【正文】 ?c heat with temperature is due to individual atoms in steelmoving farther apart, thus achieving a higher energy state. Thespike in the speci?c heat at around 750176。 b mechanical。 Constitutive relationships。HighTemperature Properties of Steel for Fire ResistanceModeling of StructuresVenkatesh Kodur, 。 Hightemperature properties。 and c deformation properties. Thermal properties determine the temperature pro?le in the steel sections resulting from ?re exposure, while the mechanicalproperties govern the loss of strength and stiffness as a functionof temperature. Deformation properties determine the extent ofdeformations of the steel member under ?re conditions.For evaluating realistic ?re performance of steel structures,due consideration should be given to thermal, mechanical, anddeformation properties. These properties vary with temperatureand are in?uenced by the phase changes that occur in steel atelevated temperatures. A review of the available constitutive models for hightemperature properties of steel is presented in thefollowing sections.Thermal PropertiesThe main thermal properties that in?uence the temperature rise insteel are thermal conductivity and speci?c heat often expressedin terms of heat capacity . There is limited test data on the speci?c heat and thermal conductivity of steel. Figs. 1 and 2 showplots of the available data on thermal conductivity and speci?cheat of steel as a function of temperature, respectively. Relationships from codes and standards European Committee for Standardization 2005。 C is due to the phasechange that occurs in steel in which the atoms transition from aface centered cubic to a body centered cubic structure. This process absorbs considerable energy heat , thus accounting for thespike around 750176。 Cooke 1988 .These variations in test methods resulted in variations in thereported mechanical properties, which in turn resulted in variations in the constitutive models speci?ed in codes and standards.The following sections present parative study of these variations.Yield Strength and Elastic ModulusAs mentioned earlier, different test regimes were used to obtainyield strength and elastic modulus of steel at elevated temperatures. The variations in test parameters resulted in different testmeasurements, thereby leading to differences in constitutive relationships presented in different codes and standards. Generally,tensile strength tests are conducted to obtain elastic modulus andyield strength of steel. There is a lack of experiments on themodulus of steel under pression. This is because in tensilestrength tests, plications that may arise due to geometric instabilities and con?nement of specimen is eliminated. However, itis generally assumed that the modulus of elasticity for steel, derived based on tensile strength tests, is the same for pressionstate.Fig. 3 and 4 show the yield strength and modulus of elasticityof steel as a function of temperature, respectively. The test dataplotted in the ?gures are piled from various hightemperatureproperty tests as shown on the ?gures. Both the yield strength andelastic modulus decrease as temperature increases. This decreasecan be attributed to the nucleus of the iron atoms in steel movingfarther apart due to rising temperature in steel, leading to decreased bond strength, which in turn reduces the yield strengthand elastic modulus.It can be seen in the ?gures that there is signi?cant variation intest data on yield strength and modulus of elasticity at temperatures above 300176。Stirland 1980 . As seen in Fig. 7, thermal strain of steel increaseswith temperature up to nearly 750176。 C. However, it was found experimentally that when thestress level is high, the effect of creep bees signi?cant in steelmembers even at temperatures of 300176。 Cand at different but constant stress levels was used. In the second case Fig. 8 b , test data from an experiment reported byHarmathy 1967 and Harmathy and Stanzak 1970 were used,Harmathy tested A36 steel rods under constant temperature of550176。 the stress was maintained constantas shown in Fig. 8 b .It can be seen in Fig. 8 a , for the three cases of constant stress49, , and 98 MPa , and constant temperature 550176。Huang and Tan 2003 . Creep tests Kirby and Preston 1988。 C, after which pointthermal strain starts to increase again.Variation of thermal strain models as speci?ed in ASCE andEC3 are also plotted in Fig. 7. Minimal differences exist betweenthe Eurocode and ASCE models for thermal strain of steel up to700176。 C, while ASCE andPoh models assume a loss of 30 and 40%, respectively, at 400176。 C, thus not capturingthe full range of temperatures observed in ?re conditions.Mechanical PropertiesA review of the literature indicated that there have been morestudies on the hightemperature mechanical properties of steelthan on thermal properties. Tests for the high temperaturesstrength properties are conducted in mainly two w