Practical reliability-based calculation tool for the post-fire assessment of concrete beams

If a structure has been able to maintain stability during fire exposure, the residual load-bearing capacity of the structural elements after fire should be determined when deciding upon the further use of the structure. Since adequate safety is a primary requirement for all structures and since many uncertainties are associated with the post-fire assessment, only a reliability-based assessment can be acceptable for real-life applications. In this contribution an easy-to-use reliability-based tool is presented for the post-fire assessment of the load-bearing capacity of concrete beams

Derivation of practical reliability-based post-fire assessment tools for structural elements

A practical reliability-based post-fire assessment method has been presented in earlier work which evaluates the maximum allowable characteristic value of the imposed load effect on concrete elements after being subjected to fire. The method is known as the ReAssess method and can be extended to cover the post-fire assessment of other material types, structural members and limit states. This extension however requires knowledge of the methodology underlying the derivation of the basic equations. In this paper a detailed overview of this methodology is presented for the first time, incorporating all the steps from the definition of the limit state problem up to the verification of the reliability obtained when applying the method. The presented methodology allows for the development of practical reliability-based post-fire assessment tools to a broad range of structural members. An example derivation is given illustrating the application of the presented concepts to the post-fire bending limit state for a simply supported concrete slab

Efficient method for probabilistic fire safety engineering

A growing interest exists within the fire safety community for the topics of risk and reliability. However, due to the high computational requirements of most calculation models, traditional Monte Carlo methods are in general too time consuming for practical applications. In this paper a computationally very efficient methodology is for the first time applied to structural fire safety. The methodology allows estimating the probability density function which describes the uncertain response of the fire exposed structure or structural member, while requiring only a very limited number of model evaluations. The application of the method to structural fire safety is illustrated by two examples in the area of concrete elements exposed to fire

Brandveiligheid beton-elementen

Het uitwerken van een veiligheidsberekening voor betonnen platen en balken die aan buiging worden onderworpen, was de primaire doelstelling van een masterproef aan de Universiteit van Gent. In dit artikel volgt een uiteenzetting van het probleem, een samenvatting van het ontwikkelde rekenmodel en een bespreking van de voornaamste resultaten

Explorative study into a simplified numerical evaluation of the bending capacity of rebar reinforced steel fibre reinforced concrete beams during fire exposure

A simplified 2D numerical model for evaluating the bending capacity of rebar reinforced steel fibre reinforced concrete (R/SFRC) beams during fire is presented. Distinct material properties of steel fibre reinforced concrete (SFRC) and reinforcing steel bars are considered. The SFRC is treated as a homogeneous concrete “composite” which combines the advantages of the compression capacity of concrete and the tension capacity of fibre elements. Three steps are associated with the numerical model for evaluating the fire resistance of R/SFRC beams. Firstly, a fire temperature calculation. Secondly, thermal analysis evaluating the temperature inside the concrete cross-section in function of time. And finally, the structural analysis where the temperature dependent material properties are taken into account. The developed model for the bending capacity of R/SFRC beams is validated with test results, which demonstrates that the proposed numerical model captures the fire resistance of R/SFRC beams with reasonable accuracy

Acceptable range for structural fire resistance in performance based design

Structural fire safety engineering is increasingly moving away from prescriptive design rules to what is generally referred to as Performance Based Design (PBD) in which the structure or structural components are designed to satisfy performance requirements. By taking into account the specific characteristics of the structure, a PBD can allow for more directed investments in safety, resulting in structures which are both more economical and safer compared to designs according to traditional prescriptive rules. Although stakeholders mostly agree that the structure should have a good fire performance, determining the specific performance requirements can prove difficult, especially when the opinions of stakeholders with respect to key design parameters diverge. In this paper a decision support tool for investments in Life Safety is introduced and applied to determine an Acceptable Range for the structural fire resistance time for concrete slabs. The support tool takes into account the uncertainty related to amongst other the fire load density and the mechanical properties of the structural element, and can be used as a tool for aligning potentially diverging positions of different stakeholders

