Ann E. Jeffers

Fiber Heat Transfer Element for Modeling the Thermal Response of Structures in Fire

This paper introduces a novel type of heat transfer finite element that can be used to model the three-dimensional thermal response of structural beams and columns subjected to elevated temperatures associated with fire. The element is a three-node heat transfer element that uses a fiber discretization to account for both transverse and longitudinal temperature variations in a structural member. This fiber heat transfer element is purposely formulated to be compatible with any fiber beam-column finite element in a sequentially coupled thermal-mechanical analysis of a structural frame subjected to fire. The element is implemented in ABAQUS using a user-defined element subroutine. To demonstrate the capabilities of the fiber heat transfer element, analyses are performed on members with various types of thermal boundary conditions. Results indicate that the fiber heat transfer element offers excellent accuracy with minimal computational expense, making the fiber heat transfer element a valuable tool for modeling the behavior of frame structures in fire.

Finite-Element Reliability Analysis of Structures Subjected to Fire

AbstractA reliability-based design methodology is urgently needed in the fire resistant design of structures to ensure adequate reliability in the face of uncertainty. This paper presents the application of the analytical reliability methods, namely the first-order reliability method (FORM) and second-order reliability method (SORM), to the design of structures subjected to fire. In particular, the FORM and SORM algorithms are implemented in a sequentially coupled thermal-structural finite-element model. A protected steel column exposed to natural fire is presented as an example. In comparison to Latin hypercube sampling (LHS), the analytical reliability method yields sufficient accuracy and provides a significant saving in computational expense. Discrepancies between the analytical methods and LHS are analyzed in depth, and it is shown that the parametric fire model produces a response surface that is highly nonlinear. Despite differences between the FORM and LHS solutions, the utilization of FORM is rec...

Analysis of Steel Structures in Fire with Force-Based Frame Elements

This paper considers the extension of the force-based element formulation to simulate the nonlinear, temperature-dependent response of structural frames exposed to fire. The two-dimensional formulation presented here accounts for thermal expansion, temperature-dependent material properties, and residual stresses. The element utilizes a fiber discretization to simulate the gradual plastification of the section. Geometric nonlinearities are included through coordinate transformations of the corotational reference frame. Analyses of benchmark experimental tests demonstrate that the force-based element formulation is computationally stable and provides accurate results for structures exposed to fire. In addition, comparisons to traditional displacement-based elements indicate that the force-based element may offer improved computational efficiency because fewer elements are needed per member.

Combining Load-Controlled and Displacement-Controlled Algorithms to Model Thermal-Mechanical Snap-Through Instabilities in Structures

This paper presents an analysis of thermal-mechanical snap-through instabilities in structures using a hybrid load-controlled/displacement-controlled algorithm. The derivation uses the finite element method with a combination of modified Newton-Raphson and arc-length methods, aimed at providing a robust and efficient means for modeling the buckling response of structures that exhibit instability in the presence of nonuniform time-varying temperature fields and temperature-dependent material response. Load control is used to model the system’s response up to the point of instability, which is identified using the method of bisections. During the instability, the analysis switches to displacement control to capture the load-shedding behavior. Once a stable point is reached, the algorithm switches back to load control. The novelty lies in the ability of the hybrid algorithm to model instabilities that are caused by material degradation under nonuniform transient temperature fields, which is particularly important in the study of structural response under fire hazards. Numerical analyses are carried out using a two-dimensional (2D) fiber-based corotational beam element. Verifications at room temperature and at elevated temperature demonstrate that the proposed approach exhibits a high level of accuracy. A brief study of toggle frames subjected to various types of heating and loading conditions is presented to illustrate the kinds of behaviors that can be captured with the proposed modeling approach.

Triangular Shell Heat Transfer Element for the Thermal Analysis of Nonuniformly Heated Structures

AbstractThis paper presents a triangular shell heat transfer element that is used to simulate the thermal response of nonuniformly heated structures. The formulation uses a combination of finite-element and control volume techniques to arrive at a layered shell element that is used to solve the 3D conduction heat transfer problem in a highly efficient manner. This paper considers a 3-node linear element and a 6-node quadratic element. The element formulation is verified against a converged continuum heat transfer model for a thick steel plate exposed to a concentrated heat flux, a thick steel pipe exposed to a concentrated heat flux, and a concrete slab exposed to a localized fire. The verification studies demonstrate that the linear and quadratic elements consistently converge to the continuum model and require a fraction of the computational cost. The verification study involving the concrete slab exposed to a localized fire demonstrates that the formulation can readily handle steep temperature gradient...

