Recent progress in fire-structure analysis

Transcription

1 EJSE Special Iue: Selected Key Note paper from MDCMS 1 1t International Conference on Modern Deign, Contruction and Maintenance of Structure - Hanoi, Vietnam, December 2007 Recent progre in fire-tructure analyi D. Duthinh K. McGrattan National Intitute of Standard and Technology (NIST), Building and Fire Reearch Laboratory, Gaitherburg, MD 20899, USA A. Khakia Mallett Technology, Laurel, MD USA ABSTRACT: One recommendation of the National Contruction Safety Team for the Federal Building and Fire Safety Invetigation of the World Trade Center Diater [1] i to enhance the capability of available computational oftware to predict the effect of fire in building, for ue in the deign of fire protection ytem and the analyi of building repone to fire. Thi paper preent two new interface in fire-thermal-tructural analyi. The firt interface ue adiabatic urface temperature to provide an efficient way of tranferring thermal reult from a fire imulation to a thermal analyi. It aign thee temperature to urface element of tructural member baed on proximity and directionality. The econd interface allow the tranfer of temperature reult from a thermal analyi modeled with olid element to a tructural analyi modeled with beam and hell. The interface alo allow the revere, namely the geometric updating of the thermal model with deflection and train obtained from the tructural analyi. Thi lat tep i particularly ueful in intene fire of long duration, where ignificant deflection and train could caue damage to inulation and diplace the tructure to a different thermal regime. The procedure can be ued for a variety of fire imulation, thermal and tructural analyi oftware. Keyword: Adiabatic urface temperature; fire; inulation; plate thermometer; tructural analyi; thermal analyi. 1 INTRODUCTION Following the invetigation of the collape of the World Trade Center (WTC), the National Contruction Safety Team (NCST) recommended, among other thing, that effort be made to enhance the capabilitie of computational method to tudy the effect of realitic fire on building, from ignition to the burn-out and cooling phae, or to collape [1]. The recommendation wa partially attributable to the difficultie experienced by the invetigator in interfacing the fire, thermal, and tructural model that were ued to tudy variou collape hypothee. Thi paper decribe two recent advance in interface development; the firt facilitate the exchange of information between a computational fluid dynamic fire model and a finite-element thermal model; the econd tranfer information both way between the thermal model and a tructural model. The goal of developing thee tool, verified by experiment, i to ait the engineering community and the tandard organization in taking fire into account a a potential tructural load. 2 ASTM E 119 STANDARD FIRE TEST In the United State, the deign of fire reitance in building ha been traditionally achieved by precriive mean. For thi purpoe individual tructural member are ubjected to tandard timetemperature curve, e.g., ASTM E 119 [2], and coated with ufficient inulation a the cae may be, to prevent them from reaching a certain temperature deemed detrimental to their performance. While thi approach i imple and ha worked well, a hown by the rarity of tructural collape due to fire of engineered tructure deigned according to current building and fire code, it offer no guidance on the actual behavior and the margin of afety of a tructure in fire. The main problem, of coure, i that a precriive time-temperature curve doe not reflect the actual temperature of variou tructural member expoed to a realitic fire that varie in time and pace. To compound the difficulty, actual tructure have many redundancie, and the increae in tructural demand due 28

