Structural Design for Fire Safety

37.1 Introduction 37-1

37.2 Fire Severity 37-2

Standard Fire Exposure • Natural Fire Exposure

37.3 Introduction to Heat Transfer 37-8

Conduction • Convection • Radiation • Some Simplified Solutions of Heat Transfer • Section Factors • Thermal Properties of Materials

37.4 Design of Structural Elements at Elevated Temperatures 37-14

General • Mechanical Properties of Steel and Concrete at Elevated Temperatures • Design of Steel Elements • Composite Composite Steel/Concrete Members

37.5 Design for Unprotected Steelwork 37-27

Integration of Structural Load Bearing and Fire Protection Functions of Concrete • Utilizing Whole Building Performance in Fire

37.6 Concluding Remarks 37-31

References 37-32

Appendix 37-33

37.1 Introduction

Structural fire safety is one of the three requirements that have to be fulfilled by a fire resistant construction, whose function is to ensure that a fire in a building is contained within the compartment of origin so that occupants in other parts of the building can escape to safety and fire damages do not become excessive. To achieve this, the load bearing structure of a fire resistant construction should not collapse in fire. The other two fire resistance requirements are

• Insulation. The unexposed surface of a fire resistant construction should not be heated excessively and cause further ignition. Clearly, whether any material will be ignited or not will not only depend on the temperature of the unexposed surface, but also on its nature and its relative position to the unexposed surface. Nevertheless, at present, regulations worldwide limit the average temperature rise on the unexposed surface to 140°C and the maximum local temperature rise to 180°C.

• Integrity. Gaps should not develop in fire resistant construction to spread fire.

The practice of dividing a building into a number of compartments bounded by fire resistant construction is called fire resistant compartmentation. It should be pointed out that fulfillment of the

above three fire resistance requirements only applies to those elements of construction that are necessary for the fire resistant compartment to contain fire. Other elements, whose failure to fulfill these requirements does not lead to a failure of the fire resistant compartment, do not require any fire safety design consideration. Before the designer commences detailed structural fire safety design calculations, he should work with the client and the fire service authority to determine the size of the fire resistant construction. This will depend on factors such as fire regulations on the maximum size of fire resistant compartmentation, insurance premium, and fire brigade access and is beyond the scope of this chapter.

Until recently, assessment of fire resistance of a construction is performed experimentally in standard fire resistance test furnaces and under the standard fire condition. Each country has its own fire resistance test standard [e.g., ASTM E-119 (ASTM 1985) in the United States, BS 476 (BSI 1987) in the United Kingdom, and ISO 834 (ISO 1975)], but they are largely similar. The standard fire resistance test has many shortcomings, for example, high cost, time consuming, limitation of specimen size, idealized loading condition, idealized support condition, lack of repeatability, and unrealistic fire exposure. It is now possible to perform some fire resistant design by calculations and the objective of this chapter is to introduce the reader to structural design calculations to ensure stability of load bearing members in the event of a fire.

It should be pointed out that the behavior of a complete structure in fire and that of isolated elements can be different because a complete structure will have characteristics, such as load redistribution, structural interactions, that will not exist in isolated elements. Also, it is worth noting that current calculation methods are based on flexural behavior at small deflections. The behavior of structural elements at large deflections can be vastly different and such a different behavior may be explored to improve structural fire safety design. Behaviors of elements at large deflections and complete structures in fire are beyond the scope of this chapter. Interested readers may consult the book by Wang (2002).

In general, design calculations to check structural safety in fire involves three parts:

1. Assessment of the fire severity to which a structural member is exposed. For structural fire safety design, a fire is usually quantified by a temperature-time relationship of the fire.

2. Evaluation of the temperature field in the structural member under the above fire condition.

3. Calculation of the remaining load carrying capacity of the structural member at elevated temperatures and comparison with the applied load.

This chapter will introduce the reader to all three aspects of structural fire safety design, while emphasizing on the third.

It is understandable that the September 11 tragedy has initiated the interest of many engineers in structural fire safety design. However, it must be mentioned that there had already been great progresses on this topic well before the September 11 event in many parts of the world, particularly in Europe and the United Kingdom. At present, there is a systematic and comprehensive coverage of structural fire safety design methods in Europe, through developments of the so-called Eurocodes. Thus, this chapter will adopt Eurocodes as the basis of its design guidance. However, it is hoped that there will be sufficient explanations of the fundamental engineering principles so that the basis of Eurocode design rules can be similarly adopted in different design environments.

