Simulation Methodology for Coupled Fire-Structure Analysis

Fire Technology manuscript No.(will be inserted by the editor)

⋆Simulation Methodology for Coupled Fire-StructureAnalysis:

Modeling localized fire tests on a steel column

Chao Zhang · Julio G. Silva · CraigWeinschenk · Daisuke Kamikawa · YujiHasemi

Received: date / Accepted: date

Abstract Advanced simulation methods are needed to predict the complexbehavior of structures exposed to realistic fires. Fire Dynamics Simulator(FDS) is a computational fluid dynamics (CFD) code, developed by NIST forfire related simulations. In recent years, there has been an increase in use ofFDS for performance-based analysis in the area of structural fire research. Thispaper discusses the FDS-FEM (finite element method) simulation methodol-ogy for structural fire analysis. The general methodology is described and a

⋆ Accepted manuscript, Uncorrected proof. cite as Zhang, C. et al.. (2015). ”SimulationMethodology for Coupled Fire-Structure Analysis: Modeling localized fire tests on a steelcolumn” Fire Technology. ,DOI: 10.1007/s10694-015-0495-9

C. ZhangNational Institute of Standards and Technology, Fire Research Division, 100 Bureau Drive,Stop 8666, Gaithersburg, MD 20899-8666, USATel.: +1 301 9756695Fax: +1 301 9754052E-mail: [email protected]

J.G. SilvaNational Institute of Standards and Technology, Fire Research Division, 100 Bureau Drive,Stop 1070, Gaithersburg, MD 20899-1070, USA

C. WeinschenkNational Institute of Standards and Technology, Fire Research Division, 100 Bureau Drive,Stop 1070, Gaithersburg, MD 20899-1070, USA

D. KamikawaWaseda University, Department of Architecture, Okubo 3-4-1, Shinjuku-ku, Tokyo, JapanPresent address: Forestry and Forest Products Research Institute, Matsunosato 1, Tsukuba,Ibaraki, Japan

Y. HasemiWaseda University, Department of Architecture, Okubo 3-4-1, Shinjuku-ku, Tokyo, Japan.

2 Chao Zhang et al.

validation study is presented. A data element used to transfer data from FDSto FEM codes, the adiabatic surface temperature, is discussed. A tool namedFire-Thermomechanical Interface (FTMI) is applied to transfer data from FDSto ANSYS. A high temperature stress-strain model for structural steel devel-oped by NIST is included in the FEM analysis. Compared to experimentalresults, the FDS-FEM method predicted both the thermal and structural re-sponses of a steel column in a localized fire test. The column buckling timewas predicted with a maximum error of 7.8%. Based on these results, thismethodology has potential to be used in performance-based analysis.

Keywords CFD-FEM simulation method · Structural fire analysis · FireDynamic Simulator (FDS) · Fire-Thermomechanical Interface (FTMI) ·Adiabatic surface temperature · Finite element simulation · Localized fires ·Steel column · Validation study

1 Introduction

In the event of fire, buildings should retain structural stability for a specifiedperiod of time to allow for full evacuation. Traditionally, structural componentsare required to fulfill the fire resistance ratings specified in prescriptive codes.The fire resistance rating of a building component is determined by a standardfire resistance test conducted on an isolated member subjected to a specifiedtime temperature curve. The standard fire resistance test, which was developedmore than a century ago, has a number of shortcomings [1]. For example, theheating used in the test bears little resemblance to a real fire environmentand the behavior of isolated members cannot represent the behavior of thecomponents in an entire structure [2]. As a result, the design approach based onprescriptive codes cannot assess the actual level of safety of a structure exposedto a fire and usually yields a fire protection design that is too conservativeand lacks certainty of the value of the safety factors [3]. Considering greenconstruction is pushing design for more sensible usage and conservation ofmaterials, the use of fire protection materials which can be shown not tobe wasteful is important. It should be noted, however, that a fire protectiondesign based on a standard test or prescriptive code is not guaranteed to beconservative [4–6].

