Practical Design Methods for Fire Resistance of Restrained Cellular Steel Beams

Thermal responses of steel beams under fire can be intricate, considering the coupling effects between material thermal-expansion, mechanical property degradation, and constraints by surrounding structural members. While research efforts have focused on catenary action of structural members without initial imperfections, few accurate and efficient methods are found to reveal the fire resistance of restrained cellular steel beams (RCSBs). In this paper, parametric and regression analysis are applied to investigate the thermal behavior of RCSBs with initial imperfections. Eight groups of RCSBs are set up to demonstrate how various design parameters may affect structural responses at elevated temperatures. The results indicate that axial restraint stiffness ratio, load ratio, and opening diameter-to-height ratio significantly affect the structural responses of RCSBs in fire, followed by the rotational restraint stiffness ratio and span-to-depth ratio as secondary effects. Through the orthogonal and regression analysis, simplified formulas for four characteristic temperatures and four characteristic internal forces are defined, which agree with finite element results to a certain extent. Meanwhile, reasonable range of each design parameter is put forward for a more efficient and applicable calculation of thermo-mechanical responses of RCSBs. The proposed formulas are practical, convenient and accurate enough to be applied for engineering design.