Fire Safety Journal 43 (20

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hypotheses. Following this recommendation, this paperIn the United States, the design of re resistance in

buildings has been traditionally achieved by prescriptive

ARTICLE IN PRESS

Corresponding author. Tel.: +1301 975 4357; fax: +1 301 869 6275.

means. For this purpose individual structural members aresubjected to standard timetemperature curves, e.g.,ASTM E 119 [1], and coated with sufcient insulation as

0379-7112/$ - see front matter Published by Elsevier Ltd.

doi:10.1016/j.resaf.2007.06.006

E-mail addresses: dduthinh@nist.gov (D. Duthinh),

kevin.mcgrattan@nist.gov (K. McGrattan), akhaskia@mallett.com

(A. Khaskia).1. Introduction

Following the investigation of the collapse of the WorldTrade Center, the National Construction Safety Team(NCST) recommended, among other things, that efforts bemade to enhance the capabilities of computational methodsto study the effect of realistic re on buildings, all the way tothe burn-out and cooling phases, or to collapse. Therecommendation was partially due to the difculties facedby the investigators in interfacing the re, thermal, andstructural models that were used to study various collapse

describes two recent advances in interface development; therst facilitates the exchange of information between acomputational uid dynamics re model and a nite-element thermal model; the second transfers informationboth ways between thermal and structural models. The goalof developing these tools, veried by experiments, is to assistthe engineering community and the standards organizationsin taking re into account as a potential structural load.

2. ASTM E 119 standard re testAbstract

One of the recommendations of the National Construction Safety Team (NCST) for the Federal Building and Fire Safety Investigation

of the World Trade Center Disaster [NIST NCSTAR 1 Final report on the collapse of the World Trade Center Towers. NCST for the

Federal Building and Fire Safety Investigation of the World Trade Center Disaster, National Institute of Standards and Technology,

Gaithersburg, MD, September 2005] is to enhance the capability of available computational software to predict the effects of res in

buildings, for use in the design of re protection systems and the analysis of building response to res. Following this recommendation,

this paper presents two new interfaces in rethermalstructural analysis. The rst interface uses adiabatic surface temperatures to

provide an efcient way of transferring thermal results from a re simulation to a thermal analysis. It assigns these temperatures to

surface elements of structural members based on proximity and directionality. The second interface allows the transfer of temperature

results from a thermal analysis modeled with solid elements to a structural analysis modeled with beams and shells. The interface also

allows the reverse, namely the geometric updating of the thermal model with deections and strains obtained from the structural analysis.

This last step is particularly useful in intense res of long duration, where signicant deections and strains could cause damage to

insulation and displace the structure to a different thermal regime. The procedures can be used for a variety of re simulation, thermal,

and structural analysis software.

Published by Elsevier Ltd.

Keywords: Adiabatic surface temperature; Deection; Finite elements; Fire; Insulation; Plate thermometer; Structural analysis; Strain; Thermal analysisRecent advances in

Dat Duthinha,, Kevin MaNational Institute of Standards and Technology (NIST), Building and

Gaithersburg, MbNational Institute of Standards and Technology (NIST), B

Gaithersburg, McMallett Technology,

Received 19 April 200

Available onlinrattanb, Abed Khaskiac

e Research Laboratory, Materials and Construction Research Division,

899-8611, USA

ing and Fire Research Laboratory, Fire Research Division,

899-8663, USA

rel, MD 20707, USA

ccepted 25 June 2007

August 200708) 161167

estructure analysis

www.elsevier.com/locate/resaf

as a means of better controlling the temperature of

ARTICLE IN PRESStyfurnaces in re tests. The plate thermometer is a thinmetallic plate with insulated backing on the face oppositethe surface of interest. It responds with negligible time lagto radiative and convective heat uxes from the furnace,and thanks to its geometry, in the same proportion as whatthe surface of interest sees. Heat transfer to the platethermometer is described by

ptqinc sT4pt hptTg Tpt 0,where qinc is the incident radiative heat ux, h theconvective heat transfer coefcient, Tg the gas temperature,e the emissivity (assumed equal to absorptivity), s theStefanBoltzman constant, and subscript pt refers to platethermometer. The net heat transfer to a surface can beapproximated as

q ssT4pt T4s hsTpt T s,the case may be, to prevent them from reaching a certaintemperature deemed detrimental to their performance.While this approach is simple and has worked well, asshown by the rarity of structural collapse due to re ofengineered structures designed according to building andre codes, it offers no guidance on the actual behavior andthe margin of safety of a structure in re. The mainproblem, of course, is that a prescriptive timetemperaturecurve does not reect the actual temperature of variousstructural members exposed to a realistic re that varies intime and space. To compound the difculty, actualstructures have many redundancies, and the increase instructural demand due to thermal expansion coupled withmaterial softening due to heating may not necessarily meanimminent collapse if alternate load paths still exist. Theseproblems point to the need to treat re as a realisticstructural load.