Over the past 30 years, there have been significant advances in structuralfire research. New insights, data, and calculation methods have been reported,which form the basis for modern performance-based (PB) codes for structuralfire safety [7]. The PB approach involves the assessment of the structural re-sponse in real fires and, therefore, requires advanced computational approachesfor fire and structural modelings. Sophisticated computational fluid dynamics(CFD) models are typically used to simulate realistic fires [8–10], while finiteelement method (FEM) codes are mostly used for structural modeling [10,11].An integrated CFD-FEM simulation approach is needed for advanced struc-tural fire analysis [12].

⋆Simulation Methodology for Coupled Fire-Structure Analysis: 3

Fire Dynamics Simulator (FDS) is an open source CFD code, developedby NIST [13]. It has been widely used in fire engineering for modeling thegas phase environment (temperature, heat flux, velocity, species concentra-tions, etc.) in fires [14, 15]. Recently, there has been increased research in theapplication of FDS for structural fire analysis [16–20]. Fire-structure inter-face tools for transferring data from FDS to particular FEM codes (such asANSYS, ABAQUS, SAFIR) have been developed [19, 21, 22]. Although bothFDS and FEM codes have been separately validated, there needs to be adirect validation for the integrated FDS-FEM simulation methodology. Thispaper validates the integrated FDS-FEM simulation methodology against alocalized fire test on steel columns reported by Kamikawa et al. [23]. Se-quential coupled fire-thermal-mechanical simulations are conducted. Two fire-structure interfaces are used in this paper, the DEVICE approach and theFire-Thermomechanical Interface (FTMI) tool [24, 25]; both interfaces trans-fer data between FDS and the commercial software ANSYS 1. A new hightemperature stress-strain model for structural steel developed by Luecke etal. [26] is used in the structural analysis.

Fires in the open or in large enclosures are characterized as localized fires,e.g. vehicle fires in transportation infrastructure [27], small shop fires in trans-port terminal halls [28], and workstation fires in open plan office buildings [29].Compartment fires begin as fires with localized burning. The current structuralfire design approaches are developed for fully-developed compartment fires,the gas temperatures of which can be approximated as uniformly distributedin the compartment. In localized fires, the gas temperature distributions arespatially non-uniform. Because of the thermal gradient, the failure model andfailure temperature of structural members in a localized fire might be differentthan those of the members in uniform heating conditions (e.g. the standardfire condition) [4–6]. Consideration of localized fires is important for safetyof structures in the modern buildings with large enclosures. From literature,e.g. [1], realistic fire test data for model validation are quite limited, especiallyfor modeling structure response to non-uniform heating conditions. This lo-calized fire test was selected for model validation because of the applicabilityto real-world thermal conditions and because the test was well controlled (e.g.the heat release rate of the fire was controlled by computer, and the axial loadwas applied by oil jack controlled by electric hydraulic pump), and detailedlymeasured (e.g. temperatures on all typical sides of the test specimen weremeasured by series of thermocouples).

1 Certain commercial entities, equipment, or materials may be identified in this documentin order to describe an experimental procedure or concept adequately. Such identification isnot intended to imply recommendation or endorsement by the National Institute of Stan-dards and Technology, nor is it intended to imply that the entities, materials, or equipmentare necessarily the best available for the purpose.

4 Chao Zhang et al.

2 Methodology

2.1 The CFD-FEM approach

Fig. 1 illustrates the CFD-FEM simulation approach for structural fire anal-ysis. The fire-structure interaction is fundamentally two-way, while one-waycoupling may be advantageous under certain conditions [12]. In a one-waycoupling, the Navier-Stokes equations, radiation transport equations, etc., forthe fluid domain in a fire compartment are solved for the complete time du-ration of interest by a CFD code to get gas temperatures, velocities, chemicalspecies, incident heat fluxes, film coefficients, etc. The heat equations for thesolid domain (building elements) use the thermal boundaries from the CFDsimulation to get the thermal response (temperature rise) within the build-ing elements. Kinematics equations, constitutive equations, etc., for the soliddomain are solved by a FEM code to get the deformations, stresses, strains,etc. Fire-structure and thermo-mechanical interfaces are used to transfer databetween different models. In a two-way coupling, the same set of equationsis solved except that at discrete time steps through the simulation the solidphase FEM code provides feedback to update the CFD model.

