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The objective of this paper is to propose relationships for the reduction in mechanical properties of cold-formed steels at elevated temperature. Predicting the degradation of strength and modulus of cold-formed steels with temperature is critical to enable fire design of cold-formed steel members. Here, the properties of elastic modulus, 0.2% proof stress, 2% stress, and ultimate stress are studied for grades up to and including 550 MPa. Data are collected from the literature as well as from recent tests conducted by the authors at Johns Hopkins University. Steady-state and transient test results in the range of 20°C–1,000°C are analyzed. Retention factors are then proposed for the mechanical properties adopting a standardized format developed through committee work with the American Iron and Steel Institute. [ABSTRACT FROM AUTHOR]

The Performance-Based Design approach provides a goal-oriented process to support safe, innovative, and resilient structural fire designs. However, adoption of this approach requires both a rigorous framework and appropriate analysis tools to assess the expected performance of structures in fire. The objective of this paper is to provide an overview of the Performance-Based Design approach, including the process and its specific elements, applied to structures in fire. First, the value of the approach is illustrated through a review of case studies. Then, the process is described with identification of the role of the structural fire engineer. Recent research in methods to enable the evaluation of the structural fire performance, conducted within the author's group at Johns Hopkins University, is discussed. Issues addressed include the coupling between the fire and thermal-structural models, the characterization of the material behavior at elevated temperature, numerical modeling of structures subjected to fire, probabilistic risk assessment, and cost-benefit analyses. The paper concludes with a discussion of some challenges and perspectives for the future of performance-based structural fire design. • Performance-based structural fire design is applied in projects worldwide. • The process integrates efforts on fire, materials, and structure evaluation. • Tools have advanced for evaluating structural fire performance and reliability. • Challenges include technical limitations, complexity, awareness, and competency. • Opportunities to support safe design for sustainability, innovation, and resilience. [ABSTRACT FROM AUTHOR]

• Numerical analysis of RC columns, beams, walls under fires with cooling phases. • Effect of thermal wave on structural stability is quantified. • Slower cooling rates increase propensity to fail after the peak fire temperature. • RC beams' stability can be linked to reinforcement maximum reached temperature. • RC columns and walls' behavior is more complex and requires thermal-structural analysis. Fire exposed structures may collapse during or after the fire decay phase, with risks for building occupants and firefighters; yet, understanding of the effects of the fire decay phase on structural loadbearing capacity remains limited. This paper describes a numerical investigation on the behavior of reinforced concrete columns, beams, and walls under natural fires including cooling down phases. Finite element models are benchmarked against experiments capturing the behavior during heating. The models are then used to simulate the structural response of the concrete members under fires with various cooling rates and load ratios. The analyses capture the irreversibility of material properties through tracing of the temperature history in the structure. The results show that temperatures and deformations continue increasing after the end of the fire heating phase. As a result, concrete columns, beams, and walls may fail during the cooling phase. Faster cooling rates reduce the likelihood of failure in cooling. For beams, failure can be inferred from the maximum reinforcement temperature reached throughout the fire, but for columns and walls a thermal–mechanical analysis of the member throughout the fire history is needed. A relationship is proposed to evaluate the burnout resistance from the fire resistance rating and cooling rate. The presented numerical method allows assessing the structural stability throughout a fire event, an important requirement for designing a fire resilient built environment. [ABSTRACT FROM AUTHOR]

This paper proposes a novel methodology for developing fire fragility functions for an entire steel building – meaning that the function is not specific to a location within the building. The aim is to characterize the probabilistic vulnerability of steel buildings to fire in the context of community resilience assessment. In developing the fragility functions, uncertainties in the fire model, the heat transfer model and the thermo-mechanical response are considered. In addition several fire scenarios at different locations in the building are studied. Monte Carlo Simulations and Latin Hypercube Sampling are used to generate the probability distributions of demand placed on the members and structural capacity relative to selected damage thresholds. By assessing demand and capacity in the temperature domain, the thermal and the structural problems can be treated separately to improve the efficiency of the probabilistic analysis. After the probability distributions are obtained for demand and capacity, the fragility functions can be obtained by convolution of the distributions. Finally, event tree analysis is used to combine the functions associated with fire scenarios in different building locations. The developed fire fragility functions yield the probability of exceedance of predefined damage states as a function of the fire load in the building. The methodology is illustrated on an example consisting in a prototype nine-story steel building based on the SAC project. [ABSTRACT FROM AUTHOR]

