Determining the Temperature Distributions of Fire Exposed Reinforced Concrete Cross-Sections with Different Methods

Transcription

1 Research Journal of Envronmental and Earth Scences 4(8): , 212 ISSN: Maxwell Scentfc Organzaton, 212 Submtted: May 21, 212 Accepted: June 23, 212 Publshed: August 2, 212 Determnng the Temperature Dstrbutons of Fre Exposed Renforced Concrete Cross-Sectons wth Dfferent Methods 1 Yousef Zand, 2 Oğuz Burnaz and 3 Ahmet Durmuş 1 Department of Cvl Engneerng, Tabrz Branch, Islamc Azad Unversty, Tabrz, Iran 2 Cvl Engneerng Department, Gümüşhane Unversty, Gümüşhane, Turkey 3 Cvl Engneerng Department, Karadenz Techncal Unversty, Trabzon, Turkey Abstract: The man purpose of ths study s to carry out the 2d nonlnear transent heat analyss of a chosen renforced concrete cross-secton, whch s exposed to standard fre, by usng smplfed, fnte dfference and fnte element method. In the fnte element analyses, t s consdered that the thermal propertes of concrete and renforcng steel vary as dependng on temperatures n tme doman. Accordng to results drawn ths study, t s put forward some conclusons and recommendatons concernng the fre desgn of renforced concrete structures. Keywords: Cross-secton, fre, renforced concrete, temperature dstrbutons INTRODUCTION It s known that all structures wthn economc lfetme must have a specfc safety n response to collapse by becomng out of servce under loadng. It s also known that the structures have to mantan these characterstcs durng probable fres. In the crcumstances, t s necessary to take nto account the fre effects n desgn, constructon and usng stages of renforced concrete structures lke other structures. The frst step of fre desgn s to choose or evaluate the temperature-tme curve whch represents the fre. After determned the envronment temperature change accordng to tme, n the second step t s possble to determne the temperature dstrbutons of structural element whch used n structural analyses. For ths reason there are many methods n techncal lteratures. These methods can be lsted n order tabulated data methods whch are developed based on tests and experences, smplfed methods and numercal methods whch provde to be carred out thermal analyses by computers (Burnaz and Durmuş, 7). The results of the thermal analyss are compared to the expermental results n the lterature and the analytcally derved structural results are also compared wth full-scale renforced concrete beams n prevous fre exposure experments. The comparson results ndcated that the calculaton procedure n ths study assessed the resdual bearng capabltes of renforced concrete beams exposed to fre wth suffcent accuracy. As no two fres are the same, ths novel scheme for predctng resdual bearng capabltes of fre-exposed renforced concrete beams s very promsng n that s elmnates the extensve testng otherwse requred when determnng fre ratngs for structural assembles (Hsu et al., 6). Analyzng the bearng capablty of RC beams after sustanng fre requres the knowledge of temperature dstrbuton n the cross sectons. Ths s determned by the thermal propertes of the materal, such as the heat capacty and thermal conductvty. A smple thermal model, whch s generally to all beams wth a rectangular cross secton, has been assessed n a separate serous of studes whch were also reported n a prevous paper Hsu et al. (6). The modelng results acheved reasonable agreement wth sothermal contours obtaned by Ln (1985) who analyzed the temperature dstrbuton of pure concrete accordng to the tme-temperature curve of standard fre. The analytcal stage n the modelng process s to ncrement the tme of the model such that the temperature experenced by the beam s ncreased. The ncrease n the ambent temperature changes the temperature dstrbuton nsde of beam s crosssectons. After sustanng hgh temperature, the mechancal propertes of renforced steel and concrete vary accordng to the fre-nduced temperature. It makes the stress dstrbuton n such beam structures a nontrval problem. The structural analyss n ths model follows Amercan Concrete Insttute (ACI) buldng code, whch consders the nfluence of temperature on renforced steel and concrete usng a lumped system method to determne flexural and shear capactes. Modelng results for flexural capactes have been compared to the calculated results usng the ACI code at room temperature and also compared wth full-scale RC beam fre exposure experments (Ln, 1985). The Correspondng Author: Yousef Zand, Department of Cvl Engneerng, Tabrz Branch, Islamc Azad Unversty, Tabrz, Iran 782