2 EJSE Special Iue: Selected Key Note paper from MDCMS 1 1t International Conference on Modern Deign, Contruction and Maintenance of Structure - Hanoi, Vietnam, December 2007 to thermal expanion coupled with material oftening due to heating may not necearily lead to imminent collape if alternate load path till exit. Thee problem point to the need to treat fire a a realitic tructural load. 3 FIRE-THERMAL INTERFACE In a ene, the time-temperature curve uch a ASTM E 119 i the fire model. The fire-tructural interface i thu nothing more than the pecification of the bounding ga temperature at all olid urface. However, in a performance-baed deign environment, it hould be poible to model potential fire cenario and pa patially and temporally reolved temperature to the tructural model. Thi will involve much more information than jut a ingle time-temperature curve, requiring ome form of interface for data tranfer. A propoed interface make ue of the adiabatic urface temperature (AST), an output of the fire model, to erve a the boundary condition for the thermal model. Adiabatic urface temperature are the virtual equivalent of temperature meaured by plate thermometer placed in the vicinity of the urface of interet. Thi conce wa firt propoed by Wicktrom [3] a a mean of better controlling the temperature of furnace in fire tet. The plate thermometer i a thin metallic plate with inulated backing on the face oppoite the urface of interet. It repond with negligible time lag to radiative and convective heat fluxe from the furnace, and thank to it geometry, in the ame proportion a what the urface of interet ee. Heat tranfer to the plate thermometer i decribed by []: ε ( q σ T ) + h ( T T ) = 0 (1) inc g where q inc = incident radiative heat flux, h = convective heat tranfer coefficient, T = temperature, ε = emiivity (aumed equal to aborivity), σ = Stefan-Boltzman contant, ubcri g refer to ga and ubcri refer to plate thermometer. The net heat tranfer to a urface can be approximated a: q ε σ ( T T ) + h ( T T ) (2) where ubcri refer to the urface. Thi i approximately equal to the more exact equation for heat tranferred from a fire to the urface: f q = ε σ ( T T ) + h ( T T ) (3) f where ubcri f refer to the fire. For thi interface, the fire analyt calculate the time hitory of the AST, or what a perfect plate thermometer in the vicinity of the tructural member would meaure, at node defined by patial coordinate and orientation. In doing o, he provide the thermal analyt the required input for heat tranfer analyi in a convenient form [5], thu eliminating the need for a radiation analyi that account for the preence of all radiating tructural member and fire at variou location in the compartment. With thi interface, one need to tranfer only one quantity, the adiabatic urface temperature, from the fire model to the thermal model, rather than heat flux, urface temperature, and convective heat tranfer coefficient. Thi i of great benefit in large cale fire-thermal-tructural analye, uch a the WTC invetigation, which involve huge dataet, in not only improving efficiency but alo in reducing the rik of error. The interface allow for two independent fire and thermal model, whoe geometrie may not coincide perfectly. Thi i a ueful feature ince the patial reolution of fire model i typically le precie than that of thermal model. The only condition i that the AST node mut not be contained within a olid material. For example, for a hollow tube, AST node that radiate to the outide urface of the tube mut be outide, and AST node that radiate to the inide of the tube mut be inide. Any AST node contained within the thickne of the tube wall are deemed to be erroneou and are not read. Since the idea i to imulate plate thermometer near the urface, the interface earche for the cloet AST node in the halfpace facing the urface element. When it find one, it check for orientation by enuring that the dot product of the orientation vector aociated with the AST node and the vector normal to the urface element i poitive. If that i not the cae, the interface expand it earch to the next cloet AST node. Thi directional check only become relevant when the dicrepancy in geometry between the fire and the thermal model i rather large, e.g., when web member of a tru are modeled a vertical plane in the fire model, wherea they are faithfully modeled a inclined round bar in the thermal model. To reolve other poible ambiguitie in aigning the correct AST node, e.g., in the cae of two parallel adjacent true placed cloely next to each other, the interface alo allow the uer to intervene and manually elect a et of relevant AST node and/or hift the entire thermal model to better center it with the AST node. 29

3 EJSE Special Iue: Selected Key Note paper from MDCMS 1 1t International Conference on Modern Deign, Contruction and Maintenance of Structure - Hanoi, Vietnam, December 2007 COMPARISON WITH EXPERIMENTAL MEASUREMENTS For verification, we ued an experimental compartment fire performed at NIST [1]. Fig. 1 and 2 how the actual fire and the imulation model. Fig. 3 and how the AST node ued in the thermal analyi of the column and one of the true (A), and Fig. 5 and 6 compare meaured temperature veru thoe calculated with two different oftware code. The calculation ue the ame inulation thickne and propertie a in the experiment. Satifactory agreement i achieved for the column, whoe imple geometry allow cloe matching of AST node with their correponding urface. A expected, for the web Fig. 1 Fire experiment member of the tru, agreement between meaurement and calculation i le cloe due to difference in model geometrie mentioned previouly. 5 THERMAL-STRUCTURAL INTERFACE The econd interface dicued in thi paper i that between the thermal and the tructural model. In the cae of one of the oftware code ued in the WTC invetigation, for example, the tranfer of temperature reult from a thermal model to a tructural model, or the tranfer of deflection and train from a tructural model to a thermal model (thi latter tep wa not done in the invetigation) can only be performed with compatible element, e.g., olid to olid or hell to hell. Thee type of element are prevalent in thermal analye, and are often ued in tructural analyi a well, epecially in maller tructure where a manageable number of olid or hell element may uffice. For larger, more complex tructure, uch a the WTC tower, the ue of beam element to model the column, floor and hat true i deirable to keep the tructural model to a reaonable ize. A procedure for efficient, general and automatic tranfer of reult between thermal and tructural analye i therefore needed. Temperature reult would be tranferred from the thermal to the tructural analyi, o the effect of thermal expanion and evolution Fig. 2 Fire imulation traight 30

