Effects of various design parameters on system-level fire fragility functions for steel buildings

The existing literature in fire engineering is mostly based on single component study of structures, as opposed to system level building performance. In current practice, fire does not need to be considered as part of the structural design of the building. The required fire protection for steel components in a building is based on prescriptive design guidelines, which are based on standard fire tests on individual structural members. In addition, the fire-structure engineering has primary focused on deterministic analysis, while the field is moving towards performance-based design in recent years. Meanwhile, the scenarios leading to a fire event and the performance of the structure at elevated temperatures involve a great level of uncertainty. This work focuses on fire-structure interaction with the objective of developing fire fragility functions that capture fire damage uncertainty for the entire building (i.e., at the system-level). A fragility function provides the probability of exceeding a damage state for a given intensity measure of a given hazard. Fire fragility functions can be developed to measure the expected losses based on performance of a building structural system, rather than a single component. Different functions can be developed for buildings with different typologies (e.g. high-rise steel building with moment resisting frame, low rise steel building with bracing). This presentation derives fragility functions based on stochastic analyses of prototype buildings. In developing the fragility functions, uncertainties in the fire model, the heat transfer model and the thermo-mechanical response should be considered; but such a large number of random variables adds to the complexity of analysis and the computational time. Based on a sensitivity analysis for steel gravity frames, this work identifies the most important input parameters to be considered as random variables when developing fire fragility functions for an entire building. The sensitivity analysis for a multi-story steel building prototype is completed considering uncertainties at the compartment and building levels. At the compartment level, uncertainty in the fire scenario, compartment geometry, applied load, thermal and mechanical properties of steel and insulating materials are considered. At the building level, the influence of fire-resistance rating, building height, and occupancy type are studied. The results of this study identify the local and global parameters needed as part of deriving system-level fire fragility functions for a steel building.Peer reviewe

Fire risk assessment of multi-story buildings based on fragility analysis

peer reviewedRecent efforts aim at assessing the fire performance of structures in a probabilistic framework. But there is still no well-established method to quantify the reliability of entire buildings. Previous works focused on isolated structural members, therefore not allowing for a determination of the global safety level of buildings. Here, a new methodology is developed to quantify the reliability of buildings in fire. The methodology uses Monte Carlo simulations for constructing fragility functions associated with different fire breakout locations in a building, then combines the functions to characterize the overall building conditional probability of failure, and finally incorporates the probabilistic models for intensity measure and fire occurrence likelihood. The methodology is applied to multi-story steel buildings. This work addresses fire reliability at the building scale, and therefore is useful for standardizing safety level as well as for evaluating community resilience

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

Exploratory study into a safety format for composite columns exposed to fire

Current performance based structural fire engineering approaches evaluate structural behaviour under prescribed fire scenarios. The mechanical properties of the materials, the load conditions and geometric parameters are all however fraught with uncertainty, and there is currently no clear safety format ensuring the reliability of the design solution. In this contribution, a safety format is explored for evaluating the fire resistance of composite columns, following results obtained in earlier studies on uncertainty quantification. Using the safety format, a single nonlinear finite element evaluation of the fire resistance time is combined with a global safety factor, defining its design value. Under the assumptions derived from earlier work, the safety format works well, but additional parameter studies indicate that good performance is limited to relatively low ambient design utilization ratios. The results thus highlight the importance of uncertainty quantification and the limitations of basing a safety format for structural fire design on limited studies. It is concluded that detailed studies into the probabilistic description of the response of composite columns exposed to fire are required to generalize the results to a broadly applicable design rule

The MaxEnt method for probabilistic structural fire engineering : performance for multi-modal outputs