2 Res. J. Envron. Earth Sc., 4(8): , 212 Table 1: Avalable desgn charts n (ENV , 1996) Member Cross-secton dmensons (mm) Standard fre resstance Slabs or walls expose to one sde Thckness = R3-R24 Beams Heght wdth = 3 16 R3-R9 and 5ºC sotherms Heght wdth = 6 3 R6-R12 Heght wdth = 8 5 R6-R24 Square columns Heght wdth = 3 3 R3-R12 and 5 C sotherms Crcular columns Dameter = 3 R3-R12 and 5 C sotherms analytcally derved shear capactes have also been compared wth expermental data (Ln, 1985; Moetaz et al., 1996; Ln et al., 1999; ACI 318R-2, 2; Buchanan, ). In order to determne the fre behavour of renforced concrete structures, there are many methods n techncal lteratures. These methods can be lsted n order tabulated data methods whch are developed based on tests and experences, smplfed methods and numercal methods whch provde to be carred out thermal and structural analyses by computers. In ths study t s used a developed computer code based on fnte element method for both thermal and structural analyses. Determnng the temperature dstrbutons of rc cross-sectons: Heat transfer s the scence to evaluate the energy transfer that takes place between materal bodes as a result of temperature dfference. The three modes of heat transfer are conducton, convecton and radaton. The thermal analyss on structural fre problems can be dvded nto two parts: The heat transfer by convecton and radaton across the boundary from the fre nto structural members The heat transfer by conducton wthn structural members The thermal analyss n structural members can be extremely complex, especally for materals that retan mosture and have a low thermal conductvty. The smplest method of defnng the temperature profle through the cross-secton s to use test data presented n tables or charts whch are publshed n codes or desgn gudes. These tabulated data are generally based on standard fre condtons. Smplfed method, the second method of determnng of temperature dstrbutons, s presented n codes and desgn gudes. It s possble to use smple heat transfer models based on one-dmensonal heat flow. However, smple computer programs are needed to solve the heat transfer equatons. Alternatvely, advance fnte-element heat transfer models can be used (The Concrete Center, 4) (a) R9 (b) R6 1 Fg. 1: Temperature profles of a concrete beam for R6 and R9 (ENV , 1996) slabs or walls, beams and columns. The avalable desgn charts are summarzed as Table 1. As an example of tabulated data, the temperature profles of a concrete beam wth 3 mm wdth for R6 and R9 (standart fre duratons, mn.) are gven n Fg. 1. MATERIALS AND METHODS Tabulated data: Annex A of ENV (1996) provdes a seres of calculated temperature profles for 783 Smplfed method: In ths study, the smple calculaton method proposed by Wckström (1987) s used for calculatng the temperatures n concrete members exposed to the standard fre. It should be

3 Res. J. Envron. Earth Sc., 4(8): , 212 noted that ths method does not take nto account of possble spallng of concrete. The fre-exposed surface temperature T s of a concrete member at a tme t s frst gven by: T w = η w T f (1) wth η w = 1-,616 t -,88, where, η w s the rato between gas and surface temperatures of concrete member ( C) and T f s the gas atmosphere temperatures ( C). For unaxal heat flow condton, the temperature rse T c at any depth x (m) beneath the fre-exposed surface of the member s a factor η x of the surface temperature T w wth n x gven by: T c = η x T f (2) where, η x =.18 ln(t h /x 2 ),81. The method can be appled to concrete members heated on parallel faces smultaneously, n whch n x s smply the supermposed total of the n x values calculated wth respect to each face. The method can also be used for corners of beams where there s accommodated heat flow from two drectons, through supermposton of the contrbutons from the orthogonal faces η x and η y as follows: T c = [ η w (η x + η y 2 η x η y ) + η x η y ] T f (3) Numercal methods: Two dmensonal heat flows s governed by the followng partal dfferental equaton: T T T ρ c = k + k + Q (4) t x x y y where, T(x, y, t), ρ, c, k and Q(x, y, t) are temperature dstrbuton hstory, densty, specfc heat, sotropc conductvty and heat generaton rate respectvely. An ntegral part of above equaton s n ts boundary and ntal condtons. The ntal condtons consst of the temperature of every pont n the structure when the analyss begns: T(x, y, t ) = T (x, y) where the temperature dstrbuton T s specfed. The boundary condtons must be defned at every pont on the structures surface and can be a specfed temperature hstory or a specfed heat flow hstory. Fg. 2: Flow dagram of the nonlnear thermal analyss 784

