Properties of Concrete at Elevated Temperatures

Table 1

Constitutive relationships of high-temperature properties of concrete.

	NSC—ASCE Manual 1992	HSC—Kodur et al. 2004 [10]	NSC and HSC—EN1992-1-2: 2004 [4]
Stress-strain relationships	𝜎𝑐=𝑓^′𝑐,𝑇1−𝜀−𝜀max,𝑇𝜀max,𝑇^2,𝜀≤𝜀max,𝑇𝑓^′𝑐,𝑇𝜀1−^max,𝑇−𝜀3𝜀max,𝑇^2,𝜀>𝜀max,𝑇,; 𝑓^′𝑐,𝑇=𝑓^′𝑐,20^∘C≤𝑇≤450^∘C𝑓^′𝑐2.011−2.353𝑇−201000,450^∘C<𝑇≤874^∘C0,874^∘C<𝑇,; 𝜀max,𝑇=0.0025+6.0𝑇+0.04𝑇^2×10^−6.	𝜎𝑐=𝑓^′𝑐,𝑇𝜀1−^max,𝑇−𝜀𝜀max,𝑇^𝐻,𝜀≤𝜀max,𝑇𝑓^′𝑐,𝑇1−30𝜀−𝜀max,𝑇130−𝑓^′𝑐𝜀max,𝑇^2,𝜀>𝜀max,𝑇,; 𝑓^′𝑐,𝑇=𝑓^′𝑐[1.0−0.003125(𝑇−20)],𝑇<100^∘C0.75𝑓^′𝑐,100^∘C≤𝑇≤400^∘C𝑓^′𝑐[1.33−0.00145𝑇],400^∘C<𝑇,; 𝜀max,𝑇=0.0018+6.7𝑓^′𝑐+6.0𝑇+0.03𝑇^2×10^−6,; 𝐻=2.28−0.012𝑓^′𝑐.	𝜎𝑐=3𝜀𝑓^′𝑐,𝑇𝜀𝑐1,𝑇2+𝜀/𝜀𝑐1,𝑇^3,𝜀≤𝜀cu1,𝑇.; For 𝜀𝑐1(𝑇)<𝜀≤𝜀cu1(𝑇), the Eurocode permits the use of linear as well as nonlinear descending branch in the numerical analysis.; For the parameters in this equation refer to Table 2.
Thermal capacity	Siliceous aggregate concrete; 𝜌𝑐=0.005𝑇+1.7,20^∘C≤𝑇≤200^∘C2.7,200^∘C<𝑇≤400^∘C0.013𝑇−2.5,400^∘C<𝑇≤500^∘C10.5−0.013𝑇,500^∘C<𝑇≤600^∘C2.7,600^∘C<𝑇.; Carbonate aggregate concrete; 𝜌𝑐=2.566,20^∘C≤𝑇≤400^∘C0.1765𝑇−68.034,400^∘C<𝑇≤410^∘C25.00671−0.05043𝑇,410^∘C<𝑇≤445^∘C2.566,445^∘C<𝑇≤500^∘C0.01603𝑇−5.44881,500^∘C<𝑇≤635^∘C0.16635𝑇−100.90225,635^∘C<𝑇≤715^∘C176.07343−0.22103𝑇,715^∘C<𝑇≤785^∘C2.566,785^∘C<𝑇.	Siliceous aggregate concrete; 𝜌𝑐=0.005𝑇+1.7,20^∘C≤𝑇≤200^∘C2.7,200^∘C<𝑇≤400^∘C0.013𝑇−2.5,400^∘C<𝑇≤500^∘C−0.013𝑇+10.5,500^∘C<𝑇≤600^∘C2.7,600^∘C<𝑇≤635^∘C.; Carbonate aggregate concrete; 𝜌𝑐=2.45,20^∘C≤𝑇≤400^∘C0.026𝑇−12.85,400^∘C<𝑇≤475^∘C0.0143𝑇−6.295,475^∘C<𝑇≤650^∘C0.1894𝑇−120.11,650^∘C<𝑇≤735^∘C−0.263𝑇+212.4,735^∘C<𝑇≤800^∘C2,800^∘C<𝑇≤1000^∘C.	Specific heat (J/kg C); 𝑐=900, for 20°C ≤ 𝑇≤100°C,; 𝑐=900+(𝑇−100),  for 100°C < 𝑇 ≤ 200°C,; 𝑐=1000+(𝑇−200)/2, for 200°C < 𝑇≤400°C,; 𝑐=1100, for 400°C < 𝑇 ≤ 1200°C.; Density change (kg/m^3); 𝜌=𝜌(20^∘C) = Reference density; for 20°C ≤ 𝑇 ≤ 115°C,; 𝜌=𝜌(20^∘C)(1−0.02(𝑇−115)/85); for 115°C < 𝑇 ≤ 200°C,; 𝜌=𝜌(20^∘C)(0.98−0.03(𝑇−200)/200); for 200°C < 𝑇 ≤ 400°C,; 𝜌=𝜌(20^∘C)(0.95−0.07(𝑇−400)/800); for 400°C < 𝑇 ≤ 1200°C,; Thermal capacity = 𝜌×𝑐.
Thermal conductivity	Siliceous aggregate concrete; 𝑘𝑐=−0.000625𝑇+1.5,20^∘C≤𝑇≤800^∘C1.0,800^∘C<𝑇,; Carbonate aggregate concrete; 𝑘𝑐=1.355,20^∘C≤𝑇≤293^∘C−0.001241𝑇+1.7162,293^∘C<𝑇.	Siliceous aggregate concrete; 𝑘𝑐=0.85(2−0.0011𝑇),20^∘C<𝑇≤1000^∘C.; Carbonate aggregate concrete; 𝑘𝑐=0.85(2−0.0013𝑇),20^∘C≤𝑇≤300^∘C0.85(2.21−0.002𝑇),300^∘C<𝑇.	All types: Upper limit: 𝑘𝑐=2−0.2451(𝑇/100)+0.0107(𝑇/100)2,; for 20°C ≤ 𝑇 ≤ 1200°C.; Lower limit: 𝑘𝑐=1.36−0.136(𝑇/100)+0.0057(𝑇/100)2,; for 20°C ≤ 𝑇 ≤ 1200°C.
Thermal strain	All types: 𝜀th=0.004𝑇^2−400+6(𝑇−20)×10^−6.	All types: 𝜀th=0.004𝑇^2−400+6(𝑇−20)×10^−6.	Siliceous aggregates: 𝜀th=−1.8×10^−4+9×10^−6𝑇+2.3×10^−11𝑇^3, for 20°C ≤ 𝑇 ≤ 700°C.; 𝜀th=14×10^−3, for 700°C < 𝑇 ≤ 1200°C,; Calcareous aggregates: 𝜀th=−1.2×10^−4+6×10^−6𝑇+1.4×10^−11𝑇^3, for 20°C ≤ 𝑇 ≤ 805°C.; 𝜀th=12×10^−3, for 805°C < 𝑇 ≤ 1200°C.