# A Method for Translating Compartment Fire Durations to Equivalent Fire Resistance Time at Standard Fire Test Condition

• Takeyoshi Tanaka
• Tensei Mizukami
Conference paper

## Abstract

In performance-based structural fire safety design, various calculation models are used to predict the structural behaviors of building elements exposed to fire. Although many of such calculation models require material properties of building elements as input data, it is often difficult, technically and economically, to obtain such material properties. A potential and practicable alternative is to make use a method to translate the fire duration in arbitrary compartment fire conditions to the equivalent fire resistance time of the existing standard fire furnace testing. This paper aims to develop a method for translating the duration of ventilation-controlled compartment fires to equivalent fire resistance time in the standard fire test. The method includes a simple calculation model integrating the radiation heat loss through window openings as well as the heat losses to compartment boundary and fuel and by ventilation. The translation formula is based on the premise that fire-resistant performance is assessed by prescribed temperature criteria. Example calculation results for equivalent fire resistance time are demonstrated. By this translation method, the fire resistance capability of building elements can be assessed without requiring their thermal properties.

## Keywords

Structural fire safety design Ventilation-controlled compartment fires ISO 834 standard fire MQH formula Equivalent fire resistance time

## Nomenclature

A

Area (m2)

C

Constant

c

Specific heat of solid (kJ/kg)

cp

Specific heat at constant pressure of air (kJ/kg)

H

Height (m)

h

Heat transfer coefficient (kW/m2 K)

I

Thermal inertia (kWs1/2/m K)

k

Thermal conductivity (kW/m K)

m

Mass flow rate (kg/s)

mb

Mass burning rate (kg/s)

Q

Rate of heat release, transfer (kW)

q

Heat flux (kW/m2)

T

Temperature (K)

t

Time (s, min)

x

Distance from surface into solid (m)

## Greek Symbols

α

Thermal diffusivity [=k/cρ] (m2/s)

Φ

Factor defined by Eq. 5

ρ

Density (kg/m3)

τ

Fire resistance time (s, min)

## Subscripts

a

Air

b

Compartment boundary

e

Building element

r

T

Total (area) of compartment boundary

w

Window

0

Initial, ambient

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