Easy Trends to Analyse Structural Profiles: Lumped Capacitance Vs Simplified Equation

Abstract

This work presents the calculation of the temperature in different cross-sections of structural profiles (IPE, HEM, L and UAP) using the lumped capacitance method and the simplified equation from Eurocode 3 part 1-2. The lumped capacitance method allows the temperature calculation of the solid body at any time instant during the heat transient process, as a constant and uniform value. The simplified equation from Eurocode 3 part 1-2 is a simple model for heat transfer based on the uniformly distributed temperature over the cross-section surface and directly proportional to section factor of the element. Steel profiles have as almost thermal behaviour uniform during the heat transfer process when submitted to fire conditions and the lumped capacitance method allows a great simplification to estimate the temperature field in the element and may be used when Biot number is lower than unity. Therefore, thermal analysis of solids with high thermal conductivity using this method is adequate. For the studied steel profiles, a thermal analysis was also performed using the simplified equation from the Eurocode 3 part 1-2 in order to validate the obtained results from the lumped capacitance method. The results from both methods are presented for discussion and analysis.

Analytical Equations Applied to the Study of Steel Profiles under Fire According to Different Nominal Temperature-Time Curves

“…Different research using experimental and numerical methodologies are used to study the behavior of different materials under fire conditions [12][13][14][15][16][17][18]. Nevertheless, there are some cases where analytical methods can be used.…”

“…Firstly, in cases where bodies can be assumed to have a uniform temperature at any instant during the transient process, so that the temperature gradient may be considered negligible, such as thin solids or metals with high conductivity. Any thermal analysis that uses this idealization can be performed using the lumped capacitance method [18][19][20][21][22][23]. Secondly, in cases when a body can be assumed semi-infinitely thick for the time span considered.…”