37.2 Fire Severity

Fire severity to structural fire safety design is akin to applied mechanical loads on a structure to structural design at ambient temperature. Fires can occur anywhere; however, for structural fire safety design, they are often assumed to take place in a building enclosure. In such a situation, starting from ignition, a fire can go through a number of stages. In the early stages, combustion is restricted to local areas near the ignition source and temperatures of the combustion gases are low, the safety of a structure exposed to fire attack is very rarely threatened. Later, under certain circumstances, a localized fire can transform very quickly to involve all the combustible materials in the fire enclosure. The transition from a localized fire to a fire engulfing the entire enclosure is called flashover and the fire at this stage is called a postflashover fire. At this stage, the combustion gas temperatures are very high and stability of the building structure may be threatened, the consequence of which can lead to rapid fire spread and loss of life and property. It is this stage of the fire behavior that will be described below. Interested readers should consult some excellent textbooks, such as Drysdale (1999) and Karlsson and Quinterie (2000), to obtain a deep understanding of enclosure fire behavior.

37.2.1 Standard Fire Exposure

There are two ways of dealing with postflashover fires for structural fire safety design. First, the standard fire temperature-time relationship may be adopted. The standard fire equation is similar in different countries of the world. In the European standard (CEN 2000a), the standard fire temperature-time relationship is given by

where the standard fire exposure time (t) is in minutes and the fire temperature Tfi and ambient temperature Ta are in degrees celsius.

Equation 37.1 is used for wood based, or cellulosic, fires. For fire resistant design of offshore structures, the standard hydrocarbon fire curve should be used. This fire has a much faster rate of initial increase in temperature. The standard hydrocarbon fire temperature-time relationship is given by (CEN 2000a)

Tfi = 1080(1 - 0.325e-°'167t - 0.675e-2:5t) + Ta (37.2)

Figure 37.1 plots the two standard fire curves. It is obvious that the standard cellulosic fire curve gives a monotonically increasing temperature-time relationship that cannot be sustained in any real fire. In order to reflect some reality in the standard fire exposure, a limiting time of fire exposure is specified. This is the familiar standard fire resistance rating. In standard fire resistance design calculations, specifications for the required standard fire resistance rating are based on very broad criteria such as the occupancy type and height of a building. Whilst these criteria give a broad indication of fire load and consequence of fire exposure, they do not consider other important factors that affect the behavior of an enclosure fire such as ventilation condition and construction materials.

37.2.2 Natural Fire Exposure

As a regulatory control tool, the standard fire exposure is simple to use. However, fires cannot be expected to behave according to the standard temperature-time relationship. For more realistic

Fire exposure time, min

FIGURE 37.1 A comparison of standard cellulosic and hydrocarbon fire temperature-time relationships.

Fire exposure time, min

FIGURE 37.1 A comparison of standard cellulosic and hydrocarbon fire temperature-time relationships.

assessment of performance of structures in fire, it is necessary to quantify realistic fire behavior. Assuming that a fire enclosure is at the same temperature during the postflashover phase, the fire temperature-time relationship may be determined by carrying out an energy balance analysis for the fire enclosure; that is heat input into the fire (heat released from combustion) = heat losses from the fire

Figure 37.2 depicts a postflashover enclosure fire situation. Heat losses from the fire include

1. Heat lost to the outside by hot gases flowing out of the fire compartment through openings (Q lc).

2. Heat lost to the enclosure lining (Qlw).

3. Heat lost to the outside environment by radiation through the opening (Q lr).

4. Heat required to increase the combustion gas temperature (Q lg).

The rate of heat release is the most important factor. At present, due to the difficulty of numerically modeling fire spread and random distribution of combustible materials in a fire enclosure, it is not possible to accurately calculate the rate of heat release of a fire. Nevertheless, from considerations of the main governing factors of burning, a number of empirical equations have been derived. From basic hydrodynamics, it can be shown that the amount of hot gases flowing out of a fire compartment is related to Av\fhv, the so-called ventilation factor, where Av is the opening area and hv is the opening height. In order to sustain burning, cold air should be supplied into the fire compartment to replenish the lost hot gases. Thus, the amount of cold air entering the fire compartment is also related to Av\fhv. It follows that the amount of fresh oxygen supply to the fire is related to Av\fhv. If burning is ventilation controlled, that is, the rate of burning is governed by the amount of fresh oxygen available, the rate of heat release of a fire is a function of Av\/hv. On the other hand, if the opening is large but the burning area is small, a fire can become fuel controlled, that is, the rate of burning is governed by the available surface area of the fuel bed or combustible materials. Also, the amount of available combustible materials, that is, the fuel load, will determine the duration of burning.

Fire development inside a fire enclosure will also be affected by thermal properties of the fire enclosure lining materials, that is, the bounding walls and floors. A material that has a low thermal conductivity, that is, heat is difficult to penetrate the material, will lose a small amount of heat through the material. A material that has a high thermal capacitance, that is, a large amount of heat is required to raise its temperature, will absorb a large amount of heat of the burning fire and vice versa. Combining these two factors, the quantity that is used to describe the thermal properties of fire enclosure lining materials is kpC where k and pC are the thermal conductivity and thermal capacitance of the lining materials, respectively.

