## Abstract

Structural steel, when exposed to a uniform heat source at temperature T, will, in the absence of conductive, convective or radiative heat loss, eventually reach the temperature T and remain at that temperature for the duration of the exposure. We calculate the increase in temperature in support columns as a function of time by using the Fourier formula for heat transfer. The formula gives rise to two equations for calculating the temperature in heated steel. The first equation results from treating the formula as a difference equation, an iterative scheme that yields second-by-second changes in temperature. The second equation results from treating the formula as a differential equation, the solution of which yields a formula for temperatures at arbitrary times into the period of a fire. The difference formula approximates the integral formula very closely. Intended as a tool for general heat calculations, the methods are illustrated for box columns and WF [wide flange] columns of varying dimensions and thicknesses. The results of the calculation are then applied to the case of the World Trade Center fuel and office fires on the morning of September 11, 2001.In addition, an estimate of office fire duration based on burning times of individual items of office furniture is provided. The temperature calculations, fire durations and other evidence are brought together to demonstrate the extreme unliklihood of the core columns ever reaching critical temperatures in the World Trade Center on the morning of September 11, 2001.

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