The research aims at developing a new multiaxial constitutive model for concrete in the fire situation. In addition to validity at the material level, a crucial feature of a constitutive model is the applicability at the structural level; yet for concrete in fire there remains a serious lack of models combining reliability and robustness. The theoretical aspects and validation of the new model, which rely on a plastic-damage formulation, have been the subject of a former publication; they are briefly summarized here. This paper explores the capabilities of the concrete model for being used in a performance-based structural fire engineering framework. Several examples of numerical simulations by non-linear finite element method are discussed, with emphasis on practical applications that are demanding for the material model. In particular, it is shown that the simulations using the new concrete model succeed in capturing, at ambient temperature, the crack pattern in a plain concrete specimen and the influence of the loading path on reinforced concrete (RC) slabs. At high temperature, the presented applications include a RC slab subjected to furnace fire and a large-scale composite steel–concrete structure subjected to natural fire. In the numerical analyses, no parameter calibration was required on the particular concrete type, except for the uniaxial strengths and tensile crack energy which are to be defined case-by-case. The results illustrate the reliability and numerical robustness of the model. Also, they suggest that satisfactory prediction of structural behavior in fire can be obtained when no additional data is available on the specific properties of the particular concrete mix that is used in the project, as is often the case in practice, by using standard values of parameters. [ABSTRACT FROM AUTHOR]

Highlights: [•] A plastic–damage model for concrete at high temperature is proposed. [•] The unilateral effect is captured by a fourth-order damage tensor. [•] Transient creep strain is explicitly included in the model. [•] The model captures the main thermomechanical phenomena exhibited by concrete. [•] The implications of the coupling between plasticity and damage are discussed. [Copyright &y& Elsevier]

This paper presents an overview of selected issues in computational modeling for reinforced concrete structures in fire. The focus is on current modeling challenges, as well as aspects that are sometimes overlooked yet important for capturing the concrete material and structural behavior at elevated temperatures. Issues addressed include the consequences of realistic thermal exposures with cooling phases on the material properties and deformations, the uncertainties in material and structural response at elevated temperature, and the effect of the tensile fracture energy on the model response. The ability to capture membrane and shear failure modes is analyzed. The modeling of the residual response and potential failure during cooling is discussed. As an example, a five-story RC shear wall-frame building is modeled under natural fire. Finally, the paper ends with a discussion on the limits, research needs and opportunities with respect to computational modeling of concrete structures in fire. • The numerical modeling of concrete structures in fire is a complex endeavor. • Sensitivity of the predicted structural response in shear and membrane modes is discussed. • Tensile behavior and fracture energy are important yet insufficiently characterized. • Numerical failure (lack of convergence) must be distinguished from actual failure. • Still, (reasoned) adoption of numerical models offer great opportunities. [ABSTRACT FROM AUTHOR]

• A method to estimate economic loss due to fire in concrete buildings is presented. • The method is based on sequential analyses for fire hazard, response, damage, and loss. • Fire-specific EDP are proposed to measure thermal and structural damage states. • Fragility and consequences functions are given based on repair cost data. • A case study of a five-story RC building shows the potential of the method. A framework is proposed for the probabilistic estimation of yearly economic losses due to fire in concrete building structures. The fire loss estimation accounts for the uncertainties in the occurrence and growth of a fire as well as the response of the building. The assessment performs a fire hazard analysis, response analysis, damage analysis, and loss analysis. The response analysis relies on three-dimensional finite element modeling of the building structure. The expected direct loss for the building is determined by summing the expected losses under fires in different locations, weighted by the annual probabilities of fire occurrence in each location. To achieve this goal, we propose fire-specific engineering demand parameters (EDP) that are measurable and associated with damage states. One EDP addresses section damage due to temperature penetration, while a second EDP addresses component damage linked to deformations. We also define a set of fragility functions and consequence functions based on the selected damage states. The presented framework is applied to a case study of a five-story reinforced concrete frame building. Direct losses are evaluated at about 188 k$ for scenarios of single-compartment fire, conditional to the occurrence of severe fire. Losses are mostly related to nonstructural components and content. Although the case study focuses on single-compartment fires, losses in case of fire spreading within the building can be incorporated as well using event tree analysis with the conditional probability of the respective fire scenarios. The yearly fire loss framework presented in this paper can be adopted for other types of buildings and can be integrated into the workflow for the hazard vulnerability assessment of a community. [ABSTRACT FROM AUTHOR]

