【正文】 ween the models presented in ASCE manual and Eurocode. On the contrary, published speci?c heat models vary considerably above 700176。 C / min.This heating rate can be suitable for unprotected steel members,but not for protected members with slow heating rates.On the other hand, the steadystate tests are generally fasterand easier to conduct than the transientstate tests. In the steadystate tests, the test specimen is heated to a speci?c temperatureFig. 3. Yield strength of steel as predicted by different models and asmeasured in different testsand after that a tensile test is carried out. Stress and strain valuesare recorded continuously under constant temperature. The testcan be either loadcontrolled loading rate is constant or strainFig. 4. Elastic modulus of steel as predicted by different models andas measured in different testsperatures for longer time duration, therefore, other factors, suchas hightemperature creep timedependent plastic strain undercontrolled strain rate is constantOutinen 2007。 Anderberg 1988 . Therefore, when used in the ?reresistance analysis, the Eurocode constitutive relationships generally produce slightly more ?exible responses as pared toASCE or Poh constitutive models. This is attributed to the factthat in the transientstate tests, adopted by the Eurocode, part ofhightemperature creep is included in the resulting temperaturestressstrain curves Buchanan 2001 . However, less informationis known about the test data that were used to derive ASCEtemperaturestressstrain curves of steel. On the other hand, Poh2001 developed generalized temperaturestressstrain relationsfor structural steel based on a large set of experimental data.These relations account for speci?c features, such as the yieldplateau and the effect of strain hardening. These temperaturestressstrain relations have been validated against the speci?edrelationships in codes and standards, and they have been shown togive more realistic predictions of ?re resistance when used inconjunction with hightemperature creep model. These constitutive relationships are presented in the “Dorn_Harmathy Modi?edCreep Model” section of the Appendix, which also illustrates theplexity of the expressions through the utilization of so manycoef?cients for determining the different aspects of thetemperaturestressstrain curves of steel.Another difference between the three constitutive models isthe assumed limits for the elastic phase. ASCE manual and Pohmodels consider a sharp yield point as an end of the linearelasticphase, while Eurocode considers another point, called the “proportionality limit” as an end of the linear phase, as shown in Fig.6. However, the end of elasticity in the Eurocode is the yieldpoint, and is de?ned as the offset stress also known as proofstress corresponding to % strain, as shown in Fig. 6.Deformation PropertiesThe deformation properties that in?uence the ?re response ofsteel structures are thermal strain and hightemperature creep. Thefollowing sections discuss the variations in deformation properties of steel at elevated temperatures.Thermal StrainThere have been many tests to characterize thermal strain of steelat elevated temperatures, results from some of which are piled in Fig. 7 Outinen 2007。 C, followed by an increasingthermal strain up to 1 , 000176。 Harmathy 1967 . Dorn’s creep theoryassumes constant stress d s / dt = 0 . However, in the case of restrained beams exposed to ?re, the ?re induced stresses vary considerably and rapidly with time and temperature, and theseconditions are not captured by Dorn’s theory. Therefore, an alternate hightemperature creep model that can capture variable stressscenarios is required to account for these extreme conditions.ANSYS 2007 provides 13 creep models that can be ?ttedempirically. ANSYS provides nonlinear regression tools for ?tting creep models with creep test data. Implicit creep ModelNumber 11 is selected since it can model both the primary andsecondary creep, and is capable of predicting creep strain regardless of any coupling between time and either stress or temperatureof steel. This is because ANSYS employs a variation of “strainhardening rule” for integrating creep strains. The fundamentaltheory for this creep model is based on the work of Zienkiewiczand Cormeau on uni?ed theory on plasticity and creep strains.The model is presented in a simpli?ed format in the ANSYStheoretical manual. Both DornHarmathy and ANSYS hightemperature creep models are presented in the Appendix.To illustrate the current contradictions with respect to hightemperature creep models, Fig. 8 shows a parison of the results from the analyzes using the ANSYS creep model andHarmathy 1967 creep model a modi?ed Dorn theory creepmodel with test data. The two creep models ANSYS and Harmathy were pared for two cases, namel