## Info

Note: The effective yield strength is defined at 2% strain.

Source: European Committee for Standardisation (CEN), 2000b, Draft prEN 1993-1-2, Eurocode 3: Design of Steel Structures, Part 1.2: General Rules, Structural Fire Design (London: British Standards Institution).

Note: The effective yield strength is defined at 2% strain.

Source: European Committee for Standardisation (CEN), 2000b, Draft prEN 1993-1-2, Eurocode 3: Design of Steel Structures, Part 1.2: General Rules, Structural Fire Design (London: British Standards Institution).

In simple calculations, the coefficient of thermal expansion of steel may be assumed to be a constant so that the incremental thermal expansion strain is given by eth =14 x 1Q-5 AT

### 37.4.2.2 Concrete 37.4.2.2.1 Thermal Strains

The thermal strain of concrete is complex and is influenced by a number of factors. According to Anderberg and Thelandersson (1976) and Khoury and coworkers (Khoury 1983; Khoury et al. 1986), the thermal strain of concrete may be divided into thermal expansion strain, creep strain, and a stress induced transient thermal strain. Interested readers should refer to the above references for more

Stress A

fc,T

ecrush,T Strain £c,T

FIGURE 37.10 Stress-strain relationship of concrete at elevated temperatures.

detailed information on how to evaluate these different strain components. Eurocode 4 (CEN 2001) takes a simple approach and gives the coefficient of thermal expansion of concrete as eth = —1.8 x 10—4 + 9 x 10—6 T + 2.3 x 10—11T3 for 20°C < T < 700°C;

### 37.4.2.2.2 Stress-Strain Relationships

The mechanical properties of concrete are more variable than those of steel. Phan and Carino (1998, 2000) recently carried out a survey of mechanical properties of concrete (including high strength concrete) at elevated temperatures. Khoury (1992) provided an explanation of the variability in concrete mechanical properties at elevated temperatures. Values in Eurocode 4 (CEN 2001) may be regarded as the lower bound values of different test results for normal strength concrete.

Figure 37.10 shows the Eurocode 4 model for the stress-strain relationship of concrete and definitions of various parameters. The stress-strain relationship is divided into two parts: the ascending part and the descending part. The Eurocode 4 equation for the ascending part is where ac,T, ec T, fc,T, ecu T, are, respectively, the stress, strain, peak stress, and strain at peak stress for concrete at elevated temperature T. From Equation 37.18, the initial Young's modulus of concrete may be obtained from

The descending part is a straight line, joining the peak point (A) with the point of concrete crush (B) in Figure 37.10.

Values of fc,T, ecu,T, and ecrush,T, are required to determine the complete stress-strain relationship of concrete at elevated temperatures. Table 37.6 gives their values recommended by Eurocode 4 (CEN 2001). This table also gives the retention factors for modulus of elasticity.

37.4.3 Design of Steel Elements 37.4.3.1 Steel Beams

In general, the load carrying capacity of a steel beam depends on the bending moment capacity of its cross-section and its slenderness if lateral torsional buckling occurs. Unlike structural design at ambient eth = 0.0014

TABLE 37.6 Strength, Strain Limits, and Elastic Modulus of Normal Weight Concrete (NWC) and

Lightweight Concrete (LWT) at Elevated Temperatures

TABLE 37.6 Strength, Strain Limits, and Elastic Modulus of Normal Weight Concrete (NWC) and

Lightweight Concrete (LWT) at Elevated Temperatures

Temperature

Kr-

= fc,Tfc,a

ecu,T x 103

ecrush,T x 103

kE,T —

Ej/Ea

0 0