Using the three quantities mentioned above, that is, the ventilation factor, the fire enclosure lining material property, and the fuel load, a number of approximate temperature-time relationships of

FIGURE 37.2 Fully developed enclosure fire, showing various heat losses. Copyright 2005 by CRC Press

postflashover enclosure fires have been developed. Among them, the so-called parametric temperature-time curves of Eurocode 1 Part 1.2 (CEN 2000a), based on the results of Pettersson et al. (1976), are widely accepted. As shown in Figure 37.3, a parametric fire curve has an ascending branch and a descending branch. The ascending branch is used to describe the temperature-time relationship of a fire during its growth and steady burning stages, when it is ventilation controlled. The descending branch describes the decay period of the fire. The ascending branch is expressed by

Tfi = 1325(1 - 0.324e-0:2t* - 0.204e-17t* - 0.472e-19t*) where the modified time t* (in hours) is related to the real time t (in hours) by t * = tr in which r is a dimensionless parameter, given by r =

ON Vl160> 2

In Equation 37.5, O is the ventilation factor defined as

Av\fhv

in which At is the total enclosure (including openings) area.

In Equation 37.5, b = \JkpC [in J/(m2s1/2K)] is the overall thermal property of the fire enclosure lining material. For a fire enclosure constructed of a combination of different lining materials, complicated equations have recently been introduced in Eurocode 1 Part 1.2 (CEN 2000a) to find an equivalent value of b.

The ascending branch of the fire temperature-time relationship terminates at time (td*) when the maximum fire temperature is obtained. This time is a function of the fire load in the fire enclosure and is given by

In Equation 37.7, qt,d is the fire load density (in MJ/m ) related to the total surface area of the fire enclosure At. Since fire load density is usually specified with regard to the floor area Af, the fire load per enclosure area qt d is related to the fire load per floor area (qf,d) using qt,d = qf,dAf/At (37.8)

It can be seen that the ascending branch of the fire temperature-time curve is not dependent on the fire load. This is because a fire is assumed to be ventilation controlled and the rate of heat release is the

Temperature ▲

Time

FIGURE 37.3 Parametric time-temperature curve of Eurocode 1 Part 1.2.

Time

FIGURE 37.3 Parametric time-temperature curve of Eurocode 1 Part 1.2.

same, depending only on the ventilation condition. The effect of fire load is to change the duration of burning t* according to Equation 37.7.

For simplicity, the descending branch is given by a straight line. Since structural behavior is only slightly affected by the descending branch of the fire temperature-time relationship, more complicated equations for the descending branch are not justified. The rate of the descending branch depends on the fire duration. The fire temperature during cooling is given by

Tfi = Tfi,max - 250(3 - t**)(t* - t**) for 0.5 < t* < 2.0 (37.9)

In Equation 37.9, Tfimax is the maximum fire temperature, obtained by substituting the time in

Equation 37.7 into Equation 37.3.

In Eurocode 1 Part 1.2 (CEN 2000a), the limit of application of the above fire temperature-time relationship is for fire compartments up to 100 m2 in floor area with the maximum compartment height at 4 m. For larger or taller compartments, the effect of nonuniform temperature distribution in the fire enclosure cannot be ignored. Unfortunately, simple methods are not available yet.

From previous discussions, it is clear that the fire temperature-time relationship depends on the amount of combustible materials (or fuel load) in a fire enclosure, the ventilation condition, and thermal properties of the fire enclosure lining material. During a design, the ventilation condition and thermal properties of the fire enclosure lining material may be estimated from construction details, that is, the window size and construction materials. Thermal properties of some enclosure lining materials maybe found in Table 37.1.

The design fire load is building specific. However, since the exact type and amount of combustible materials will not be known during the design stage, it is unlikely that the design fire load can be known with any certainty. In fire engineering design calculations, it is common to specify a generic fire load for a type of building, depending on its proposed use. This is similar to specifying a general structural load for structural design at ambient temperature. Values in Table 37.2 may be used as a guide. More detailed information on fire load maybe obtained from a Conseil International du Batiment (CIB) report (CIB 1986). It is important to point out that there are many uncertainties about the design fire load. When conducting a fire engineering design, the designer should perform a sensitivity study to investigate the consequence of adopting a range of possible fire loads.

EXAMPLE 37.1 Natural fire exposure

Figure 37.4 shows the dimensions and other design data of a fire enclosure. Evaluate the postflashover fire temperature-time curve inside the enclosure.

TABLE 37.1 Thermal Properties of Generic Fire Protection Materials
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