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Glass as a construction material has become indispensable and is still on the rise in the building industry. However, there is still a need for numerical models that can predict the strength of structural glass in different configurations. The complexity lies in the failure of glass elements largely driven by pre-existing microscopic surface flaws. These flaws are present over the entire glass surface, and the properties of each flaw vary. Therefore, the fracture strength of glass is described by a probability function and will depend on the size of the panels, the loading conditions and the flaw size distribution. This paper extends the strength prediction model of Osnes et al. with the model selection by the Akaike information criterion. This allows us to determine the most appropriate probability density function describing the glass panel strength. The analyses indicate that the most appropriate model is mainly affected by the number of flaws subjected to the maximum tensile stresses. When many flaws are loaded, the strength is better described by a normal or Weibull distribution. When few flaws are loaded, the distribution tends more towards a Gumbel distribution. A parameter study is performed to examine the most important and influencing parameters in the strength prediction model.

PurposeThis paper aims to investigate the state of the art for the reliability evaluation of reinforced concrete beams in a fire situation. Special emphasis is placed on addressing which parameters were considered probabilistically or deterministically, the prescribed probabilistic models for the assumed stochastic variables, the treatment of the heat transfer mechanism, the quantification of the structural fire performance and the assumed target reliability levels.Design/methodology/approachResearch papers were identified through a search on the Web of Science, Google Scholar and detailed searches within the journals Journal of Structural Fire Engineering, Fire Technology and Fire Safety Journal, supplemented with references known by the authors.FindingsConsidering the state-of-the-art review, gaps in the literature are identified related to (1) the probabilistic evaluation of shear capacity for standard fires and parametric fires, and bending capacity for parametric fires, (2) the absence of reference fragility curves for immediate design application/code calibration and (3) the specification of target safety levels for reliability-based design.Originality/valueThe lack of research papers gathering studies on the reliability of reinforced concrete beams in fire situation makes it difficult to further develop research in the area. The value of this work lies precisely in the collection of the basic information, making it possible to identify gaps to be addressed in future research and the suggestion of a research framework.

The interest in probabilistic methodologies to demonstrate structural fire safety has increased significantly in recent times. However, the evaluation of the structural behavior under fire loading is computationally expensive even for simple structural models. In this regard, machine learning-based surrogate modeling provides an appealing way forward. Surrogate models trained to simulate the behavior of structural fire engineering (SFE) models predict the response at negligible computational expense, thereby allowing for rapid probabilistic analyses and design iterations. Herein, a framework is proposed for the probabilistic analysis of fire exposed structures leveraging surrogate modeling. As a proof-of-concept a simple (analytical) non-linear model for the capacity of a concrete slab and an advanced (numerical) model for the capacity of a concrete column are considered. First, the procedure for training surrogate models is elaborated. Subsequently, the surrogate models are developed, followed by a probabilistic analysis to evaluate the probability density functions for the capacity. The results show that fragility curves developed based on the surrogate model agree with those obtained through direct sampling of the computationally expensive model, with the 10**(–2) capacity quantile predicted with an error of less than 5%. Moreover, the computational cost for the probabilistic studies is significantly reduced by the adoption of surrogate models.

Probabilistic analysis is receiving increased attention from fire engineers, assessment bodies and researchers. It is however often unclear which probabilistic models are appropriate for the analysis. For example, in probabilistic structural fire engineering, the models used to describe the permanent and live loads differ widely between studies. Through a literature review, it is observed that these diverging load models are based on surveys conducted between 1893 and 1976 and that widely adopted assumptions, such as the rule for combining permanent and live loads into the total load effect, are commonly adopted based on precedent. The diverging current models however relate to mostly the same underlying datasets and basic methodologies. Differences can be attributed (largely) to specific assumptions in different background papers, which have become consolidated through repeated use in research papers and adoption in background documents to codes. By reviewing the studies underlying currently applied probabilistic load models in structural fire engineering, a consolidated probabilistic load model is proposed in this paper. It is concluded that the total load effect is ideally described by KE·(G + Q), with KE the model uncertainty for the load effect, G the permanent load, and Q the imposed load. The model uncertainty KE can be described by a lognormal distribution with mean equal to unity and coefficient of variation (COV) of 0.10. The permanent load is preferably modelled by a normal distribution with mean equal to the nominal permanent load, and a COV which can either be assessed on a project specific basis, or can be set to 0.10 for a first assessment. For common occupancies (office, residential), the live load is preferably modelled by a Gamma distribution. The mean live load can be taken as 0.2 times the nominal, and the live load COV can be taken as 0.60 for large load areas (> 200 m2) and 0.95 for smaller load areas (

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 parameters. The recently published PD 7974‐7:2019 provides five routes to demonstrate 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, specified on the level of individual members and with respect to a standardized heating regime. 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.