3. Firethermal interface

In a sense, the timetemperature curve such as ASTM E119 is the re model. The restructural interface is thusnothing more than the specication of the bounding gastemperature at all solid surfaces. However, in a perfor-mance-based design environment, it should be possible tomodel potential re scenarios and pass spatially andtemporally resolved temperatures to the structural model.This will involve much more information than just a singletimetemperature curve, requiring some form of interfacefor data transfer.A proposed interface makes use of the adiabatic surface

temperature (AST), an output of the re model, to serve asthe boundary condition for the thermal model. ASTs arethe virtual equivalent of temperatures measured by platethermometers placed in the vicinity of the surfaces ofinterest. This concept was rst proposed by Wickstrom [2]

D. Duthinh et al. / Fire Safe162where subscript s refers to the surface. This is approxi-mately equal to the more exact equation for heattransferred from a re to the surface:

q ssT4f T4s hsT f T s,where subscript f refers to the re. For this interface, there analyst calculates the time history of the AST, or whata perfect plate thermometer in the vicinity of the structuralmember would measure, at nodes dened by spatialcoordinates and orientation. In doing so, he provides thethermal analyst the required input for heat transfer analysis[3] in a convenient form, thus eliminating the need for aradiation analysis that accounts for the presence of allradiating structural members and re at various locationsin the compartment.The interface allows for two independent re and

thermal models, whose geometries may not coincideperfectly, a useful feature since the spatial resolution ofre models is typically less precise than that of thermalmodels. The only condition is that the AST nodes must notbe contained within a solid material. For example, for ahollow tube, AST nodes that radiate to the outer surface ofthe tube must be outside, and AST nodes that radiate tothe inside of the tube must be inside. Any AST nodescontained within the thickness of the tube walls are deemedto be erroneous and are not read. Since the idea is tosimulate plate thermometers near the surface, the interfacesearches for the closest AST node in the half-space facingthe surface element. When it nds one, it checks fororientation by ensuring that the dot product of theorientation vector associated with the AST node and thevector normal to the surface element is positive. If that isnot the case, the interface expands its search to the nextclosest AST node. This direction check only becomesrelevant when the discrepancy in geometry between the reand the thermal models is rather large, e.g., when webmembers of a truss are modeled as vertical planes in the remodel, whereas they are faithfully modeled as inclinedround bars in the thermal model. To resolve other possibleambiguities in assigning the correct AST nodes, e.g., in thecase of two parallel adjacent trusses placed closely next toeach other, the interface also allows the user to interveneand manually select a set of relevant AST nodes and/orshift the entire thermal model as a rigid body to bettercenter it with the AST nodes.

4. Comparison with experimental measurements

For verication, we used an experimental compartmentre performed at NIST [4]. Figs. 1 and 2 show the actualre and the simulation model. Figs. 3 and 4 show the ASTnodes used in the thermal analysis of the column and oneof the trusses (A), and Figs. 5 and 6 compare measuredtemperatures versus those calculated with two differentsoftware codes. The calculations use the same insulationthickness and properties as in the experiments. Satisfactoryagreement is achieved for the column, whose simple

Journal 43 (2008) 161167geometry allows close matching of AST nodes with theircorresponding surfaces. As expected, for the web members

of the truss, agreement between measurements andcalculations is less close due to differences in modelgeometries mentioned previously.

