Abstract
The subject of this report is the derivation of the method of estimating the temperature rise curves of rooms subjected to fire conditions. Taken into consideration in the estimation are the opening factor and the thermal conductivity of the structure. The opening factor is given by the expression H1/2 AB/AT, where H is the height of the opening (m), AB is the area of the wall openings (m2), and AT is the total area of the inside surfaces of the structure (m2). Fig. 1 shows a model of a concrete building while Fig. 2 shows the influence of H on the opening factor.
By the principle of conservation of energy, the generated heat should be equal to the sum of all the heat losses. The equation of heat balance is as follows :
QH = QW + QB + QG (1)
where QH = quantity of heat produced by combustion of all inflammable materials in a room,
QW = quantity of heat lost by conduction through the walls,
QB = quantity of heat lost by radiation through wall openings, and
QG = quantity of heat carried away with the combustion gas,
all quantities in the same heat unit (kcal.).
The quantity of generated heat QH is calculated by the formula QH = Rq where q is the calorific value of wood determined to be 2575kcal/kg. representing 60% complete combustion, and R is the rate of combustion (kcal/hr). R is obtained by the use of the formula R = 5.5H1/2 AB (kcal/min) = 330H1/2 AB (kcal/hr). This formula for value of R had been determined theoretically and had been verified experimentally. (See Fig. 3).
The quantity of heat lost by conduction QW is obtained from the expression :
QW = AC λ dt/dx (2)
where AC is the total area of the inside surfaces exposed to the heat (m2), λ is the thermal conductivity of the walls (kcal/m.hr.°C) and dt/dx is the temperature gradient of the wall which can be determined graphically by Schmidt’s method for non steady thermal conduction. (See Fig. 4). Heat losses QB and QG are functions of the opening factor and of the thermal conductivity. Those quantities are graphed as ratios of QH for some values of H1/2 AB/AT and λ. (See Fig. 10).
The fire temperature rise curves are graphed against fire duration in Fig. 8. Values of opening factors are from 0.02 to 0.12 and values of the thermal conductivity used are λ = 1 kcal/m.hr.°C for concrete wall, λ = 0.5kcal/m.hr.°C for plaster wall, and λ = 0.1kcal/m.hr.°C for perlite board.
Buildings are classified according to the value of their opening factors into 9 classes, Class A to Class I. (See Table 4.) By the use of the temperature curves, fire temperatures for 7 classes of actual buildings (Class A to Class G ) were estimated and the results are shown on Fig. 12. Assumptions used in the estimate are as follows:
1. Values of fire load W are 100kg/m2 and 50kg/m2 of floor area. These values were obtained from results of surveys conducted on various concrete buildings in Japan.
2. Duration of the fire is given by the formula T = W/R, where T is the time in minutes and R = 5.5H1/2 AB kcal/min.