2.2 The FDS code

Fire Dynamics Simulator is a large-eddy simulation (LES) based CFD code [13].For the simulations performed in this study, FDS version 6.1.1 was used. LESis a technique used to model the dissipative processes (viscosity, thermal con-ductivity, material diffusivity) that occur at length scales smaller than thosethat are explicitly resolved on the numerical grid. In FDS, the combustion isbased on the mixing-limited, infinitely fast reaction of lumped species, whichare reacting scalars that represent mixtures of species. Thermal radiation iscomputed by solving the radiation transport equation for gray gas using theFinite Volume Method (FVM) on the same grid as the flow solver. FVM isbased on a discretization of the integral forms of the conservation equations. Itdivides the problem domain into a set of discrete control volumes (CVs) andnode points are used within these CVs for interpolating appropriate field vari-ables. The governing equations are approximated on one or more rectilineargrids. Obstructions with complex geometries are approximated with groupsof prescribed rectangles in FDS. One-dimensional (1D) heat conduction is as-sumed for solid-phase calculations. Detailed descriptions of the mathematicalmodels used in FDS can be found in [30].

2.3 The fire-structure one-way coupling

Heat can be transferred from flames and hot gases to structures by radiationand convection. The net heat flux q̇′′ can be defined by the sum of these two


terms:

q̇′′ = εs(q̇′′in − σT 4

s ) + hc(Tg − Ts) (1)

where εs is emissivity of the exposed surface; q̇′′in is incident radiative flux;Tg is temperature of the surrounding gas; Ts is temperature of the exposedsurface; hc is film coefficient; and σ is Stefan-Boltzmann constant.

Advanced fire simulation models (such as FDS) are capable of providingthe three-dimensional evolution of the fire, the incident radiative flux and thetemperature within the gas phase. Nevertheless, these software packages arenot typically capable of accurately evaluating temperature distributions insolids. Therefore, the total heat flux to a solid may not be correctly calculatedat the end of the fire simulation and an additional approach is necessary.

2.3.1 The concept of adiabatic surface temperature

Consider an ideal adiabatic surface exposed to a heating condition; the netheat flux to the surface is by definition zero, thus

εAS(q̇′′in − σT 4

AS) + hc,AS(Tg − TAS) = 0 (2)

where εAS is emissivity of the adiabatic surface; TAS is temperature of theadiabatic surface or adiabatic surface temperature; and hc,AS is film coefficientbetween the adiabatic surface and the surrounding gas.

From Eq. 2, the incident radiative flux to a surface can be calculated froman adiabatic surface temperature,

q̇′′in =hc,AS(TAS − Tg)

εAS+ σT 4

AS (3)

Consider a real surface exposed to the same heating condition, the net heatflux to the surface can be calculated by

q̇′′ = εsσ(T4AS − T 4

s ) +εsεAS

hc,AS(TAS − Tg) + hc(Tg − Ts) (4)

If the emissivity of the adiabatic surface is taken as the emissivity of the realsurface (εAS = εs), and the film coefficient between the adiabatic surface andthe surrounding gas is equal to the film coefficient between the real surfaceand the surrounding gas (hc,AS = hc), we get

q̇′′ = εsσ(T4AS − T 4

s ) + hc(TAS − Ts) (5)

Eq. 5 shows that the net heat flux to a surface can be approximatelycalculated by using a single parameter TAS . In practice, the adiabatic surfacetemperatures of interest can be approximately measured by a plate thermome-ter [31]. Consider the case at high temperature (above about 400 ◦C), whereconvection is not the dominant mode of heat transfer in fire [32]; from Eq. 4or 5 the adiabatic surface temperature measured by a plate thermometer canbe used to predict the net heat flux to a surface with a different emissivity.

6 Chao Zhang et al.

FDS [13] includes an output quantity of adiabatic surface temperature calcu-lated by Eq. 5 according to the idea proposed by Wickstrom [33]. It shouldbe noted that the calculated adiabatic temperature of a surface is fundamen-tally influenced by the convection or film coefficient (see Eq 4) so that thevalue for film coefficient should be carefully selected when using the conceptfor calculations where convection is important [34].