When a concrete slab is excessively loaded due to an accidental event, compressive membrane action can be activated in order to generate an alternative load transfer to the remaining supports, which can considerably enhance the load-carrying capacity. This can increase the structural reliability of the components, delay or even prevent a progressive collapse and consequently increase the robustness of concrete structures. Although the beneficial effects of compressive membrane action in reinforced concrete slabs have been recognized for decades, only limited research has been focusing on this effect in prestressed concrete members, like hollow core slabs. Therefore, a novel realscale test set-up has been developed in order to assess this phenomenon in real-scale hollow core slabs. The results indicate that, despite the presence of the large hollow cores, compressive membrane action can significantly improve the load-carrying capacity of hollow core slabs under excessive loading. In parallel, a numerical finite element model has been established in order to model the structural behavior (i.e., compressive membrane action) as per the investigated test program. The model was able to correlate the results from the experiments very well, and emphasized the large influence of the concrete tensile strength on the ultimate failure load of concrete hollow core slabs in compressive membrane action.

It is common for agencies around the world to conduct some form of cost-benefit analysis (CBA) when proposing an investment in a safety measure. Since resources are limited, expenditure on one particular safety measure reduces the availability of those resources for other measures. Due to finite financial resources, an investment in a safety scheme thus requires a trade-off. As such, the objective of a CBA is to assess whether the proposed measure provides a net-benefit to society or whether resources would be better directed elsewhere. Fire safety measures, such as sprinkler systems, are one means to reduce the risk posed by fire in buildings. Sprinkler systems have a long record of property and life protection but there is a cost associated with their installation and ongoing maintenance. For many years various agencies have examined whether sprinkler systems should be mandated in some or all buildings within their jurisdiction, and as a result have conducted different forms of CBA. However, there are a number of challenges when carrying out such assessments particularly when it comes to placing a value on a preventable fatality. This paper revisits previous CBA studies available in the literature for the installation of residential (domestic) sprinkler systems in single family dwellings. This paper applies recent work to extend the J-value methodology which employs the life quality index (LQI) concept as a means of valuing the benefit of increasing life expectancy through the mitigation of consequences, or reduction in the occurrence rate of a hazard. Similar to the earlier work, the paper finds that the unilateral installation of sprinkler systems in single family homes mostly results in a net-disbenefit to society (depending upon jurisdiction). Widespread adoption of sprinklers is generally only found to be cost-beneficial where the installation and maintenance costs can be split across a number of properties per installation, e.g. apartment buildings. This conclusion is reached through the adoption of a novel and objective judgement scalar that is easy to implement and interpret.

Probabilistic Risk Assessment methodologies are gaining traction in fire engineering practice as a (necessary) means to demonstrate adequate safety for uncommon buildings. This induces a need to apply uncertainty quantification to structural fire engineering problems. Yet, the combination of probabilistic methods and advanced numerical fire engineering tools has been limited due to the absence of a methodology which is both efficient (i.e. requires a limited number of model evaluations) and unbiased (i.e. without prior assumptions regarding the output distribution type). In this paper, the recently proposed MaxEnt method is combined with the dedicated structural fire engineering software SAFIR to evaluate the ability of the method to achieve efficient, unbiased assessments of structural fire performance. The case studies include the probability density function (PDF) of (i) the standard fire resistance of a composite column; (ii) the load bearing capacity of a composite floorplate exhibiting tensile membrane action, after 90 min of standard fire exposure; (iii) the load bearing capacity of the same composite floorplate, considering a parametric fire exposure including cooling phase; and (iv) the maximum temperature reached in a protected steel element under realistic fire exposure. In the first application, the MaxEnt PDF correctly and efficiently captures the distribution obtained using Monte Carlo Simulations. The floorplate example under parametric fire exposure shows the true strength of the MaxEnt method as an unbiased assessment, as different failure modes are observed in the cooling phase resulting in an irregular shape of the load-bearing capacity PDF. For this case, reliance on a traditional assumption of lognormality for the capacity would result in an overestimation of the capacity at lower quantiles. The last case study yields a bi-modal output due to the physics-based duality between localized (traveling) and post-flashover fire development. While the MaxEnt captures this bi-modality, it does not accurately reproduce the distribution obtained by Monte Carlo Simulation. Limitations of the MaxEnt method and needs for further research are discussed at the end of the paper.