4 EJSE Special Iue: Selected Key Note paper from MDCMS 1 1t International Conference on Modern Deign, Contruction and Maintenance of Structure - Hanoi, Vietnam, December 2007 of material propertie with temperature can be determined over time; converely, tructural deflection and train would be tranferred back to the thermal model. Thi lat tep i epecially important in the cae of intene fire of long duration, where ignificant tructural deflection and train may caue local damage to the inulation and move the tructure to a different thermal regime. Furthermore, tructural deflection may lead to change in boundary condition, uch a new opening, that may affect the fire. Thi feedback would affect not jut the thermal analyi, but the fire analyi a well. Thi lat apect i, however, beyond the cope of thi paper. The interface require Fig. 3 AST node for inide and outide face of column. that the thermal and tructural model be geometrically compatible, within the tolerance pecified by the finite-element program (default) or the uer, and ue compatible coordinate ytem. 5.1 Temperature data tranfer In the thermal model, the temperature field i interpolated between corner node, linearly or quadratically depending on the finite element. For hell element in the tructural model, temperature data are input in the ame format a element body load at the corner of the outide face of the element and at the corner of the interface between layer, where, for the purpoe of temperature data tranfer, additional tranfer node are created. The tructural model node at the outide face and the tranfer node between layer are then mapped onto the thermal model, and temperature at thee location interpolated from the temperature at the node of the thermal model. For beam element in the tructural model, at each end node of the beam, temperature are alo input in the ame format a element body load, in the form of a mean temperature and two temperature gradient in the element Y and Z direction (X i the longitudinal beam direction). The actual input at each beam end take the form of three temperature at (x, 0, 0), (x, 1, 0) and (x, 0, 1), where x i either 0 or L (length of beam element). The location of the temperature data tranfer node depend Fig. AST node for tru 31

5 EJSE Special Iue: Selected Key Note paper from MDCMS 1 1t International Conference on Modern Deign, Contruction and Maintenance of Structure - Hanoi, Vietnam, December 2007 Fig. 5 Comparion of meaured and calculated temperature for column, upper location. Fig. 6 Comparion of meaured and calculated temperature for tru A, middle teel Fig. 7 Some common beam cro ection and their tranfer point 32

6 EJSE Special Iue: Selected Key Note paper from MDCMS 1 1t International Conference on Modern Deign, Contruction and Maintenance of Structure - Hanoi, Vietnam, December 2007 on the cro ection. A number of commonly ued cro ection, either ingly or doubly ymmetric, are upported by the newly developed interface macro (Fig. 7). If later or different verion of the oftware tranfer temperature reult directly to beam at pecific point, rather than through a mean and two gradient, the preent interface would till work with minor adaation. 5.2 Deflection tranfer Solid element node from the thermal model are firt mapped onto the undeformed tructural model. Diplacement u' at the mapped node are calculated from tructural diplacement u and rotation r from the nearet beam or hell node by the kinematic vector equation (in bold), where d i the ditance between the mapped node and the undeformed nearet tructural node: u' = u + r d, where denote the vector cro-product. 5.3 Strain tranfer Since train tranfer i done olely for the purpoe of determining inulation damage, it i not available at thi tage for hell, which are typically ued to model uninulated lab. For tructural beam, train reult are available at both beam end at the corner node of cro ectional cell created automatically by the tructural oftware for variou common ection. The train ε xx (x i the beam longitudinal axi) at variou node on thee ection perimeter i mapped onto the thermal model and ued to calculate by interpolation the train at any node of the interface between teel and inulation. The interpolation i linear over three dimenion, and ue the thermal olid element hape function. Currently, the uer can input a failure criterion, uch a the tenile train at the interface between teel and inulation exceeding 5%. When the criterion i reached for a given finite element, the inulation i aumed to fail and it thermal propertie degraded over it entire thickne. Thi criterion may be refined a experimental data become available. 5. Uer-defined, multi-material beam cro ection For the cae where the mechanical propertie of the inulation are known to the level that they can be incorporated into the tructural analyi, the thermal-tructural interface make available a cro ection whoe geometry and meh can be defined by the uer, who may aign different material (e.g., teel or inulation) to variou cell. Croection cell are ued for thermal body load calculation by area averaging, and the uer control the accuracy by defining the number and ditribution of cell. The uer alo define the inulation fail- Fig. 8 Temperature reult ( C) from thermal model, hown without inulation. Fig. 9 Structural model temperature ( C) input a body load. 33