2.3.2 The DEVICE approach in FDS

In FDS, point measurements (devices) can be used to record the adiabaticsurface temperatures. The output adiabatic surface temperatures (with anassumed constant film coefficient) are converted to inputs to the FEM thermalmodel. The data points are interpreted as the effective black body temperatureand bulk (gas) temperature to calculate the radiative and convective heatfluxes to the structural elements, respectively. Because point measurementsare used, it can be intractable to have measurement devices located in everycomputational cell where the solid has an exposed surface. Therefore, linearinterpolation is used to determine the adiabatic surface temperature betweentwo recorded data. This is called the DEVICE approach for fire-structurecoupling.

One limitation of this approach is measurement density. It may not beknown a-priori where the point measurements need to be to capture the nec-essary adiabatic surface temperature (AST) gradients. A lack of appropriateAST resolution could have an impact on the FEM analysis for predictingstructural behavior. Additionally, for CFD models with complex geometry,this issue could become more significant. A second limitation is the use ofa constant film coefficient. Following normative procedures [35] this variableis usually considered a constant [17]. However, its value drives whether heattransfer is dominated by radiation or convection. Also, the spatial distributionand temporal evolution during the fire can be important for calculating theheat flux from the fire simulation for thermo-mechanical analysis. As discussedin Section 2.3.1, an improper selection of the film coefficient can influence theheat flux and the resulting FEM analysis.

2.3.3 The Fire-Thermomechanical Interface (FTMI)

The goal of the FTMI model is to create the appropriate boundary conditionbetween the fire simulation and the thermo-mechanical analysis. Followinga CFD fire simulation, the heat flux is evaluated in the thermo-mechanicalmodel using Eq 5, depending on TAS and hc obtained by the fire simulationand the surface temperature calculated at each time step during the thermo-mechanical analysis.

To correctly calculate the heat flux, boundary condition information mustbe passed from CFD to FEM models. In this task, the exposed surfaces in theFEM model need to be mapped to the same surfaces from the CFD model [24].


This mapping is realized by a collection of I keypoints (of x coordinates) local-ized at the center of each external face (with normal n), as illustrated in Fig. 2.The position and the number of I keypoints is based on the mesh generatedfor the thermo-mechanical analysis. In this way, the coupling procedure canbe achieved for different discretization levels. Also, small modifications anddimensioning to the structural model does not require the CFD solution tobe recomputed, as the data can be remapped. This also allows for data to beproperly transfered from the CFD model to the FEM model without requiringthe two models to have identical computational meshes.

To compute this mapping, a Fortran code was written (fds2ftmi [24, 25]).This code is based on the fds2ascii routine [13], which was written to parse FDSbinary output files. Basically, fds2ftmi traces the exposed surfaces in the FEMmodel (ANSYS), defines and collects the I keypoints and the corresponding nnormals (related to the element surface). Based on each I keypoint position,the code is able to search into the output data from FDS to iterate over time,orientation, and mesh, and then pass the correct surface thermal exposureresults (TAS , hc) into a ANSYS APDL language script file.

In the ANSYS model, the goal of this interface procedure is to create aniterative solution capable of using the surface temperature (obtained at eachtime step during the thermo-mechanical analysis) to evaluate the heat fluxat each node of the exposed surface through Eq 5. Therefore, the surfaceeffect element SURF152 (ANSYS nomenclature) is employed. This element isattached to the solid or shell elements to prescribe a boundary condition. Inthis case, it applies a heat flux vector at each node of the exposed surfacebased on Eq 5. The adiabatic surface temperature needs to be prescribed atthe element’s extra node and film coefficient is applied at the element’s surface.If this procedure is used with shell elements, the heat flux vector is calculatedand prescribed at the top and bottom layers of the shell section.

2.4 Thermal-structure interface

ANSYS offers two distinct methods for thermal-structure analyses: the directmethod and the load transfer method. The direct method usually involves justone analysis that contains all necessary degrees of freedom: displacements, ro-tations, and temperatures. The thermal and structural calculations are cou-pled by the interal solver in ANSYS. This method is advantageous when thecoupled interaction involves strongly-coupled physics or is highly nonlinear.Unfortunately, the direct method works only for a specific set of bilinear solidselements (hexahedrons and tetrahedrons). Use of these elements can becomecomputationally expensive.

