined. The subsequent feasibility study however indicates that the assumption of a lognormal distribution is problematic in case of fire. A conceptual alternative to the global safety factor is explored, where the load on the slab is step-wise increased up to the point where a predefined deflection criterion is reached. This alternative approach seems promising, as it results in a known distribution type for the calculated maximum distributed load. Next steps for the development of this concept are identified.
In fire safety engineering, cost–benefit analysis provides a systematic method to assess whether the projected benefits from a fire safety measure outweigh its costs. However, there remains a wide ...discrepancy between methods used in the field for cost–benefit analysis, as well as a lack of quantitative data on the costs and economic impact of fire protection in buildings. In a recent research project, a reference methodology was proposed based on Present Net Value evaluation and on a combination of specialized construction database, fire statistics, and numerical modeling for estimation of the cost components. This paper presents the application of the methodology to four case studies. The case studies allow describing the methodology, the collection of data, fire statistics, and loss estimation, as well as illustrating how the methodology can support decision-making when multiple alternatives are compared. Under the assumptions adopted for the single-family house and the residential timber building case studies, it is found that for every 1$ invested in sprinklers, $1.06 is saved. This benefit–cost ratio increases with increasing valuation of indirect losses and statistical value of life. Sensitivity analyses are provided to explore the robustness of the investment recommendations. The results of evaluations, adapted from the presented case studies with project-specific inputs, can support decision making for policy makers, insurance companies, and individual building owners.
The post-fire assessment of concrete structures is a complex task that requires the integration of multiple measurements from different techniques. The current approach to integrate information from ...different sources relies mainly on expert judgement, meaning that no explicit consideration is given to the precision of different techniques. This paper presents a Bayesian updating methodology that integrates information from different sources about the maximum temperature the concrete experienced during fire exposure at a certain depth, such as discoloration and rebound hammer measurements, by considering the uncertainties and errors associated with measurements. The data is then used to update the prior information on the uncertain parameters of interest, here the fire load density and opening factor. These updated distributions provide a better estimate of the fire exposure, thermal and damage gradient and the residual condition of the structure. The proof-of-concept and effectiveness of the proposed methodology are demonstrated through a case study. The results show that the proposed methodology is able to effectively incorporate the uncertainties and errors associated with the assessment techniques, producing more reliable estimates of the fire severity. This method has the potential to improve the post-fire assessment process and provide more accurate information for the rehabilitation of concrete structures.
Fires can lead to costly building damage as well as loss of lives and injuries. Installed to protect buildings from fire, or to limit the damage from such outbreaks, fire protection measures are a ...common feature in buildings. However, these features come at a cost. Although quite ubiquitous in buildings, the value of these features to private individuals and to society is not fully understood. To understand their value, a cost benefit analysis detailing the costs and benefits of fire protection measures is needed. Carrying out such an analysis requires methods for computing both the cost of these fire protection measures, and losses from fires (including both direct and indirect losses). This study outlines methodologies for evaluating those costs and losses. An exhaustive collection of available data necessary for estimating both costs and losses is presented. Several limitations in current methodologies and data constraints were identified, with recommendations proposed to address these shortcomings. Relevant sections of a study by the authors that refines fire protection cost estimation at national and sub-national levels are emphasized, including updated building categories, guidance on computing multipliers, and detailed cost calculation methods for installation and maintenance costs. The calculation uses regularly updated U.S. Census Bureau construction data, ensuring timely multiplier updates. The insights and suggestions presented in this study will ultimately refine the process of selecting fire protection strategies that maximize the net benefit of fire protection measures for both private stakeholders and society at large.