Probabilistic Risk Assessment (PRA) methodologies are gaining traction in fire engineering practice as a (necessary) means to demonstrate adequate safety for uncommon buildings. Further, an increasing number of applications of PRA based methodologies in structural fire engineering can be found in the contemporary literature. However, to date, 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). An uncertainty quantification methodology (termed herein as MaxEnt) has recently been presented targeted at an unbiased assessment of the model output probability density function (PDF), using only a limited number of model evaluations. The MaxEnt method has been applied to structural fire engineering problems, with some applications benchmarked against Monte Carlo Simulations (MCS) which showed excellent agreement for single-modal distributions. However, the power of the method is in application for those cases where ‘validation’ is not computationally practical, e.g. uncertainty quantification for problems reliant upon complex modes (such as FEA or CFD). A recent study by Gernay, et al., applied the MaxEnt method to determine the PDF of maximum permissible applied load supportable by a steel-composite slab panel undergoing tensile membrane action (TMA) when subject to realistic (parametric) fire exposures. The study incorporated uncertainties in both the manifestation of the fire and the mechanical material parameters. The output PDF of maximum permissible load was found to be bi-modal, highlighting different failure modes depending upon the combinations of stochastic parameters. Whilst this outcome highlighted the importance of an un-biased approximation of the output PDF, in the absence of a MCS benchmark the study concluded that some additional studies are warranted to give users confidence and guidelines in such situations when applying the MaxEnt method. This paper summarises one further study, building upon Case C as presented in Gernay, et al

Evaluating uncertainty in steel-composite structure under fire : application of the ME-MDRM

Probabilistic applications of structural fire engineering will be central to the realisation of complex buildings, where reliance on precedent / experience is insufficient, and an adequate level of safety must be explicitly demonstrated. The practical application of probabilistic methods in structural fire safety has, to date, been limited to simplistic structural systems due to a lack of an efficient, unbiased calculation methodology. Herein, two examples are presented whereby the Maximum Entropy Multiplicative Dimensional Reduction Method, ME-MDRM for short, is applied to estimate the probability density function of performance metrics output from finite element analyses. Given a limited number of model realisations (order of 101), it is shown that the MEMDRM can give valuable insight into the distribution of failure time, and maximum supported load under ISO fire conditions for a composite column, and composite slab panel, respectively. The former is benchmarked against Monte Carlo Simulations, with excellent agreement. Finally, limitations in the stochastic data and in the application of the ME-MDRM itself are discussed, with future research needs identified

Probabilistic Measures of Earthquake Effects on Fire Performance of Tall Buildings

peer reviewedCascading multi-hazard events, such as fires following an earthquake, can trigger progressive collapse of structures. Risk or the probability of reaching a limit state after an extreme event is related to (a) the probability of occurrence of the hazard, and (b) the probability of reaching the limit state given the hazard. In this paper, earthquake effects on fire performance of tall buildings in a community are studied. First, the proba-bility of fire ignition due to an earthquake is modeled based on historical data and properties of the built en-vironment. In the second step, the effect of earthquake on structural fire performance of a steel frame is studied using system level probabilistic approaches. The results show that the earthquake does not increase the probability of reaching different limit states under fire, however, post earthquake fire can increase the drift demand on columns located on the perimeter of the structure, and may cause instability

Permanent and live load model for probabilistic structural fire analysis : a review

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 load differ widely between studies. Through a literature review, it is observed that these diverging load models largely relate to the same underlying datasets and basic methodologies, while differences can be attributed (largely) to specific assumptions in different background papers which have become consolidated through repeated use in application studies by different researchers. Taking into account the uncovered background information, consolidated probabilistic load models are proposed

Probabilistic model for steel yield strength retention factor at elevated temperatures : influence of model choice on structural failure fragility curve for steel columns exposed to fire

Abstract: Interest in quantifying the risk and reliability within a Performance Based Design approach for application in structural fire engineering is increasing. Yet, a well-established and commonly accepted set of models to capture uncertainty, especially when quantifying material properties at elevated temperatures, does not currently exist. The choice of probability distribution for material properties that captures scatter in data over a range of temperatures can influence the simulated structural response. There is also a need to ensure continuity in reliability appraisals during transition from normal to elevated temperatures. This research aims to quantify uncertainty in the yield strength of steel at elevated temperatures using different modeling approaches and investigates the influence of such model choices on the response of a steel column during a fire. The model choices are related to a collection of experimental data from the literature, and a study of the obtained histograms of the yield strength reduction factor for elevated temperatures. Model efficiency in capturing the fragility curve of failure temperature is discussed and exemplified through probabilistic structural fire analysis of steel columns

Probabilistic models for thermal properties of concrete

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