5. Thermalstructural interface

The second interface discussed in this paper is thatbetween the thermal and the structural models. In the caseof one of the software codes used in the WTC investiga-tion, for example, the transfer of temperatures from athermal model to a structural model, or the transfer ofdeections and strains from a structural model to a thermalmodel (this latter step was not done in the investigation)can only be performed with compatible elements, e.g., solidto solid or shell to shell. These types of elements areprevalent in thermal analyses, and are often used instructural analysis as well, especially in smaller structureswhere a manageable number of solid or shell elements may

sufce. For larger, more complex structures, such asthe WTC towers, the use of beam elements to model thecolumns, oor and hat trusses is desirable to keep thestructural model to a reasonable size. A procedure forefcient, general, and automatic transfer of results betweenthermal and structural analyses is therefore needed.Temperature results would be transferred from the thermalto the structural analysis, so the effects of thermalexpansion and evolution of material properties withtemperature can be determined over time; conversely,structural deections and strains would be transferred backto the thermal model. This last step is especially importantin the case of intense res of long duration, wheresignicant structural deections and strains may causelocal damage to the insulation and move the structure to adifferent thermal regime. Furthermore, structural deec-tions may lead to changes in boundary conditions, such asnew openings, that may affect the re. This feedback would

ARTICLE IN PRESSD. Duthinh et al. / Fire Safety Journal 43 (2008) 161167 163Fig. 1. Fire experiment.Fig. 2. Fire siFig. 3. AST nodes for outside of column (inside nodes not shown).mulation.

ARTICLE IN PRESStyD. Duthinh et al. / Fire Safe164affect not just the thermal analysis, but the re analysis aswell. This last aspect is, however, beyond the scope of thispaper. The interface requires that the thermal andstructural models be geometrically compatible, within thetolerances specied by the nite-element program (default)or the user, and use compatible coordinate systems.

5.1. Temperature results transfer

In the thermal model, the temperature eld is inter-polated between corner nodes, linearly or quadraticallydepending on the nite elements. For shell elements in thestructural model, temperatures are input in the same

Fig. 4. AST nod

Fig. 5. Comparison of measured and calculated temperatures for column,

upper location.Journal 43 (2008) 161167format as element body loads at the corners of the outsidefaces of the element and at the corners of the interfacesbetween layers, where, for the purpose of temperatureresults transfer, additional transfer nodes are created. Thestructural model nodes at the outside faces and the transfernodes between layers are then mapped onto the thermalmodel, and temperatures at these locations interpolatedfrom the temperatures at the nodes of the thermal model.For beam elements in the structural model, at each end

node of the beam, temperatures are also input in the sameformat as element body loads in the form of a meantemperature and two temperature gradients in the elementY and Z directions (X is the longitudinal beam direction).

es for truss.

Fig. 6. Comparison of measured and calculated temperatures for truss A,

middle steel.

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etyThe actual input at each beam end takes the form of threetemperatures at (x, 0, 0), (x, 1, 0) and (x, 0, 1), where x iseither 0 or L (length of beam element). The location ofthe temperature transfer nodes depends on the crosssection. A number of commonly used cross sections, eithersingly symmetric or doubly symmetric, are supported bythe newly developed interface macros (Fig. 7). If later ordifferent versions of the software transfer temperatureresults directly to beams at specic points, rather thanthrough a mean and two gradients, the present interfacewould still work with minor adaptation.

5.2. Deflection transfer

Solid element nodes from the thermal model are rstmapped onto the undeformed structural model. Displace-ments u0 at the mapped nodes are calculated fromstructural displacements u and rotations r from the nearestbeam or shell nodes by the kinematic vector equation(in bold), where d is the distance between the mapped nodeand the undeformed nearest structural node: u0 u+r d,where denotes the vector cross product.

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D. Duthinh et al. / Fire Saf5.3. Strain transfer

Since strain transfer is done solely for the purpose ofdetermining insulation damage, it is not available at thisstage for shells, which are typically used to modeluninsulated slabs. For structural beams, strain results areavailable at both beam ends at the corner nodes of cross-sectional cells created automatically by the structuralsoftware for various common sections. The strains exx(x is the beam longitudinal axis) at various nodes on thesesection perimeters are mapped onto the thermal model andused to calculate by interpolation the strains at any nodesof the interface between the steel and insulation. Theinterpolation is linear over three dimensions, and uses thethermal solid element shape functions. Currently, the usercan input a failure criterion, such as the tensile strain at theinterface between steel and insulation exceeding 5%. Whenthe criterion is reached for a given nite element, theinsulation is assumed to fail and its thermal propertiesdegraded over its entire thickness. This criterion may berened as experimental data become available.