In the load transfer method, the thermal and structural analyses are solvedindependently. The results from the thermal analysis are applied as loads inthe structural analysis. For coupling situations which do not exhibit a highdegree of nonlinear interaction, the load transfer method is more efficient andflexible [36]. Also, this method works with more element types, including shell

8 Chao Zhang et al.

and beams elements, which are extensively used to model global structures [22].In this study, the load transfer method is used for coupled thermal-structureanalysis. The temperature data from heat transfer analysis are transferred tothe mechanical model for structural analysis. Thermal shell element SHELL131and structural thermal element SHELL181 are used in the ANSYS analyses.Previous work conducted at NIST [22] focused on transferring data betweenthe thermal analysis and the structural analysis, including cases with differentmeshes and different element types. In this analysis, the element type andmesh remained the same for both the thermal and structural computations.

3 Validation study

3.1 Description of the experiment from Kamikawa et al. [23]

Fig. 3 shows the experimental setup [23]. A 0.3 m square diffusion burner waslocated just beside a square steel column (STKR400, 0.1 m × 0.1 m, 3.2 mmthick and 1.6 m tall). Propane was used as the fuel, and the heat release rate(HRR) was 52.5 kW. The height of the burner was 0.25 m (from the base ofthe column). Four tests (cases) with various loading and restraint conditionswere conducted. A new column specimen was used for each test. In all cases,the column was fixed at the base. In this paper, just case 1 and case 4 areconsidered, the names are kept for easier comparison to the previous work.Case 1 was intended to address the thermal expansion due to heating andbending due to the thermal gradient. Therefore, the structure was unrestrainedexcept for the base. The fire was extinguished after 60 min, when the columnbehavior (temperature and displacement) reached steady-state. In case 4, thehorizontal displacement toward the fire source was restrained; Fig. 4 showsthe locations of the vertical and horizontal displacement restraints. Also, avertical force was applied and increased gradually after the steel temperaturein the column became steady (about 52 min after ignition); the column buckledabout 90 min after ignition with a vertical force of approximately 374 kN. Thefire was extinguished only after the column buckled.

In all cases, the temperature distributions of the column side surfaces, thehorizontal displacements at various heights, and the vertical displacement atcolumn top were measured. Temperatures were measured by K-type (chromel-alumel) thermocouples (0.65 mm bead diameter) fixed on column side surfaceswith spot-welded steel foil. Tension coupon tests were conducted to obtain themechanical properties of the steel. Fig. 5 shows the measured stress-straincurves at various temperatures for the steel as well as those produced fromthe material model developed by Luecke et al. [26]. The material model isdiscussed in detail in Section 3.2. The elastic modulus and yield strength (offsetyield point at 0.2% strain) at ambient temperature are about 202,000 MPa and400 MPa, respectively. The material model is discussed in detail in Section 3.2.

An uncertainty analysis was not conducted as part of the experimentalanalysis. For discussion of the experiments, the nominal values for the fire size


and loads applied are presented. For experimental data presented, measure-ment uncertainty presented is from representative values found in literature.For thermocouple measurements of surface temperature on exposed steel, theuncertainty, for elevated steel temperatures (T > 300 ◦C), can be estimatedto be +1 ◦C to -9 ◦C [37]. For displacement measurements during fire tests,the uncertainty can be estimated to ±3 % [38].

3.2 Material properties

To appropriately model the response of the exposed steel member, its materialproperties need to be defined. Thermal properties for structural steel specifiedin the Eurocode [39] were used. Figs. 6 and 7 plot the temperature-dependentspecific heat and thermal conductivity for structural steel, respectively. Theemissivity of steel was taken as 0.9, typical for steel in fire conditions. Formechanical properties, the stress-strain model developed by Luecke et al. [26]was used. While stress-strain measurements were performed as part of theseexperiments [23], experimental data may not always be available. Therefore,to be more representative of a practical engineering application, a model formechanical properties was used. The model is defined by the following set ofequations [26]

σ = εET (ε ≤ fyTET

) (6a)

σ = fyT + (k3 − k4fy20) exp[−(T

k2)k1 ](ε− fyT

ET)n (ε ≥ fyT

ET) (6b)

with k1 = 7.820, k2 = 540 oC, k3 = 1006 MPa, k4 = 0.759, and n = 0.503.The elastic modulus and yield strength at elevated temperature are give by