This paper describes a recent development in a finite element software dedicated to the modeling of structures in fire which deals with the way connections are simulated in global structure analyses. This development allows modeling semi-rigid, temperature-dependent connections between beam-type finite elements. It relies on the definition of additional internal degrees of freedom in the elements. The objective is to enable efficient analysis of the influence of semi-rigid connections on the global structural response and on the demands for these connections. The theory and implementation are described in a geometrically non-linear software with large displacements. Then, a 3D frame structure is analyzed as a case study. The analyses show that structural capacity and failure mode depend on the degree of rotational restraint at the beam-column connections and at the base of the columns. The maximum fire resistance is obtained for an intermediate degree of restraint between beams and columns, while higher restraints lead to an unfavorable sway failure mode. The case study illustrates the capabilities introduced by the new development, and demonstrates that the effects of the connections on global response is complex, justifying the need for practical numerical methods for design and parametric analyses of structures in fire. [ABSTRACT FROM AUTHOR]

Adoption of performance-based approaches in structural fire engineering is now largely recognized as having the potential to deliver benefits in terms of safety, resilience, sustainability and cost for the built environment. However, there is no systematic design guidelines for defining performance objectives, design fire scenarios, and methods of analysis. This paper focuses on steel framed buildings with composite floor slabs and provides an in-depth analysis of the structure under fire using performance-based fire engineering supported by computational modeling. First, a set of performance objectives and associated fire scenarios are defined. The scenarios include single- and multi-compartment fires as well as fire as a secondary event following a column loss. Then, response of the structure and effects of design changes are studied using different modeling approaches. Single slab, single slab with restraint, and full building models are investigated to understand the influence of continuity in the boundary conditions notably on the development of tensile membrane action. The full building model exhibited the most favorable behavior, while the single panel model without horizontal restraint was the most conservative. Best practices for computational modeling of a steel framed building under fire are discussed and recommendations are provided. The paper demonstrates an iterative design procedure, where systematic design changes are introduced to address the observed failure modes. It is shown that performance-based fire design can harness advanced computational models to examine the fire-structure behavior for multiple design alternatives and hazard scenarios. • A systematic procedure is applied for performance-based fire design of a building. • Hazard scenarios include low probability multi-compartment fires and column loss. • The procedure rely on nonlinear finite element modeling of the 3D structure. • Design recommendations are given to achieve the target performance objectives. • Modeling recommendations are given on the effects of continuity and restraints. [ABSTRACT FROM AUTHOR]

• Numerical modeling of the fire response of a code-designed RC frame building. • Focus on post-fire damage and deformations as they affect resilience and recovery. • Large residual deformations and loss of capacity are observed in the columns. • Thermal deformations of beams and slabs have large effects on the RC columns behavior. • Models of the structural system are needed to capture these thermal restraint effects. Reinforced concrete (RC) structures often remain stable under fire, but exhibit damage and residual deformations which require repairs. While repair operations and building downtime are expensive, current fire design approaches do not consider post-event resilience. The first step to enable predicting the resilience of RC structures under fire is to develop capabilities to model the damage of these structures after various fire exposures. This paper focuses on the prediction of the residual (post-fire) deformations of RC columns within a code-designed five-story RC frame building. Computational modeling approaches to capture the fire behavior of the columns are investigated. The models range from isolated columns with linear springs at the boundaries to full building model coupling beam and shell elements, with intermediate approaches. The analyses highlight the critical nonlinear role of the thermal expansion-contraction of the surrounding beams and slabs on the column deformations. Large transversal residual deformations develop particularly in perimeter columns, combined with residual shortening. This invalidates models based on isolated column or 2D frame. A parametric study of the residual deformations of RC columns is then conducted, with due consideration of the 3D restraints and interactions, to investigate the effects of different design parameters and fire scenarios on the residual deformations after a fire event. The results of the parametric study indicate that fire load density and opening factor significantly influence the residual deformations of RC columns, compared to the thermal conductivity of concrete and live loads. This research improves the understanding and provides recommendations for numerical modeling of the effect of fire on the residual capacity and deformations in RC structures. [ABSTRACT FROM AUTHOR]

