FIRE DESIGN OF STEEL MEMBERS - Civil and Natural Resources ...

The variation of yield stress data is shown in Figure 3.5. This graph plots the
variation in ultimate and yield strength of steel as taken from experimental data.
The spread of data results as seen in this graph explains how difficult it is to
compare the equations recommended by different parties, and choose one as being
‘better’ than another. Most data is found for temperatures below 600 °C, which is
probably why there is greater spread in this region of the graph.
3.1.3 Determination of Limiting Steel Temperature:
The formula to determine the temperature at which the member being analysed
will fail is a direct rearrangement of the formula for the variation of the yield stress
of steel for temperatures over 215 °C. This implies that the only factor affecting
the steel strength is the yield stress with temperature.
T = 905 − 690
3.6
l
r f
where rf
is the ratio of the design action on the member under the design load for
fire specified in NZS 4203, to the design capacity of the member at room
temperature, ie R f /φR u . This formula can be used for three or four-sided exposure
to fire, and for steel beams and columns.
The design capacity of the steel section is based on the yield stress and the cross
sectional area of the beam, so assuming the cross section of the beam remains
constant and a uniform temperature is maintained throughout the steel, then this
formula is valid. This only occurs with four-sided exposure, as with three-sided
exposure to a fire, there will be significant temperature differences across the cross
section of the steel. When attempting to use this formula for three-sided exposure
a finite element approach is used to obtain a limiting temperature that accounts for
the temperature gradient in the steel.
Eurocode 3 has a different formula to calculate the limiting or critical temperature
of a steel member. This method can be used as an alternative to the strength
criteria that must be met as stated in 3.1.1. The critical temperature is based on the
degree of utilisation of the element and is given by the following equation:
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