Calculator for Transient Steel Heating Under Fire Conditions
This tool calculates the lumped transient temperature of steel under fire conditions using standard time-temperature curves. You can select unprotected or protected steel, and various input parameters can be changed.
The ISO 834 time-temperature curve is given by 
The ASTM E119 time-temperature curve is approximated by 
The rate of change temperature of the unprotected steel is given by ![dT_{steel}/dt = F/V \cdot 1/(\rho_s c_s) \cdot [h(T_{fire} - T_{steel}) + \epsilon \sigma(T_{fire}^4 - T_{steel}^4)]](http://s.wordpress.com/latex.php?latex=dT_%7Bsteel%7D%2Fdt%20%3D%20F%2FV%20%5Ccdot%201%2F%28%5Crho_s%20c_s%29%20%5Ccdot%20%5Bh%28T_%7Bfire%7D%20-%20T_%7Bsteel%7D%29%20%2B%20%5Cepsilon%20%5Csigma%28T_%7Bfire%7D%5E4%20-%20T_%7Bsteel%7D%5E4%29%5D%20&bg=ffffff&fg=000000&s=0 "dT_{steel}/dt = F/V \cdot 1/(\rho_s c_s) \cdot [h(T_{fire} - T_{steel}) + \epsilon \sigma(T_{fire}^4 - T_{steel}^4)]")
The rate of change temperature of the protected steel is given by ![dT_{steel}/dt = F/V \cdot k_i/(d_i \rho_s c_s) \cdot [\rho_s c_s / (\rho_s c_s + (F/V d_i \rho_i c_i) / 2)] \cdot (T_{fire} - T_{steel})](http://s.wordpress.com/latex.php?latex=dT_%7Bsteel%7D%2Fdt%20%3D%20F%2FV%20%5Ccdot%20k_i%2F%28d_i%20%5Crho_s%20c_s%29%20%5Ccdot%20%5B%5Crho_s%20c_s%20%2F%20%28%5Crho_s%20c_s%20%2B%20%28F%2FV%20d_i%20%5Crho_i%20c_i%29%20%2F%202%29%5D%20%5Ccdot%20%28T_%7Bfire%7D%20-%20T_%7Bsteel%7D%29%20&bg=ffffff&fg=000000&s=0 "dT_{steel}/dt = F/V \cdot k_i/(d_i \rho_s c_s) \cdot [\rho_s c_s / (\rho_s c_s + (F/V d_i \rho_i c_i) / 2)] \cdot (T_{fire} - T_{steel})")
More information on the above equations can be found in the textbook Structural Design for Fire Safety by Buchanan
This calculator is powered by the free and open source tools Python, Numpy, and matplotlib, and the source code is freely available here.
Please send any bug reports or comments to me at koverholt@gmail.com.