4 Res. J. Envron. Earth Sc., 4(8): , 212 The heat flow equatons for two dmensonal bodes are very complex and have nearly no closedform soluton. An approxmate numercal method must be used n order to obtan a soluton. In ths study fnte dfference and fnte element method has been used. The thermal analyss of RC cross-sectons wth fnte dfference method can be seen exhaustve n Burnaz (3). The fnte element equatons can be vsualzed physcally n matrx form. That s, at each node n the dscretzaton: { T ( t )} + ( K ){ T ( t )} { Q ( t )} ( C ) & = (5) where, (C), (K), {Q}, {T} and { T & } are capacty matrx, conductvty matrx, external heat flow vector, temperature vector and temperature tme rate of change vector respectvely. The temperature rate of change vector { T & } at any t can be approxmated n terms of nodal temperatures: { T ( t )} = { T ( t ) - T ( t- 1 )}/ t & (6) where, t s the tme step between t -1 and t. So the Eq. (5) can be wrtten as: C ( C ) ( K + ) -1 t t { T ( t )} = { Q ( t )} + { T ( t )} (7) The step-by-step assembly and soluton of Eq. (4) gradually traces out the temperature hstory n the structure (Idng et al., 1977). These steps are presented n some detal n the flow dagram of Fg. 2. Fg. 3: The cross-secton of R.C. beam In ths study ISO-834 standard fre curve whch s accepted to represent the fre around the beam s used. The curve s calculated as: T = 345 log (8 t + 1) + T (8) f 1 where, T f, T and t are fre envronment temperature, ambent temperature and tme, respectvely. Heat exchange at the boundares of the fre exposed member depends on the heat transfer coeffcents of both emssvty and convecton. These factors and thermal propertes of concrete (thermal conductvty, specfc heat and densty) whch are functon of temperature were adopted n Burnaz and Durmus (7). Numercal examples: The cross-secton of R.C. beam s shown n Fg. 3. The dameter and longtudnal bars were gnored n the thermal analyss because of not effectng results too much. Fgure 4 shows thermal cross-secton fnte element model of the beam whch was subjected to ISO-834 standard fre (T f (t)) from three sdes and the thermal boundary condtons T = 25 o C, ε rw =.8, α w = 9 W/m 2 K T f, ε rf =.56, α f = 25 W/m 2 K Fg. 4: Thermal fnte element model of beam and boundary condtons 785

5 Res. J. Envron. Earth Sc., 4(8): , 212 Fg. 5: The changng of thermal propertes of concrete accordng to temperatures t = 15 mn t = 3 mn t = 6 mn t = 9 mn t = 12 t = 18 t = Fg. 6: The changng of temperature dstrbutons of R.C. beam cross-secton accordng to fre duratons (envronment temperature, resultant emssvty ε r and convecton factor h c ) for fre exposed and unexposed surfaces. On the other hand, the changng of thermal propertes of concrete accordng to temperature s gven n Fg. 5. The thermal analyss wth fnte element method was carred out n order to obtan temperature dstrbuton hstory of beam cross-secton. Ths was determned by usng a developed computer code (Burnaz and Durmus, 7) based on nonlnear fnte element method. Durng thermal analyss.5 h was used as a tme step. Fnally the temperatures of all elements of beam cross-secton were calculated accordng to each tme steps. 786 Same numercal example was also solved wth fnte dfference method. In ths method, the thermal propertes of concrete (thermal conductvty 1, 2 W/mºC, specfc heat 11 J/kgºC ve densty 2 kg/m 3 ) were accepted to take nto constant. RESULTS AND DISCUSSION After runnng the aforementoned fnte element thermal analyzng program, the temperatures of all elements of R.C. beam cross-secton were determned accordng to each tme steps. Some temperature dstrbutons obtaned from the analyss were gven n Fg. 6 for 15, 3, 6, 9, 12, 18 and 24 mn by usng