5.4. User-defined, multi-material beam cross section

For the cases where the mechanical properties of theinsulation are known to the level that they can beincorporated into the structural analysis, the thermalstructural interface makes available a cross section whosegeometry and mesh can be dened by the user, who mayassign different materials (e.g., steel or insulation) tovarious cells. Cross-section cells are used for thermal bodyload calculations by area averaging, and the user controlsthe accuracy by dening the number and distribution ofcells. The user also denes the insulation failure criteria andintervenes to degrade the insulation elements that havefailed. The geometry of the user-dened section is limitedto a quadrilateral in the current version.

6. Test case

As an example, a oor slab supported by an open web

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Journal 43 (2008) 161167 165truss was tested. The truss is made of three differentsections modeled with beam elements, and the oor slab ismodeled with three-layered shell elements. The thermalmodel uses solid elements and, in addition, link elements totie together the various members at the corners for thermalconduction. Insulation is present in the thermal model, butnot in the structural model. A thermal ux of 10 kW/m2

was applied to the bottom surface of the insulated lowerchord and concrete slab, except where it is in contact withthe top chord, while a lower ux of 5 kW/m2 was applied tothe other surfaces, except the top of the slab, where aconvection boundary with a lm coefcient of 25W/(m2 1C) applied.Fig. 8 shows the temperature contours for steel

and concrete at 1800 s from the thermal model. Thetemperature transfer macro was invoked after thethermal analysis was completed. Fig. 9 shows the tem-perature body loads as transferred by the macro for the

ARTICLE IN PRESStyD. Duthinh et al. / Fire Safe166full model and the slab. Differences in the temperaturecontours between the thermal and the structural modelsare due to the different mesh densities. In addition tothe thermal body loads, the truss dead weight wasactivated together with symmetrical boundary conditionalong the long edges of the concrete slab and simplesupports where the truss met the slab ends. Largedeection solution of the model resulted in deectionsshown in Fig. 10. The deection transfer macro was

Fig. 8. Temperature results (1C) from ther

Fig. 9. Structural modeltempera

Fig. 10. Structural modeldeections (mm) under thermal loads and

dead weight.Journal 43 (2008) 161167invoked, resulting in an updated thermal model. Fig. 11shows the deected thermal model, detection andremoval of failed insulation based on strains exx at1800 s and insulation failure criterion exx45% at theinterface with steel. The continuity of temperatures,deections, and strains appears satisfactory. Furtherverication of the software code against theoretical andexperimental results is in progress and will be reportedin a forthcoming publication.

mal model, shown without insulation.

tures (1C) input as body loads.

Fig. 11. Thermal modelupdated geometry based on structural deec-

tions and failed insulation (red).

7. Conclusion

This paper presents two user-friendly interfaces thatcomplement the existing rethermalstructural analysissoftware. The rst interface uses adiabatic surface tem-peratures to provide an efcient way of transferringthermal results from a re simulation to a thermal analysis.It assigns these temperatures to surface elements ofstructural members based on proximity and directionality.The second interface allows the transfer of temperatureresults from a thermal analysis modeled with solid elementsto a structural analysis modeled with beams and shells.The interface also allows the reverse, namely the geometricupdating of the thermal model with deections and strainsobtained from the structural analysis. This last step isparticularly useful in intense res of long duration, wheresignicant deections and strains could cause damage toinsulation and displace the structure to a different thermal

regime. The procedures can be used for a variety of resimulation, thermal, and structural analysis software.

References

[1] ASTM. E 11907: Standard test methods for re tests of building

construction and materials. ASTM International, West Conshohocken,

PA, 2007.

[2] Wickstrom, U. The plate thermometera simple instrument for

reaching harmonized re resistance tests. Fire Technol 2 May 1994; 30:

195208.

[3] Wickstrom U, Duthinh D, McGrattan K. Adiabatic surface tempera-

tures for calculating heat transfer in re exposed structures. 11th

International Conference on Fire Science and Engineering Interam,

London, 35 September 2007.

[4] NIST NCSTAR 1 Final report on the collapse of the World Trade

Center Towers, National Construction Safety Team for the Federal

Building and Fire Safety Investigation of the World Trade Center

Disaster, National Institute of Standards and Technology, Gaithers-

burg, MD, September 2005.

ARTICLE IN PRESSD. Duthinh et al. / Fire Safety Journal 43 (2008) 161167 167

Recent advances in fire-structure analysisIntroductionASTM E 119 standard fire testFire-thermal interfaceComparison with experimental measurementsThermal-structural interfaceTemperature results transferDeflection transferStrain transferUser-defined, multi-material beam cross section

Test caseConclusionReferences