The design limit states form the basis of current structural fire design approaches. These design practices overlook the post-fire resilience and repairability of the structure. Consequently, a minor fire might lead to an irreparable structure and a need of demolishing it. We propose a framework to evaluate during the design phase the anticipated repair cost for a structure in case of a fire event, in order to enable consideration of post-fire resilience in design decisions. We apply the framework to evaluate the repair cost for a composite slab panel comprising a concrete slab, two girder and two boundary beams at opposite edges, and two central beams at the center. Two fire designs for the composite slab panel satisfying the nominal fire design requirement are considered: a prescriptive design and a performance-based design which harnesses tensile membrane action and omits insulation on central beams. The repair costs are evaluated and compared for both designs for a range of natural fire exposures, demonstrating that the performance-based design achieves its target of stability during fire, but also results in higher anticipated post-fire damages. This concept of pre-evaluation of repair cost can further be implemented in life-cycle cost optimization procedures to allow an optimized structural design.

A simple framework for setting risk tolerability limits is proposed following a literature review of risk acceptance in fire safety engineering and a feedback round with international fire safety professionals. The framework provides practical guidance for the application of international fire safety guidance, such as the recently published UK guidance document on probabilistic risk assessment (PRA) for the fire design of buildings, PD 7974-7:2019, which provides a state-of-the-art framework to assess adequate safety for complex fire engineering designs. However, the application of this guidance document is hindered by two main constraints: (i) PD7974-7:2019 requires risk tolerability limits to be set, but lacks guidance on defining them for a specific building project, and (ii) no reference case studies are given that demonstrate the application of PRA methods to fire engineering design. In order to help fill this gap, a risk tolerability framework is developed and proposed herein. Finally, it is applied to a reference case study of a UK office building. Considering the developed framework, further research needs are identified. It is expected that the proposed risk tolerability framework and the presented reference case study can support the application of PRA to fire engineering design and ease stakeholder communication on setting risk tolerability limits.

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.

The alternative load path (ALP) method is widely used to investigate the performance of reinforced concrete (RC) buildings in case of progressive collapse (or disproportional collapse) scenarios. This kind of analysis can be carried out either in a static way or in a dynamic way. In this contribution, these methods are compared by means of nonlinear static and nonlinear dynamic analysis methods. A 5-storey RC frame subjected to two different sudden column removal scenarios is adopted as a case study. The probabilistic analysis considers 12 random variables. On the basis of the stochastic results, a dynamic amplification factor (DAF) is calculated. The mean values of the DAF are 1.114 and 1.102 for the external column removal scenario (Case A) and the internal column removal scenario (Case B), respectively. Compared to the failure probabilities obtained through a static analysis, the failure probabilities for the incremental dynamic analysis results are 184.0% and 180.7% higher for Case A and Case B, respectively.

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.

A machine learning algorithm was applied to predict the onset of flashover in archival experiments in a 1/5 scale ISO 13784-1 enclosure constructed with sandwich panels. The experiments were performed to assess whether a small-scale model could provide a better full-scale correlation than the single burning item test. To predict the binary output a logistic regression model was chosen as machine learning environment. Because results indicated a high variance/low bias issue regularization was applied. It was found that lasso-regression significantly reduced the amount of variance at a negligible increase in bias. With the regularized model, it was possible to discern the predictive variables and determine the decision boundary. In addition, a methodology was put forward on how to use the decision boundary to iteratively update the learning algorithm. As a result, it was shown how a learning algorithm can be used to facilitate ongoing experimentation. At first as a crude guideline, and in later stages, as an accurate prediction algorithm. It is foreseen that, by iteratively updating the algorithm, by compiling existing and new experiments in databases, and by applying fire safety knowledge, the final learned algorithm will be able to make accurate predictions for unseen samples and test conditions.