Reliability-based decision making for concrete elements exposed to fire

Fire is one of the most severe load conditions for structures and may cause premature failure of structural components, potentially resulting in human casualties and considerable economic losses. A number of recent fire-induced failures as for example the partial collapse of the Windsor Tower in Madrid (2005) and the collapse of the Architecture faculty of the TU Delft in the Netherlands (2008) have stressed the importance of structural fire design and structural fire safety, but up to now little research exists with respect to the safety level obtained during fire exposure. For concrete elements in the European Union structural fire design is governed by EN 1992-1-2. While this standard gives detailed material models and calculation rules, the safety level which is targeted by the standard is not stated explicitly. Furthermore, EN 1992-1-2 relates the fire performance of concrete elements to the idealized ISO 834 standard fire, further complicating the evaluation of the appropriateness of the standard with respect to real (natural or parametric) fire exposures. In this dissertation a numerical calculation tool is presented which allows to determine the safety level obtained by concrete elements during exposure to both standard fires and natural fires. The tool is based on a discretization of the cross-section and takes into account the non-linear and time-dependent temperature distribution in the cross-section, as well as the uncertainties which may exist with respect to basic parameters as for example the concrete compressive strength, the reinforcement yield stress and the concrete cover. While the initial evaluations are based on crude Monte Carlo simulations, improved computational efficiency is obtained by determining the probability density function describing the resistance effect during fire exposure, and the application of advanced structural reliability methods. Especially for concrete slabs a significant improvement is obtained by the introduction of the mixedlognormal distribution for describing the bending moment capacity during fire. It is observed that a more traditional choice for a standard lognormal distribution is not capable of accurately describing the distribution of the moment capacity and results in an unsafe approximation for the obtained safety level. Furthermore, parametric studies are executed and the obtained results stress the importance of the concrete cover for structural fire safety. The developed methodology is applied to determine the implicit target reliability index incorporated in the current Eurocode design format, and to generalize the Eurocode definition of the structural fire resistance time. This generalized reliability-based definition is in full accordance with EN 1992-1-2 but expands its applicability to existing structures and structures with reduced or improved quality control. Although the generalized methodology can be considered as a more refined tool not suitable for everyday applications, it gives very strong mathematical support – based on the current Eurocode design rules – for the much more practical option of defining the structural fire resistance time by a target reliability index of 0.7 (when considering a 50 year reference period for the imposed load effect). Often real fires are not so severe as to threaten the structural stability of concrete elements, and thus the residual load-bearing capacity after fire exposure has to be assessed. Currently few deterministic methods can be found in literature, but since safety is one of the main – possibly the main – consideration in the post-fire assessment of structures, deterministic methods are incapable of providing a solution which is in agreement with the reliability-based concept of EN 1990 (basis of structural design). In order to solve this problem, an easy-to-use reliability-based method is proposed to determine the maximum allowable characteristic value of the imposed load after fire exposure. The method is based on the application of pre-calculated graphs, called “assessment interaction diagrams”, and a limited number of analytical formulas. The analytical formulas give an approximation for the mean value and coefficient of variation of the resistance effect, and allow to incorporate data from inspections or test results (and the associated uncertainties) in the assessment. The deviations introduced by the approximations are taken into account by an additional model uncertainty which is calibrated to result in a very precise and conservative assessment, and which has been incorporated directly in the analytical formulas – avoiding any complications for the practical application of the method. When the obtained values for the mean and coefficient of variation of the resistance effect are indicated in the assessment interaction diagram, an assessment of the maximum allowable load ratio is obtained (and consequently, the maximum allowable characteristic value of the imposed load). While very practical and easy-to-use, the proposed method is considered to be the only simplified method currently available which is in agreement with the reliability-based background of the Eurocodes. Considering the behavior of concrete elements during fire exposure and the maximum allowable load after fire exposure, the optimum investment in structural fire safety for new structures is determined, taking into account amongst others the uncertainty of fire exposure, the uncertain fire severity given fire exposure, the failure costs, and discount rates. The optimum is defined by the concept of Lifetime Cost Optimization, balancing additional investments in the construction phase with reductions in expected failure costs during the lifetime of the structure. The derived mathematical formulations are generally applicable. Considering the importance of the concrete cover ascertained in the first chapters, the optimum concrete cover is determined for concrete slabs in an application example, and the influence of basic parameters