## Example 374

Temperatures in protected steelwork

For the cross-section in case 2 of Example 37.2, calculate the protected steel temperature under the natural fire condition obtained in Example 37.1. Fire protection is by sprayed lightweight concrete whose thermal properties are given in Table 37.1. Assume the same steel thermal properties as in Example 37.3.

Calculation results

The calculations are performed for intervals of 5 s and results of only the first time increment are shown.

Equation 37.17 gives f = 1.129 and DTs = —2.54°C. As pointed out in Section 37.3.4, this negative number should be changed to 0.

Figure 37.5 plots the protected steel temperature development. The maximum steel temperature is 602.58° C, reached at 51.25 min.

37.4 Design of Structural Elements at Elevated Temperatures

### 37.4.1 General

The remaining sections of this chapter will introduce the reader to design calculations to assess structural stability at elevated temperatures. In Europe, the structural fire safety design of steel elements is covered in ENV 1993-1-2 (CEN 2000b), commonly known as Eurocode 3 Part 1.2 (to be referred to as Eurocode 3 hereafter), composite steel/concrete elements in ENV 1994-1-2 (CEN 2001) or Eurocode 4 Part 1.2 (Eurocode 4), reinforced concrete structures in ENV 1992-1-2 (CEN 1996), or Eurocode 2 Part 1.2, timber structures in ENV 1995-1-2 (CEN 2000c) or Eurocode 5 Part 1.2 and masonry structures in ENV 1996-1-2 (CEN 1997) or Eurocode 6 Part 1.2. At present, design calculations for steel and composite steel/concrete structures are advanced. Design calculations for concrete and timber structures are relatively brief and there is a significant lack of information for fire safety design of masonry structures. Also, there is very little information available to enable fire safety design calculations for structures made of more ''specialist'' construction materials such as glass, fiber reinforced plastics, aluminum. This chapter will present detailed information to enable fire safety design calculations of steel and composite steel/concrete structural elements. Structures using other materials will be not be dealt with in this chapter due to a significant lack of information.

It should be borne in mind that fire is an accidental event and its coincidence with extreme structural loading is rare. Fire attack is more likely to occur during normal use of a building. Therefore, for structural fire safety design, the design structural loads should be those present during normal service of a building, and further reduced to allow for occupant escape and combustible materials burning off.

Investigations into the collapse of the World Trade Center (FEMA 2002) have raised concern over the reliability of fire protection materials. It is assumed in this chapter that a fire protection material is able to fulfill its intended functions during the life of the protected structure and also during a fire exposure. This may be ensured by making sure that the fire protection material can stick to the protected structure or by limiting deflections of the structure. Also, fire protection materials may get damaged. At present, there are very few studies of this problem and there is insufficient information to help develop a sensible simple design guide to assess the acceptable extent of damage to fire protection materials. In the light of this, the designer has to ensure that any damage to the fire protection material is repaired.

The structural fire safety design criterion is the same as at ambient temperature, that is, the residual load carrying capacity of a structural member should not be lower than the applied load under the fire condition.

37.4.2 Mechanical Properties of Steel and Concrete at Elevated Temperatures

### 37.4.2.1 Steel

The stress-strain relationships of steel at elevated temperatures depend on whether steady state or transient state testing is employed. In steady state testing, the material temperature is held at a constant value and stress is changed. In transient state testing, stress is applied and the material temperature is then changed. Transient state testing is preferred since it reflects the realistic situation of a structure in fire, where structural loads are applied before fire exposure. In transient state testing, the rate of heating has some influence due to creep strain. But since the steel creep strain is small, mechanical testing of steel at elevated temperatures is usually carried out by using a typical heating rate of about 10° C/min as found in realistic steel structures exposed to fire conditions.

In Eurocode 3, the stress-strain curve of steel consists of a straight line for the initial response, followed by an elliptical relationship and then a plateau. Table 37.4 gives the mathematical descriptions used in Eurocode 3 and Figure 37.9 provides an illustration of this model and shows various parameters to be used in the mathematical model. In order to use this model, the reduced strength and stiffness of steel at elevated temperatures are required as input data and Table 37.5 gives their values, expressed as ratios of the values at elevated temperatures to that at ambient temperature. These ratios are often referred to as retention factors.

The thermal expansion strain (eth) of steel is given by eth = -2.416 x 10-4 + 1.2 x 10-5T + 0.4 x 10-8T2 for T < 750°C eth = 0.011 for 750 < T < 860° C

TABLE 37.4 Mathematical Model of the Stress-Strain

Relationship of Steel at Elevated Temperatures

Strain range Stress s e < ep,T

Parameters

### Functions

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).

fy,T

Stress o fyT

fp,T

FIGURE 37.9 Stress-strain relationship of hot-rolled steel at elevated temperatures.

0 0