Thermal conductivity and specific heat of concrete are highly influential parameters for the heat transfer into the material during fire exposure. Reviewing the available literature has shown that there is a large scatter in the data for these thermal parameters. To quantify that uncertainty, novel probabilistic models for thermal conductivity and specific heat of concrete at elevated temperatures are developed. Analysis of available experimental data indicates that a temperature-dependent Gamma distribution can be recommended for both thermal properties. Closed-form equations for the temperature-dependent mean and standard deviation are derived. Thus, for both the thermal conductivity and the specific heat, a continuous probability distribution as a function of temperature is obtained, which can be easily implemented in numerical simulations. Using the example of the probabilistic analysis of a simply supported concrete slab exposed to the standard fire, the models are compared with the commonly used deterministic representation of the thermal properties. It is shown that the calculated probabilities of failure using the deterministic models are an order of magnitude lower and therefore unconservative. This analysis suggests that accounting for the uncertainty in thermal properties for concrete slabs can have a significant effect on evaluating the safety and therefore should not be ignored in cases of high importance.

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 protected based upon the US prescriptive approach. A set of columns with a range of section factors are selected to study the influence of utilization ratio, restraint conditions, 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 influence of fuel load density is presented in the form of fragility functions, where the probabilities of failure for expected fuel load density values are discussed. In addition, the probability of failure for columns across different stories of a building is calculated, leading to the conclusion that further harmonization of safety levels can be achieved if reliability-based quantifications are introduced in the design process.

This paper incorporates a probabilistic fire loss assessment method for reinforced concrete structures into a cost-benefit analysis to optimize a structural fire design. Economic losses in case of failure and survival of the structure are both quantified with, in the latter case, an estimate of the damage and repairs costs. As a case study, a cost-benefit optimization of the position of rebars in a concrete column is investigated. The column response in fire is evaluated using finite element simulations in SAFIR. Variations in cover thickness result in variations in failure probabilities and, for cases where no failure occurs, variations in repair costs due to heat penetration and residual out-of-plane deformation of the column. The optimum cover thickness is the one that offers the best trade-off between the various repair costs across the range of likely fire intensity levels. This optimum is sensitive to repair decisions such as the tolerance on the acceptable residual out-of-plane deformation after a fire. For the studied cases, the optimum cover thickness is smaller in slender columns than in stocky columns due to greater out-of-plane deformations in the former.

Common structural fire design relies on recommendations from design codes, or (a single or small set of) more advanced numerical analyses. When applying such procedures to the design of structures under normal loading conditions, adequate safety is ensured through calibrated safety factors and ample experience with structural failures. This is however not the case when considering accidental fire loading, where the stochasticity in the structural fire behaviour is rarely fully acknowledged. Therefore, a significant interest in the use of probabilistic approaches to evaluate structural fire performance, which take into account the uncertainty associated with model parameters, can be observed among researchers, with a special focus on the development of fragility curves. The calculation of fragility curves is, however, a laborious task, demanding huge computational expense, mainly attributed to the adoption of advanced calculation procedures and the need for a large number of model evaluations. The present study contributes to addressing the limitations imposed by these computational requirements through the development of surrogate models for fire exposed structural members. To achieve this, a framework for carrying out probabilistic studies of structures under fire through the use of surrogate modelling is presented. The framework is applied to a concrete column subjected to a standard fire and proves efficiency and accurateness for the selected simple example. Future studies will investigate the applicability of the framework to structural assemblies under physically-based fires.

Structural risk assessment against fire requires robust material models that take into account the uncertainty in material behavior over a range of elevated temperatures. Such probabilistic...

