Carstensen, Josephine Voigt

Jomaas, Grunde

Pankaj, P.

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Downloaded from orbit.dtu.dk on: Dec 18, 2017Material Modelling of the Post-Peak Response of Reinforced Concrete at ElevatedTemperaturesCarstensen, Josephine Voigt; Pankaj, P.; Jomaas, GrundePublication date:2011Document VersionPublisher's PDF, also known as Version of recordLink back to DTU OrbitCitation (APA):Carstensen, J. V., Pankaj, P., & Jomaas, G. (2011). Material Modelling of the Post-Peak Response ofReinforced Concrete at Elevated Temperatures. Poster session presented at 10th International Symposium onFire Safety Science, Maryland, United States.MATERIAL MODELLING OF THE POST‐PEAK RESPONSE OF REINFORCED CONCRETE AT ELEVATED TEMPERATURESJ.V. Carstensen a,  P. Pankaj b  and  G. Jomaas aa  Department of Civil Engineerig at the Technical University of Denmark (DTU)b  BRE Centre for Fire Safety Engineering at the University of EdinburghBRE Centre for Fire Safety EngineeringUniversity of EdinburghTENSION STIFFENINGThe uncracked part of the concrete still contri-butes to the strength after cracking is initiated.ConcreteSteelTension stiffeningcuts !ts fct,m="#"#"c "0 yts"u"PserviceConcrete doesnot crackConcrete is assumedto be fully plasticP crConcrete has notensile strength aftercrackingTensile stiffening, δΔPure reinforcementδPThis can be modelled based on the fracture energy by an interaction stress contribution as suggested by Cervenka et al. and Feenstra and de Borst. FRACTURE ENERGYThe fracture energy is a material invariant that coresponds to the area beneath the stress-plastic displacement (or cracking) diagram.Element is too largeCompressive behaviour Tensile behaviour; combined concrete and interaction stress contributionThe reinforcement ratio is too smallElement is too smallElement is too largeProblems in the Ambient ConditionA validity range for the element size and a minimum reinforcment ratio is formulated.MOTIVATIONFor FE-analysis of reinforced concrete at elevated temperatures the current material models yield convergence problems for different mesh sizes. For ambient conditions, it has been established that using a fracture energy based material model cir-cumvents this issue. It is therefore relevant to extend these models to the elevated temperature conditions.200 400 600 800 100000.511.5 T [oC] GcT/Gc  200 400 600 800 1000050010001500 T [oC] hmaxT [mm]  Lie and LinAnderberg and ThelanderssonLi and PurkissEurocode 2Compressive Fracture EnergyTensile Fracture EnergyBased on the model by Terro, GfT follows the decay of tensile strength;GcT is found for the models by;200 400 600 800 100000.511.5 T [oC] GcT/Gc  200 400 600 800 1000050010001500 T [oC] hmaxT [mm]  Lie and LinAnderberg and ThelanderssonLi and PurkissEurocode 2200 400 600 800 100000.511.5 T [oC] GcT/Gc  200 400 600 800 1000050010001500 T [oC] hmaxT [mm]  Lie and LinAnderberg and ThelanderssonLi and PurkissEurocode 2GfT = x(T) . GfEVOLUTION OF FRACTURE ENERGY WITH TEMPERATUREThe inherent fracture energies are found as function of temperature for the existing elevated tempe-rature behaviour models for concrete.And the models including the effect of the load induced thermal strains (LITS) by;EXAMPLEREINFORCED CONCRETE SLAB= 8 mm!= 6 mm= 1 mW= 4 mL= 150 mms= 150 mmDc = 25 mmc = 25 mmL = 4 m= 10.7 kN/mq50 mmp!pxyThe validity range for the element size:Tmax = 715 oC and the hence72.5 mm < h < 129.6 mmThe level of reinforcement is found to be suifficient.Concrete grade C30 and steel Grade 500 andGcT as is computed as inherent in Eurocode 2.200 400 600 800 1000050010001500 T [oC] h [mm]  hmaxTCompressive ParametershmaxTTensile ParametershminTAdmissiblevalues of hCONCLUSION- GfT follows the decay of material strength.- There is a significant spread in the existing  compressive post-peak behaviours.- The LITS does not appear to influence GcT.- For the considered example, analysis above 800 oC will not converge.REFERENCESCervenka et al., Computer Aided Analysis and Design of Concrete Structures, Pineridge Press, 1-21 (1990)Feenstra and de Borst, Journal of Engineering Mechanics 121: 587-595 (1995)Anderberg and Thelandersson, Lund (1976)Lie and Lin, Fire Safety: Science and Engineering 882: 176-205 (1985)Li and Purkiss, Fire Safety Journal 40(7): 669-686 (2005)Eurocode 2 - Part 1-2, CEN (2004)Terro, ACI Structural Journal 95(2): 183-193 (1998) 0 0.01 0.0200.20.40.60.81κCσ C /f cm  h = 100 mmh = 500 mmh = 2000 mm0 1 2x 10−300.20.40.60.81εctσ ct /fct,m  ρs,eff = 0.04ρs,eff = 0.035ρs,eff = 0.0250 1 2x 10−300.20.40.60.81εctσ ct /fct,m  h = 50 mmh = 25 mm0 1 2x 10−300.20.40.60.81εctσ ct /fct,m  h = 500 mmh = 1000 mm

Material Modelling of the Post-Peak Response of Reinforced Concrete at Elevated Temperatures

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Material Modelling of the Post-Peak Response of Reinforced Concrete at Elevated Temperatures

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