6 Res. J. Envron. Earth Sc., 4(8): , Temperature (oc) [1] Tf [2] FEM (2.) [3] WSM (2.) [4] FDM(2.) [5] FEM (64.) [6] WSM (64.) [7] FDM(64.) [8] FEM (154.) [9] WSM (154.) [1] FDM(154.) Tme (mn) Fg. 7: The comparson of dfferent methods for determnng of temperature dstrbutons of R.C. cross-sectons sotherm curves. As t s seen, the temperatures ncrease wth tme ncrement through nsde the cross-secton. At the end of the two hours, the temperature of some area of cross-secton exceeds 1ºC. The results are very smlar to the tabulated data n EN for 6 and 9 mn. The results obtaned from nonlnear Fnte Element Method (FEM) are compared wth the Fnte Dfference Method (FDM) and Wckström s Smplfed Method (WSM) n Fg. 7. T f curve n ths fgure shows the standard temperature-tme curve. If the temperaturetme curves of 2 th node at the bottom corner of the cross-secton were compared, t s seen that the curve of WSM s very smlar to FEM, but these curves are dfferent from FDM. In the other nodes (64 and 154), dfferences between these methods are more than 2 th node. The temperatures obtaned from FEM n 64 and 154 th nodes are hgher than the other methods. CONCLUSION The comparson whch has been made between nonlnear fnte element, fnte dfference and Wckström smplfed method shows that these method s results are dfferent from each other, but the FEM s results are very smlar to graphcs n EN Consequently, the computer codes whch were developed by usng nonlnear fnte element method can be used for determnng the temperature dstrbutons of the R.C. cross-sectons exposed to fres. 787 However, the other methods can also be used for practcal purposes. It s obvous that these conclusons are vald for ths example and ts condtons. Therefore there s beneft to take nto account dfferent cross-sectons, real fres and spallng of concrete n the thermal analyses of R.C. structures accordng to fre. The studes about ths subject have been contnued. REFERENCES ACI 318R-2, 2. Buldng Code Requrements for Structural Concrete and Commentary. Amercan Concrete Insttute, Mchgan. Buchanan, A.H.,. Structure De-sgn for Fre Safety. John Wley and Sons, LTD, UK. Burnaz, O., 3. Fre n Renforced Concrete Structures and Investgaton of Fre Desgn on a Model. MsD, K.T.Ü., Trabzon. Burnaz, O. and A. Durmuş, 7. Nonlnear thermal analyss of renforced concrete beams exposed to fre. Proceedng of ULIBTK7 16th Natonal Thermal Scence and Technology Congress, Kayser, Turkey, (In Turksh). ENV , Eurocode 2: Desgn of Concrete Structures- Part 1-2: General Rules-Structural Fre Desgn. CEN, Brussels. Hsu, J.H., C.S. Ln and C.B. Hung, 6. Modelng the effectve elastc modulus of RC beams exposed to fre. J. Mar. Sc. Technol., 14:

7 Res. J. Envron. Earth Sc., 4(8): , 212 Idng, R., B. Breslerand and Z. Nzamuddn, FIRES-T3: A computer program for the Fre response of structures-thermal. Report UCB FRG 77-15, Unversty of Calforna, Berkeley. Ln, T.D., Measured temperature n concrete beams exposed to astme 119 standard fre. Research and De-velopment Report, Portland Cement Assocaton, Skoke. Ln, I.J., S.T. Chen and C.J. Ln, The Shear Strength of Renforcng Concrete Beam after Fre Damage. Structure Safety Evaluaton after Fre Dam-Age, Scentfc and Techncal Publshng Co. Ltd., Tawan, pp: Moetaz, M.E., M.R. Ahmed and E. Shada, Effect of fre on flexural behavour of rc beams. Constr. Buld. Mater, 1(2): The Concrete Center, 4. Concrete and Fre, Usng Concrete to Acheve Safe, Effcent Buıldngs and Structures Ref. TCC/5/1, ISBN Wckström, U., A very Smple Method for Estmatng Temperature n Fre Exposed Concrete Structures. Swedsh Natonal Testng Insttute, SP Report, Boras, Sweden. 788