Although traditionally the fire resistance rating of concrete elements is determined through standardized tests or tabulated data, there is a growing trend towards the use of performance-based approaches to evaluate structural behaviour during or after a fire. The safety format to be applied with these advanced numerical evaluations is however unclear. In this paper, the applicability of the concept of a global resistance factor (GRF) safety format is explored for simply supported concrete slabs exposed to the Eurocode parametric fire curve for a wide range of parameters. The safety of the slab is evaluated in relation to its ability to withstand a complete burnout scenario, i.e. its ability to resist the applied loads throughout the entire duration of a fire including the cooling phase. Using a full-probabilistic model, the required GRF is numerically derived for a specified target safety level in case of fire. Additionally, a calculation method is provided which allows to determine the GRF of fire exposed slabs for any given compartment through the use of a reference compartment and equivalency equations.

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.

This paper presents the results of four fire tests on full-scale cast-in-situ, hollow core concrete slabs, constructed using filler boxes and an assembly box system. Experimental data include the furnace temperature, temperature distribution in the slab, and vertical and horizontal deflections during the heating and cooling phases, as well as observed cracking patterns. The test data indicate that the tested hollow slabs with plastic filler boxes have good performance in case of standard fire exposure with small vertical deflections and high deflection recovery in long duration testing. For slabs with assembly box systems serious spalling was observed, resulting in integrity failure after 69 minutes in one of the tests. Nevertheless, load bearing capacity was maintained for all tests. The tests highlight the importance of the boundary conditions and the arrangement of the filler system on the fire behaviour of the hollow slabs, particularly with respect to the observed cracking, spalling and structural integrity.

A probabilistic risk assessment (PRA) is commonly accepted as a tool for performance based design in fire safety engineering, but the position of PRA in the design process, the relationship between different acceptance concepts (absolute, comparative, ALARP), and the responsibilities of the designer remain unclear. Aiming to clarify these aspects, the safety foundation of fire safety solutions is investigated, indicating that PRA is necessary for demonstrating adequate safety when no appeal can be made to the collective experience of the profession. It is suggested that PRA is not a methodology for ‘future fire safety engineering’, but rather a necessary methodology to provide an objective safety foundation for uncommon fire safety designs. Acknowledging that what constitutes ‘acceptable safety’ is subjective and may change over time, an objective proxy of ‘adequate safety’ is defined and proposed as a benchmark against which to assess the adequacy of fire safety designs. In order to clarify the PRA process, a hierarchy of different acceptance concepts is presented. Finally, it is shown how, depending on the applied acceptance concepts, the designer takes responsibility for different implicit assumptions regarding the safety performance of the final design.

The alternative load path method is widely used to assess the progressive collapse performance of reinforced concrete structures. As an alternative to an accurate non–linear dynamic analysis, an energy–based method (EBM) can also be adopted to approximately calculate the dynamic load–bearing capacity curve or the dynamic resistance based on a static capacity curve. However, dynamic effects cannot be explicitly taken into account in the EBM. The model uncertainty associated with the use of the EBM for evaluating the dynamic ultimate capacity of structural frames has not yet been quantified. Knowledge of this model uncertainty is however necessary when applying EBM as part of reliability calculations, for example, in relation to structural robustness quantification. Hence, this article focuses on the evaluation of the performance of the EBM and the quantification of its model uncertainty in the context of reliability–based assessments of progressive or disproportionate collapse. The influences of damping effects and different column removal scenarios are investigated. As a result, it is found that damping effects have a limited influence on the performance of the EBM. In the case of an external column removal scenario, the performance of the EBM is lower as the response is not a single deformation mode according to the results in the frequency domain. However, a good performance is found in the case of an internal column removal scenario in which the assumption of a single deformation mode is found to be sufficiently adequate. Probabilistic models for the model uncertainties related to the use of the EBM compared to direct dynamic analyses are proposed in relation to both the resistances and the associated displacements. Overall, the EBM shows to be an adequate approximation, resulting in a small bias and small standard deviation for its associated model uncertainty.