• Fracture experiments were performed on dual-phase steel at temperatures from 20 to 700 °C. • Five specimen shapes were used to generate stress triaxialities from 0 to 0.51. • Finite element analyses with a plasticity-damage model were calibrated on the experiments. • The dependency of the damage and fracture initiation strains with stress state and temperature was identified. • The calibrated material model can be used to simulate fracture of steel members in fire. Structural steels can be subjected to a range of stress and temperature conditions, and accurate characterization of their limit states is a requirement for structural design. Yet data on ductile fracture at elevated temperatures remains relatively scarce especially for high-strength steel grades. This paper describes an experimental and numerical investigation of the ductile fracture of a high-strength dual-phase steel under multiaxial stress states at temperatures up to 700 °C. Experiments were carried out on five geometries of specimens and at four temperatures to identify the temperature-dependent fracture locus across a range of stress triaxialities. Finite element analyses of the experiments provided the equivalent strain at fracture initiation. It was found that the fracture initiation strain varies markedly with stress triaxiality and increases with temperature. The effect of strain rate become significant at 500 °C. A temperature-dependent plasticity-damage model was calibrated to predict ductile fracture initiation in the dual-phase steel. The proposed model can be used in finite element analyses to support performance-based design of steel structures at elevated temperatures resulting from accidental events such as fire. [ABSTRACT FROM AUTHOR]

• Machine Learning (ML) is applied to predict the capacity of slender steel columns in fire. • A validated shell finite element model is used to generate the dataset. • Artificial neural networks (ANN), support vector regression (SVR), and polynomial regression (PR) models are considered. • The trained ML models outperform state-of-the-art analytical design methods. • The ANN and PR models accurately capture experiments not seen in the training dataset. Due to the interaction between local and global instability modes at elevated temperatures, predicting the capacity of thin-walled columns in the fire situation is a complex endeavor. This work investigates the application of machine learning techniques to assess the resistance of slender steel columns with I-shaped cross-sections at elevated temperatures. First, a validated finite element model is used to evaluate the columns' response and generate a large dataset for a range of cross-sections, slenderness, and temperature. The dataset is then used for training and testing machine learning models based on support vector regression, artificial neural network, and polynomial regression. The machine learning models outperform the current analytical design method for the training and testing datasets, demonstrating the potential usefulness of data-based methods for structural fire design. The limits of the approach are explored by applying the trained models for predicting experiments with features outside those of the dataset. The results suggest that machine learning techniques can be used to derive efficient surrogate models for the capacity prediction of slender steel members in fire within the boundaries of the training dataset. [ABSTRACT FROM AUTHOR]

For thin-walled beams in fire, the development of simple analytical models is hindered by the complexity of the interaction between local and lateral-torsional buckling combined with the temperature reduction of steel properties, resulting in overly conservative fire design rules. This paper investigates the application of machine learning models to predict the capacity of steel beams with thin-walled sections at elevated temperatures. Machine learning models provide a pathway to deliver fast and accurate methods to predict complex non-linear problems, which may overcome limitations of existing design methods, time-consuming finite element simulations, and expensive laboratory tests; yet these models remain unexplored in this particular field of study. This work describes the development, validation, and application of artificial neural networks, support vector machines, polynomial regression and random forests using an extensive dataset of numerical results from previously validated finite element models. It is shown that these models can also predict the capacity for beams with loading and boundary conditions outside the training dataset range. Finally, the machine learning models are compared against existing design proposals to demonstrate the benefits of using these advanced techniques to calculate the capacity of thin-walled beams at elevated temperatures. [ABSTRACT FROM AUTHOR]