ET

E20= exp[−1

2(T − 20

639)3.768 − 1

2(T − 20

1650)] (7)

andfyTfy20

= 0.09 + 0.91 exp[−1

2(T − 20

588)7.514 − 1

2(T − 20

676)] (8)

respectively. Where E20, ET are elastic modulus of steel at room and elevatedtemperatures, respectively; and fy20, fyT are yield strength of steel at roomand elevated temperatures, respectively. Fig. 5 also shows the stress-straincurves calculated by Eq. 6 using the measured ambient temperature elasticmodulus and yield strength. The constitutive model is a creep free model [26]while creep strains have not been subtracted from the total measured strains.Creep is usually regarded to be important for temperatures above 400 oC [40].Therefore, there are divergences between the measured and calculated stress-strain curves.

The equation for thermal expansion coefficient recommended by NIST TN1681 [41] was used

αs = 1.17× 10−5 + 1.34× 10−8T − 9.7× 10−12T 2 + 1.67× 10−16T 3 (9)

10 Chao Zhang et al.

3.3 Numerical models

Fig. 8 shows the FDS model geometry and computational mesh for Kamikawaet al.’s experimental configuration. Dimensions of the computational domainare 0.75 m × 0.45 m × 1.8 m. The grid size used is an important numericalparameter in CFD because of its impact on numerical accuracy. The necessaryspatial resolution for a proper LES simulation of a free burning fire is custom-arily defined in terms of the characteristic diameter of a plume, D∗, which isdefined as [13]

D∗ = (Q̇

ρ∞cpT∞√g)2/5 (10)

where Q̇ is the heat release rate; ρ∞ is ambient density; cp is the specific heatof air at constant pressure; T∞ is ambient temperature; and g is accelerationof gravity. The special resolution, R∗, of a numerical grid is defined as,

R∗ =dx

D∗ (11)

where dx is characteristic length of a cell for a given grid. For the FDS model,a uniform grid size of 0.025 m in XYZ directions (R∗ ≈ 1/12). The computa-tional domain, therefore, consisted of 43,200 control volumes.

Fig. 9 shows the FEM models for thermal and structural analyses. TheFEM thermal model and the FEM structural model use the same mesh, asshown in Fig. 9 (left). For both analyses the mesh was uniform with 10 equallysized elements along the web and the flange and 120 elements along the heightof the column. The support conditions were applied to replicate the experi-mental set (3.1) and are presented at Fig. 9 (center and right). In case 1, thecolumn is free to expand and bend, which means that except for the columnbase, there are no vertical or horizontal restraints along the column. In case4, a horizontal restraint at a height of 1400 mm is introduced. Additionally,the load applied at the top of the column also acts as a restraint (3.1).

The boundary conditions from FDS will be translated to FEM by twomethods. In the first method, the thermal boundaries in the FEM thermalmodel are represented using the adiabatic surface temperatures from FDSsimulation (recorded using Devices [13]), and the film coefficients on all sidesurfaces of the column were taken as 9 W/m2K according to [34]. In FTMI,the thermal boundaries are evaluated automatically using the adiabatic sur-face temperatures and the film coefficients (read from FDS output files [13])calculated by FDS at each exposed FEM element.

4 Results

4.1 Fire environment

To visualize flame exposure of the column during the fire tests, Fig. 10 showsthe simulated flame geometry at three distinct times. Note that the flame


shape changes with time because of the turbulent combustion processes. Cor-respondingly, Fig. 11 shows the adiabatic surface temperature spatial distri-butions at the same three time instances as Fig. 10. To better quantify thesurface temperatures, Fig. 12 shows the time averaged adiabatic surface tem-peratures along the mid-line of the column surfaces: front, back, and side.The front surface directly faces the flame, including direct flame impingement,and therefore has the highest adiabatic surface temperatures (AST). The ASTpeaks at approximately 640 ◦C at 0.4 m above the burner. Comparatively, theback surface cannot “see” the flame (a view factor near zero) and thereforeremains significantly cooler than the front surface, < 50 ◦C. The side surfacescan see parts of the flame (the maximum AST is about 125 ◦C). In additionto the variation in view factor, the non-uniform gas temperature distributions(see Fig. 13) contribute to the non-uniformly distributed ASTs.