The rise of Performance Based Design methodologies for fire safety engineering has increased the interest of the fire safety community in the concepts of risk and reliability. Practical applications have however been severely hampered by the lack of an efficient unbiased calculation methodology. This is because on the one hand, the distribution types of model output variables in fire safety engineering are not known and traditional distribution types as for example the normal and lognormal distribution may result in unsafe approximations. Therefore unbiased methods must be applied which make no (implicit) assumptions on the PDF type. Traditionally these unbiased methods are based on Monte Carlo simulations. On the other hand, Monte Carlo simulations require a large number of model evaluations and are therefore too computationally expensive when large and nonlinear calculation models are applied, as is common in fire safety engineering. The methodology presented in this paper avoids this deadlock by making an unbiased estimate of the PDF based on only a very limited number of model evaluations. The methodology is known as the Maximum Entropy Multiplicative Dimensional Reduction Method (ME-MDRM) and results in a mathematical formula for the probability density function (PDF) describing the uncertain output variable. The method can be applied with existing models and calculation tools and allows for a parallelization of model evaluations. The example applications given in the paper stem from the field of structural fire safety and illustrate the excellent performance of the method for probabilistic structural fire safety engineering. The ME-MDRM can however be considered applicable to other types of engineering models as well.

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.

Fire safety engineering designs should comply with the ALARP requirement, meaning that fire safety measures should be implemented to ensure that fire risks are As Low As Reasonably Practicable (ALARP). However, previous approaches have often been contradictory or unclear, especially with respect to the concepts of risk aversion, the valuation of risk to life, the concept of disproportionality, and the need to take into account monetary benefits resulting from life safety investments. First, the As Low As Reasonably Practicable (ALARP) criterion is specified to a societal, risk-neutral, and scalar cost-benefit analysis in the field of fire safety engineering. This is done to overcome the shortcomings in current practice with respect to utilizing the ALARP criterion for Probabilistic Risk Assessment (PRA). Second, the ethical dilemma of the valuation of risk to human lives is addressed by application of the Life Quality Index (LQI), as has been suggested in the field of structural engineering through the recent ISO 2394:2015 standard. Contrary to the existing literature, the proposed interpretation for the ALARP requirement corresponds to an application of the LQI maximum societal benefit criterion. This ensures that safety resources are allocated so as to maximize the number of lives saved, and implies that the ALARP criterion results in stronger minimum requirements for life safety investments, i.e. societal lower bound investment levels. Third, the valuation of costs and benefits by the fire safety engineer is addressed by emphasizing the duty of care, and by specifying a benchmark criterion for the objective, diligent, and competent fire safety professional. This reinforces self-reflection amongst fire safety professionals, and diminishes the need for often unjustified or poorly specified disproportionality factors. Finally, the relationship between fire safety design and private actor cost-optimisation considerations is discussed, and the presented concepts are illustrated using three examples. These clarify the application of the presented concepts and demonstrate how the societal ALARP requirement interacts with the (safety) preferences of private investors. The examples highlight the importance of the societal ALARP evaluation and show that this governs the safety investment when the private investor values damages low, applies a high discount rate, or takes into account indirect costs (e.g. aesthetic costs) related to the safety investment.

The Alternative Load Path (ALP) method is widely used to assess progressive collapse resistance of reinforced concrete (RC) structures by notional removal of one or more load-bearing elements. In general, a nonlinear time history analysis (NTHA) is needed to perform such an analysis if dynamic effects are explicitly taken into account. To avoid cumbersome nonlinear dynamic analyses, the energy-based method (EBM) is a promising technique to predict the maximum dynamic responses of a structural system. In this article, the accuracy and precision of the EBM is evaluated based on a validated finite element model of a tested RC slab subjected to a sudden column removal scenario, in particular in relation to the investigation of tensile membrane action (TMA). Influences of dynamic effects are evaluated, i.e. in relation to strain rate effects, damping, and the time duration of support removals. Strain rate effects are observed to have only slight influences on the dynamic responses. The strain rate dependency of reinforcement is found to have a more significant influence on the responses in TMA stage, although also to a limited extent. The magnitude of the load has a significant influence on the dynamic response, as do increasing damping ratios due to the corresponding significant energy dissipation. Finally, the dynamic response reduces with increasing time duration of the column removal. Based on the results of the stochastic analyses, the EBM is observed to perform well based on a comparison with the results of NTHA in both flexural and TMA stages. Furthermore, in relation to the analyzed case studies on reinforced concrete slabs, the model uncertainty of the responses obtained through the EBM compared with the NTHA is found to be represented well by a lognormal distribution with mean of 0.95 and a standard deviation of 0.20, for evaluating the loads of first rupture of reinforcement. Furthermore, a lognormal distribution with mean 0.96 and standard deviation 0.13 is found appropriate to represent the model uncertainty on ultimate load-bearing capacity predictions. Model uncertainties are also obtained with respect to the model predictions for displacements at the moment of the first rupture of reinforcement, displacements at the ultimate load-bearing capacities, and both loads and displacements at second load peaks.