Stochastic Analysis of Structures in Fire by Monte Carlo Simulation

This paper describes a preliminary study to explore the use of Monte Carlo simulation to assess the reliability of structures in fire given uncertainty in the fire, thermal, and structural model parameters. The methodology requires (1) the probabilistic characterization of the uncertain parameters in the system, (2) a stochastic model for the thermo-structural response, and (3) a limit state function that describes the failure of the system. The study focuses on assessing the failure probability of a protected steel beam under natural fire exposure. The system was modeled stochastically using a series of sequentially coupled thermo-structural finite element analyses that were embedded within a Monte Carlo simulation. Although the example considered here is relatively simplistic in that it focuses on member level performance, it effectively demonstrates the application of the proposed reliability method and provides insight into the practicalities of extending the approach to more complex structural systems.

Robustness assessment of a generic steel fire-protected moment-resisting frame under travelling fire

Due to their vulnerability to high temperatures, steel structures are typically protected against fire by insulation materials, as recommended by fire codes. The fire resistance rating of a protected member is determined based on a standard fire test, which simulates post-flashover fire conditions. Empirical evidence has shown that fires in large open-plan compartments do not burn uniformly, and a method called “traveling fire” has been introduced in previous research to simulate the effects of spreading fires. An investigation is performed here to examine the robustness of a generic four-story moment-resisting steel structure with one-hour fire resistance rating subjected to travelling fire. Various fire sizes are considered: 12.5, 25, 50 and 100% of the floor area. The results show that while no collapse occurs during the 12.5, 50 and 100% fire sizes, the structure collapses under the 25% fire size at 85 min due to the inability of the system to transfer the load after one of the columns buckles. This seems to be in contradiction with traditional belief that a fire covering a larger portion of the floor plan would reduce the safety margin. The investigation performed underlines that the fire protection of structures based on the standard time-temperature curve does not necessarily provide adequate resistance under travelling fires. With the lack of adequate fire regulations codified for large compartments, more research is required before arriving at a better understanding of the application of travelling fire to large compartments.

Performance of Axially Restrained Hollow and Concrete Filled Oval Steel Columns Subjected to Hydrocarbon Fire

This paper represents the outcomes of the first research in the world involving experimental and validated theoretical study to investigate the performance of axially restrained steel columns with hollow and concrete filled elliptical sections subjected to fire. The test programme involved 9 hollow and concrete filled columns with 200 × 100 × 8 mm oval section yielding a slenderness λ=51 and tested under the severe hydrocarbon fire curve. The 1800 mm columns were tested under loading ratios = 0.2, 0.4 and 0.6 of the ultimate strength. The paper presents the obtained experimental results including measured axial and lateral displacements, restraint forces and failure time. A three-dimensional model was built using the finite element method (FEM) and was validated using the obtained tests results. By using variable with temperature thermal expansion coefficient and the EC3 thermal parameters, the finite element model demonstrated an excellent agreement with test results of failure temperatures, failure modes, axial displacements and generated axial forces. The verified finite element model was used to conduct a parametric analysis involving a range of parameters of loading level and slenderness. The study has shown that the concrete filled sections have demonstrated an improved fire resistance when compared to the hollow sections under low loading ratios. The research indicates that imposing axial restraint has reduced the fire resistance of columns by approximately one third on the time domain. The study has also shown a non-linear relationship between the loading ratio and slenderness of elliptical columns and that the load ratio has more effect on fire resistance of columns with high slenderness.

Computational simulation of steel moment frame to resist progressive collapse in fire

Purpose This paper aims to address a need for improving the structural resilience to multi-hazard threats including fire and progressive collapse caused by the loss of a column. Design/methodology/approach The focus is on a steel moment frame that uses welded-unreinforced flange-bolted web connections between the beams and columns. A three-dimensional finite element (FE) model was created in ABAQUS with temperature-dependent properties for steel based on the Eurocode. The model was validated against experimental data at ambient and elevated temperature. Findings The failure mechanisms in the FE model were consistent with experimental observations. Two scenarios were considered: fixed load with increasing temperature (i.e. simulating column failure prior to fire) and fixed temperature with increasing load (i.e. simulating column failure during fire). Originality/value A macro element (or component-based) model was also introduced and validated against the FE model and the experimental data, offering the possibility of analyzing large-scale structural systems with reasonable accuracy and improved computational efficiency.

Effect of span length on alternate path capacity of welded unreinforced flange-bolted web connections

In this study, the effect of span length on progressive collapse resistance capacity of Welded Unreinforced Flange-Bolted web (WUF-B) connections was investigated by using the alternate path method as per Unified Facilities Criteria (UFC). Towards this aim, several nonlinear analyses were performed for three generic moment resisting frames with WUF-B connections considering various span lengths. In order to reduce the simulation time, a macro-element, or component-based model is introduced and verified against the NIST test results. The analysis results revealed that for a certain frame length, by decreasing the span length (increasing the number of spans) as an indirect approach, it is possible to enhance the alternate path capacity WUF-B connections and decrease the risk of progressive collapse occurrence. For example, for the cases studies here, it was shown that by decreasing the span length to half the failure overload factor of the frame increases more than twice.