The only difference between case 1 and case 4 for the fire environment andthe thermal response, is that in case 1 the fire was extinguished at 60 min(after achieve a steady state behavior), while in case 4 the fire continued untilthe column buckled (Section 3.1).

4.2 Thermal response

The predicted steel temperature distributions for both the DEVICE approachand FTMI approach are shown in Fig. 14. In both cases, the distributions arehighly non-uniform across and along the column. The radial profile aroundthe maximum temperature observed with the DEVICE changed for FTMI(Fig. 14). This is caused by the addition of film coefficient distribution in thethermal boundaries in the FTMI compared to the constant value used with theDEVICE. To assess the model predictions, the simulated temperatures werecompared to experimentally measured values at 4 locations over the durationof the experiment: front and corner measurements 400 mm above the burnerand side and back measurements 600 mm above the burner. This compari-son is presented in Fig. 15, which shows the agreement between the measuredand predicted maximum steel temperatures by both methods for case 1. Thetemperature evolution of corner and side surfaces is highly influenced by theheat conduction from the front surface (Fig. 15). Since their temperaturesare higher than the adiabatic surface temperature, Fig. 11, these surfaces arein fact, emitting heat to the surrounding environment (Section 5). The heattransfer at the back surface is dominated by convection while, as discussed be-fore, the equation used in FDS to calculate the adiabatic surface temperatureis for radiation dominated situations. This might explain the under-predictionof the steel temperature for the back surface.

4.3 Structural response

In case 1 the column has no support at the top. It is free to expand and benddue to heating and thermal gradient respectively. The displacements at lateral


(δx) and vertical (δz) directions were provided by the experimental measure-ments and are used here to compare with the numerical results. Fig. 16 andFig. 17 compares the measured and predicted δx and δz, respectively. The max-imum lateral displacement at a height of 1440 mm is 27 mm achieved duringthe heating phase (≈ 7.5 min). After the fire achieves a steady state and thetemperatures were close to a constant value (from 10 to 15 min, Fig. 15), thethermal gradient and the horizontal displacement decreased (Fig. 16), leadingto an increase in vertical displacement (Fig. 17). The vertical displacement ob-tained with FTMI showed better agreement than the DEVICE for the heatingand the cooling of the column. However, the maximum displacement at 1 hrof fire, obtained with the DEVICE is closer to the experimental data.

For case 4, the experimental work only presents the vertical displacementat column top, and a discussion about the failure mode. The structural sup-port conditions for case 4 are more complex than in case 1. The horizontaldisplacement is restricted in the x direction at the height of 1392 mm (Fig. 4),but there are no restraints (in x or y directions) at the top of the column. Nev-ertheless, to apply the load in a proper manner, these displacements at columntop should not change the position of the experimental apparatus (Fig. 3 andFig. 4). Also, as the load increases, the generated forces will apply some re-strictions to these horizontal displacements. In the numerical model, failing toconsider horizontal restrictions at column top leads to a global buckling be-havior, bending in y direction. Despite this, the failure time was in agreementwith the experimental results. For both methods, Fig. 18 shows the agreementbetween the measured and predicted column behavior for case 4. The pre-dicted buckling time was about 88.5 min after ignition for using the DEVICEmethod and 83 min for FTMI. The measured buckling time was about 90 minafter ignition, which means that the error was about 1.7% for AST and 7.8%for FTMI. For the numerical models, buckling was determined when a lack ofconvergence would lead to nonphysical displacements. In this situation, thereis a lack of confidence in the numerical response model due to nonlinearitiesand instabilities. In numerical simulations, a lack of convergence does not nec-essarily mean buckling has occured. The user should assess the results basedon knowledge and experience to find the cause for nonconvergence.

In practice, the applied force will produce some restraints to the horizon-tal displacements at the column top. Modifying the FEM structural modelby adding horizontal restraints at the column top, the local buckling of platesfound in the test was observed in the numerical simulation, as shown in Fig. 19.The predicted vertical displacement by the modified structural model usingFTMI is also presented in Fig. 18. The failure time was 86.5 min, which repre-sents a 3.9% error. The comparison between the experiment and FTMI localbuckling is presented in Fig. 19.