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. It is discussed that traditional (structural) fire safety design is deterministic, with the safety foundation premised upon the collective experience of the profession. However, it is noted that building forms are increasingly uncommon in nature, due to material choice, height, failure consequences, etc. Within the framework presented in PD 7974–7:2019 there is an expectation that probabilistic risk assessment (PRA) methods be employed to demonstrate adequate safety for cases where the collective experience of the profession cannot be called upon to guide design approaches. In doing so, any design must be demonstrated to be tolerable to society, and the residual risk as low as is reasonably practicable (ALARP). In support of the PD 7974–7:2019 framework, the paper assesses the failure probabilities of isolated steel elements in function of insulation thickness, utilization, load ratio and (mean) fire load. In support of a generalized definition of target safety levels for structural fire safety engineering, optimum target safety levels for insulated steel beams are then determined as a function of the fire characteristics by applying life-time cost optimization (LCO) techniques. The LCO results in an assessment of the optimum investment level as a function of the fire, and damage and investment cost parameters characterizing the building. It is intended that the current contribution can be a steppingstone towards rational and validated reliability targets for performance-based design (PBD) in structural fire safety engineering.

Three-dimensional concrete printing (3DCP) is a fast-evolving manufacturing technique in the construction industry with numerous advantages over traditional construction methods. Nevertheless, many unknowns about 3DCP in the manufacturing stage still remain, such as the maximum number of printed layers before failure or the maximum speed at which a certain design can be properly printed. In this paper, a numerical model for the simulation of the structural behaviour of 3D printed fresh concrete is proposed and discussed. In order to obtain complete control over the additive process, material properties and layer interactions, the finite element mesh needs to be created from the ground up in a layer-wise manner. Therefore, a parametric tool was developed, which allows for the creation of finite element models without requiring extensive manual modelling. The main advantage of the developed tool is the possibility to automate the pre-processing step for the numerical analysis and simulate the structural behaviour of a randomly shaped object during printing. Additionally, it allows for finding the appropriate material properties for a certain print object at a desired print speed and vice versa. As such, the printing process can first be virtually simulated and improved upon without physical experimentation and the corresponding material waste. Ultimately, the developed tool can assist in an entire 3DCP workflow with regard to efficiency and material usage. Models created with the presented tool were evaluated and validated based on experimental and numerical results from literature. Finally, the case study of a geometrically complex print object is presented, demonstrating the tool’s potential.

This study reports an experimental exploration of the combustion inhibition efficiency of iron short-chain perfluorocarboxylates, namely, iron trifluoroacetate (FeTFA) and iron pentafluoropropionate (FePFP). The aim is to develop a new phosphor-free fire-extinguishing agent. The synthesized FeTFA and FePFP were characterized by ultraviolet-visible spectroscopy, Fourier-transform infrared spectroscopy, X-ray fluorescence measurements, and fast-atom bombardment mass spectrometry. The FeTFA and FePFP ligands (i) coordinate with the iron ions in bridging form via carboxylate oxygens, (ii) contain no Cl-, and (iii) are hexanuclear complexes with chemical formulas of C18F27O22Fe6 and C27F45O22Fe6, respectively. Suppression trials and thermogravimetric measurements revealed that (i) both FeTFA and FePFP have higher combustion inhibition ability at lower suppressant concentrations than ammonium dihydrogen phosphate (an active component in conventional fire-extinguishing agents), (ii) FePFP is remarkably more inhibition-efficient than FeTFA, and (iii) neither FeTFA nor FePFP hinder cellulose pyrolysis and char combustion in the condensed phase. Thermogravimetry-mass spectrometry measurements confirmed that (i) the main gas-phase decomposition product of FeTFA and FePFP is CF3, and (ii) FePFP is a better CF3 generator than FeTFA. The different inhibition abilities of the two complexes were attributed to their different CF3 generation abilities and eases of decomposing the complex.