7 EJSE Special Iue: Selected Key Note paper from MDCMS 1 1t International Conference on Modern Deign, Contruction and Maintenance of Structure - Hanoi, Vietnam, December 2007 ure criteria and intervene to degrade the inulation element that have failed. The geometry of the uer-defined ection i limited to a quadrilateral in the current verion. 6 TEST CASE A an example, a floor lab upported by an open web tru wa teted. The tru i made of three different ection modeled with beam element, and the floor lab i modeled with three-layered hell element. The thermal model ue olid element and, in addition, link element to tie together the variou member at the corner for thermal conduction. Inulation i preent in the thermal model, but not in the tructural model. A thermal flux of 10 kw/m2 wa applied to the bottom urface of the inulated lower chord and concrete lab, exce where it i in contact with the top chord, while a lower flux of 5 kw/m2 wa applied to the other urface, exce the top of the lab, where a convection boundary with a film coefficient of 25 W/(m2. C) applied. The interface alo allow other type of thermal input normally ued in finite-element analyi. Fig. 8 how the temperature contour for teel and concrete at 1800 from the thermal model. The temperature tranfer macro wa invoked after the thermal analyi wa completed. Fig. 9 how the temperature body load a tranferred by the macro for the full model and the lab. Difference in the temperature contour between the thermal and the tructural model are due to the different meh denitie. In addition to the thermal body load, the tru dead weight wa activated together with ymmetrical boundary condition along the long edge of the concrete lab and imple upport where the tru met the lab end. Large deflection olution of the model reulted in deflection hown in Fig. 10. The deflection tranfer macro wa in voked, reulting in an updated thermal model. Fig. 11 how the deflected thermal model, detection and removal of failed inulation baed on train εxx at 1800 and inulation failure criterion εxx > 5 % at the interface with teel. The continuity of temperature, deflection and train appear atifactory. Further verification of the oftware code againt theoretical and experimental reult i in progre and will be reported in a forthcoming publication. 7 CONCLUSION Thi paper preent two uer-friendly interface that complement exiting fire-thermal-tructural analyi oftware. The firt interface ue adiabatic urface temperature to provide an efficient way of tranferring thermal reult from a fire imulation to a thermal analyi. It aign thee temperature to urface element of tructural member baed on proximity and directionality. The econd interface allow the tranfer of temperature reult from a thermal analyi modeled with olid element to a tructural analyi modeled with beam and hell. The interface alo allow the revere, namely the geometric updating of the thermal model with deflection and train obtained from the tructural analyi. Thi lat tep i particularly ueful in intene fire of long duration, where ignificant deflection and train could caue damage to inulation and diplace the tructure to a different thermal regime. The procedure can be ued in a variety of fire imulation, thermal and tructural analyi oftware. 8 REFERENCES - [1]NIST NCSTAR 1: Final Report on the Collape of the World Trade Center Tower, Na Fig. 10 Structural model deflection (mm) under thermal load and dead weight. Fig. 11 Thermal model updated geometry baed on tructural deflection and failed inulation (red). 3

8 EJSE Special Iue: Selected Key Note paper from MDCMS 1 1t International Conference on Modern Deign, Contruction and Maintenance of Structure - Hanoi, Vietnam, December 2007 tional Contruction Safety Team for the Federal Building and Fire Safety Invetigation of the World Trade Center Diater, National Intitute of Standard and Technology, Gaitherburg, MD, Se [2] ASTM: E : Standard tet method for fire tet of building contruction and material, ASTM International, Wet Conhohocken, PA 1928, [3] Wicktrom, U.: The plate thermometer- a imple intrument for reaching harmonized fire reitance tet, Fire Technology, May 199, 30 (2): [] Wicktrom, U.: Heat tranfer calculation in fire afety engineering, Propoal to SFPE Standard Committee on Calculating Fire Expoure to Structure, June [5] Wicktrom, U., Duthinh, D. and McGrattan, K.: Adiabatic urface temperature for calculating heat tranfer to fire expoed tructure, Proceeding of 11th Interflam Int. Conf., London, 3-5 Se