5 Conclusions

This paper discusses the FDS-FEM simulation methodology for advancedstructural fire analysis. Two fire-structure interfaces were applied: the DE-VICE approach and Fire-Thermomechanical Interface (FTMI) to transfer datafrom FDS to ANSYS. By comparing the predicted and measured thermal andstructural responses of a steel column in a localized fire condition, the FDS-FEM method was tested. For temperature measurements in case 1, predictionswere within estimated experimental uncertainty except for the more convec-tively dominated rear side of the column. Also for case 1, the lateral and verti-cal displacement were generally within the estimated experimental uncertaintyfor both the DEVICE and FTMI methods. In case 4, however, the vertical dis-placements underpredicted the vertical displacements. The final buckling timewas predicted within 10 % of the experimentally measured time for all of thecases analyzed. The methods described in this study provide a feasible way tostudy the complex behavior of structures in realistic fires.

A localized fire was used for validation based on the availability of the testdata and because localized fires are realistic fires which are easily controllableand reproducible. While there are various types of realistic fires, the simula-tion methodology described in this paper is regarded to be valid for all firescenarios because of the consideration that localized fires represent a univer-sal fire condition in which both temperature rising and thermal gradient areincluded.

Acknowledgements Valuable suggestions and review comments from Dr. Anthony Hamins,Dr. Fahim Sadek, Dr. Matthew Bundy and Mr. Keith Stakes of NIST are acknowledged.

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Fig. 1 Coupled CFD-FEM simulation approach for structural fire analysis


Fig. 2 Illustration of the exposed surfaces and the mapping procedure: a) thermomechanicalmodel b) fire simulation


Fig. 3 Experimental setup in Kamikawa et al’s test [23]


Fig. 4 Loading and restraint conditions in Kamikawa et al’s test [23]


Fig. 5 Stress-strain curves for the steel in Kamikawa et al’s test [23] (the stress-straincurves calculated by the constitutive model given by Luecke et al. [26] are also presented.)


Fig. 6 Specific heat for structural steel specified in the Eurocode [39]


Fig. 7 Thermal conductivity for structural steel specified in the Eurocode [39]


Fig. 8 FDS model for Kamikawa et al’s test [23]: Front view (left) side view (center) andcomputational domain (right)


Fig. 9 FEM models for Kamikawa et al’s test [23]: FE thermal/structural model (left) andboundary conditions (center and right). The restraint conditions shown are for the test Case4.


Fig. 10 FDS predicted flame behavior at 360 s (left), 900 s (center) and 3600 s (right)


Temperature◦C

20

120

220

320

420

520

620

720

Fig. 11 FDS predicted adiabatic surface temperature at 360 s (left), 900 s (center) and3600 s (right)


Fig. 12 Time-averaged adiabatic surface temperature distributions along the mid-line ofthree column surfaces


Temperature◦C

20

100

200

300

400

500

600

700

800

900

1,000

Fig. 13 FDS predicted gas temperature slices at 360 s (left), 900 s (center) and 3600 s(right) along the centerline of the burner and column.


Fig. 14 FEM predicted steel temperature distributions using the AST method (top) andthe FTMI method (bottom) at three different times: 360 s (left), 900 s (center) and 3600 s(right)


Fig. 15 Comparison between measured and predicted steel temperatures incase 1 inKamikawa et al’s test [23]. Front and corner measurements are at z = 400 mm and theside and back measurements are z = 600 mm.


Fig. 16 Comparison between measured and predicted lateral displacements at 4 differentheights along the column in case 1 in Kamikawa et al’s test [23]


Fig. 17 Comparison between measured and predicted vertical displacements in case 1 inKamikawa et al’s test [23]


Fig. 18 Comparison between measured and predicted vertical displacements in case 4 inKamikawa et al’s test [23]


Fig. 19 Illustration of x displacement distribution and local buckling achieved by the FTMIcoupling method: a) perspective view; b) expanded views of the buckling region; c) picturefrom experiment [23]

Documents

Simulation Methodology for Coupled Fire-Structure Analysis