For design situations in case of ambient temperature, both EN1992-1-1 and ACI318 provide guidelines for the design of columns, and for evaluating the structural capacity in case of biaxial bending. ...However, the effect of fire on these columns subjected to biaxial bending is not mentioned in the provisions. Hence, it is important to evaluate the mechanical behavior of columns in case of biaxial bending combined with fire and to provide guidelines for fire resistance design. In this paper, first a simplified method proposed by Bresler is presented for design under ambient temperature in order to predict the interaction curves of concrete columns subjected to biaxial bending and axial loading, based on a calculation of the uniaxial bending capacity. In order to verify whether this method can be adopted in case of fire, a cross-sectional calculation tool is introduced and validated with experimental data. Further, the results from the simplified method are compared with those obtained with the calculation tool. Subsequently, the simplified method is elaborated further in order to take into account the effect of an ISO 834 standard fire for a column loaded by a symmetrical biaxial load. Finally, the results of a parametric study are presented. Suggestions are given for implementing this method for design of relatively short concrete columns subjected to biaxial bending in case of an ISO 834 fire.
Uncommon structural fire engineering designs must demonstrate adequate safety, in principle, through a balancing of the uncertain future costs and benefits of safety investments. In structural design ...for normal load conditions (‘ambient design’) this level of detail is commonly avoided through the application of reliability targets. In order to inform the development of reliability targets for structural fire design, the background of the ambient reliability targets is discussed. It is found that different common ambient reliability targets are broadly comparable when taking into account differences in assumptions and applications. As recent reliability targets have been informed by simplified cost-optimizations, the derivation of such a model is presented. The derivation allows identification of possible pitfalls when extending ambient reliability targets to structural fire design. It is concluded that ambient safety targets cannot readily be scaled as a function of the fire occurrence rate for application to structural fire engineering problems. The underlying cost-optimization model is, however, applicable as a concept. A number of issues requiring further attention are identified.
Contemporary societal concerns emphasize the importance of cost optimization and sustainable constructions. However, with respect to structural fire safety, the application of prescriptive design ...rules remains common practice and optimization procedures are generally limited to a few examples of performance based design. Both methods consider an explicit or implicit prescribed safety level which is based on societal and empirical considerations. A more rational approach is to take into account the characteristics of the structure and to determine the economic optimum fire safety design. This economic optimum is obtained by minimizing the total costs, explicitly taking into account e.g. the fire ignition frequency, the probability of successful fire suppression and the damage costs due to a fire-induced failure. Applying this methodology to the design of simply supported concrete slabs indicates that in specific situations additional investments beyond the legally required minima constitute a more cost-effective design. It is concluded that the cost optimization of structural fire safety is a powerful tool to assess the utility of additional safety investments beyond the legal requirements.
Previous research has investigated and developed systematic probabilistic models for parameters involved in determining the reliability of a structure under fire. The established models have been ...summarized and applied in this paper to quantify and compare the reliability of steel columns that are protected based upon the US prescriptive approach. A set of columns with a range of section factors are selected to study the influence of demand to capacity utilization ratio, dead to live load ratio, restraint conditions, thermal properties of insulation, and fuel load density on the probability of failure under fire. The results show a relatively large variation in the value of probability of failure for columns with similar fire protection rating but different section factors and utilization ratio. The probability of failure is sensitive to the thermal properties of insulating material, while only limited information is available on the behaviour of such properties as a function of temperature. The influence of fuel load density is presented in the form of fragility functions, where the probabilities of failure for deterministic fuel load density values are discussed. Results suggest that further harmonization of safety levels can be achieved provided reliability-based quantifications are introduced in the design process, and the fire protection design considers specifics of a design such as the applied load and slenderness ratio.
Abstract
Many theoretical methods for evaluating robustness have been developed in the last decades. Especially probability‐based robustness quantification promises to provide a rational basis for ...decision‐making. To allow for this type of robustness evaluation, the probability of failure (or the corresponding reliability index) of the structural system in the damaged and the undamaged state has to be determined. In this paper, the Probability Density Evolution Method (PDEM) is used to evaluate the dynamic reliability, taking into account the randomness which comes both from the excitation and from the stochastic system properties. The efficiency of the PDEM for robustness quantification is evaluated through a simple cargo crane example case. In addition, the instant equivalent extreme‐value event, which is quite different from the equivalent extreme‐value event for one variable, is applied to obtain the extreme value of reaction forces for each sample at instant time.
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