as for example the discount rate are investigated. For many practical applications however, deviations from the optimum level of investment will exist. First of all, in most applications the fire safety design is governed by design codes and these design codes intend to be applicable to a wide range of structures, necessarily resulting in underinvestment for some realizations, and overinvestment in others. Secondly, even if only a single structure is considered, many parameters cannot be determined with certainty. For example the fire load density in the building and the consequences of structural failure are difficult to determine at best, and economic parameters as the discount rate are uncertain as well. Thirdly, many psychological effects influence the decision making process, and risk perception, availability effects and loss aversion may significantly influence the investment level chosen by the decision maker. Clearly, in many practical situations the decision makers will qualitatively take into account the many aspects mentioned above, and the chosen levels of investment will depend on a consensus in for example a standardization committee. The reliability-based theoretical optimum investment will be only one of many considerations. It is acknowledged that the decision maker should have the freedom to deviate from the calculated optimum for reasons of policy, but as severe underinvestment is unacceptable from the perspective of life safety, and severe overinvestment claims valuable resources which could be put to better use in other areas of public safety and health, it is questioned whether this freedom to deviate is without limits. In order to clarify the limits to the discretionary competence of the decision maker imposed by unacceptable levels of under- and overinvestment in safety, a decision-support tool is presented which calculates an Acceptable Range for the decision. Within this Acceptable Range the decision maker is free to take into account issues as risk perception, policy aims and political feasibility. The limits of the Acceptable Range are determined by maximum acceptable deviation factors for over- and underinvestment in safety, and – as some uncertainty is inherently associated with any type of evaluation – by limiting probabilities for the respective situations of over- and underinvestment. Once these parameters have been determined on a general basis, they ensure that the optimum safety is always taken into account during the decision making process. Furthermore, the Acceptable Range and the limited set of governing parameters (i.e. the maximum acceptable deviation factors and the limiting probabilities) allow for a much clearer communication between technical specialists, decision makers and the general public. The decision support tool is elaborated in detail in two application examples. In the first application example the Acceptable Range for the target reliability index for concrete slabs in normal design situations is determined, giving a clear overview of the proposed methodology and the calculation procedure. The second – and from a practical perspective much more important – example is concerned with the Acceptable Range for the structural fire resistance time required by the decision maker for the design of new structures. It is observed that in case of low failure costs (relative to the initial construction cost), the uncertainty with respect to the fire severity (fire load density) results in an incompatibility of the criteria of unacceptable overinvestment and unacceptable underinvestment, i.e. due to the large variation in fire load density a specific fire resistance time will always constitute a severe overinvestment in some structures, while at the same time being a severe underinvestment in others. Only when the failure costs are high, an Acceptable Range develops. The unavailability of an Acceptable Range in case of small failure costs does not constitute a problem for the proposed method. On the contrary, it clarifies to the decision maker and to the public that it is impossible to determine a single requirement which is applicable to a wide range of structures and at the same time does not result in large probabilities of unacceptable over- or underinvestment. Many options exist to alleviate this difficulty. For example, it is possible to differentiate between different types of structures (based on their fire load density). Alternatively, large probabilities of overinvestment (or theoretically as well underinvestment) could be accepted. However, thanks to the decision support tool these choices are now clear to both the decision maker and to the public

Probabilistic analysis of concrete beams during fire

In this paper a simple computational tool is presented, which provides insight in the time and temperature dependent reliability of concrete beams during fire. The uncertainty of basic variables is taken into account through Monte Carlo simulations, resulting in a quantification of the uncertainty regarding the bending of these full-probabilistic simulations are compared with the semi-probabilistic calculation methods as specified in EN 1992-1-2

Demonstrating adequate safety for a concrete column exposed to fire, using probabilistic methods

Demonstrating adequate safety for exceptional designs and new design applications requires an explicit evaluation of the safety level, considering the uncertainties associated with the design. The recently published PD 7974-7:2019 provides five routes to demonstrating adequate safety through probabilistic methods but does not include worked examples. The case study in this paper presents three state-of-the-art approaches for demonstrating achievement of an absolute safety target (acceptance concept ‘AC3’ in PD 7974-7:2019) for a concrete column in an office building with stringent reliability requirements. The case study shows how fragility curves listed by, for example, industry organizations can support probabilistic approaches and a more comprehensive understanding of design performance