The objective of this paper is to provide experimental results related to the elevated temperature performance of connections between cold-formed steel members and sheathing. Cold-formed steel building structures rely on sheathing for their mechanical benefits including bracing against member twist, global flexural and flexural-torsional buckling, and cross-section distortional buckling, as well as to supply lateral strength and energy dissipation in shear walls and diaphragms. Sheathing is also relied upon for non-structural benefits, including: fire, acoustic, and thermal performance. Predicting the degradation of the connection performance between cold-formed steel members and sheathing at elevated temperature is critical for any attempt to predict the structural performance of cold-formed steel buildings under fire demands. Steady-state connection tests were conducted under in-plane shear and pull-through at temperatures up to 400 °C for cold-formed steel members attached to gypsum board and oriented strand board. By combining the conducted tests with others in the literature retention factors for initial stiffness and ultimate strength of the connections are proposed. • Sheathing bracing is critical to the performance of cold-formed steel studs employed in buildings. • Performance of OSB and gypsum sheathing connections degrade precipitously with elevated temperature causing a loss of stud bracing. • Fire performance-based design of CFS structures is enabled through retention factors for cold-formed steel-to-sheathing connections. [ABSTRACT FROM AUTHOR]

Strap-braced, cold-formed steel framed walls are frequently used as the lateral force resisting system in cold-formed steel construction. While the behavior of these walls has been studied under lateral loading and (to a lesser extent) under fire conditions, there is a need to comprehend the influence of multi-hazard interactions, in particular the effect of fire pre-damage on the lateral load resistance of the walls. In this paper, a numerical model of a strap-braced cold-formed steel wall is developed to analyze the thermal and structural response when subjected sequentially to fire followed by shear deformation. The numerical model is validated against full-scale experiments. Coupon tensile tests are conducted to characterize the post-fire properties of the cold-formed steel that are used as inputs to the model. The results show that the numerical model can capture the post-fire response of the cold-formed steel walls including the wall strength, stiffness and ductile failure by yielding of the strap. The lateral behavior of the walls depends primarily on the maximum temperature reached in the cold-formed steel members and the resulting residual properties. Thermal analysis by the finite element method can be used to predict the maximum temperatures across a wall section under a variety of design-relevant fire scenarios, but the results are strongly affected by the quality of the data on thermal properties and by the loss of integrity of the gypsum sheathing. This study validates the numerical modeling strategy and suggests that the post-fire lateral capacity of the walls can be predicted from ambient temperature methods with use of the cold-formed steel residual mechanical properties. • Propose a numerical strategy to assess the post-fire lateral capacity of CFS strap-braced walls. • Conduct new material tests to obtain the post-fire retention factors for CFS. • Simulate four experimental tests to validate the proposed numerical strategy. • Capable to model the failure mode, stiffness and ultimate strength of fire-damaged CFS walls. [ABSTRACT FROM AUTHOR]

This paper assesses the stability and strength of sheathed cold-formed steel studs at elevated temperatures. Short and intermediate-length studs braced with gypsum, fire-rated gypsum, and oriented strand board were subjected to compressive axial load and temperatures ranging from 20 °C to 600 °C. A total of 40 tests were conducted in the steady-state regime, where the studs were first heated, then a compressive axial load was applied until failure occurred. Results show that the load-carrying capacity of the structural members decreases with increasing temperature, as the mechanical properties of the cold-formed steel reduce, and the bracing provided by the sheathing degrades. Local and distortional cross-section buckling failures are observed in the cold-formed steel member. The stabilizing effect and increase of load-carrying capacity attributed to the sheathing at ambient temperature is eventually lost at elevated temperature and the behavior of the sheathed studs becomes similar to the behavior of unsheathed members. Direct Strength Method design equations provided in the U.S. AISI S100 design specification are used with experimentally determined elevated temperature properties to predict the load-carrying capacity of the studs, then compared to experimental results to explore the feasibility of current design methods for performance-based fire design applications. • Degraded strength of sheathing-braced cold-formed steel studs is measured as temperature is increased. • OSB sheathing provides beneficial bracing for temperatures less than 350 °C while fire-rated and normal gypsum boards provide sheathing bracing for temperatures less than 600 °C. • The Direct Strength Method of AISI S100 can reliably be extended to predict the strength of uniformly heated bare and sheathed studs at elevated temperature. [ABSTRACT FROM AUTHOR]