# Parametric Study on the Buckling of Unbraced Steel Frames under Fire Situation
###### Abstract
This method identifies significant fire scenarios that cause instability at the story level, using temperature and locality functions to quantify the severity of these scenarios. The method allows to identify the critical columns. In one study [18], a new method for computing the lateral stiffness of an unbraced semi-rigid steel story frame with three-segmented members was proposed. Their method can be applied towards many modeling problems where non-linear or piece-wise temperature gradients occur longitudinally in members. The story stability of unbraced steel frames subjected to non-uniform elevated temperature distribution has been studied in [19]. A review of the progressive collapse mechanisms of steel frames in the case of fire is provided in [20], and it has been identified that the load ratio, fire scenario, bracing layout, and fire protection are key factors affecting the collapse mechanism of steel structure. [PERSON] et al. [21] have investigated experimentally and numerically the collapse modes of single span frames in the case of fire and identified four main collapse modes, including column lateral collapse, column buckling collapse, and overall collapse modes (inward and outward). The authors also identified that the heating conditions and rotational stiffness of the column base had a great influence on these collapse modes. In addition, the collapse modes related to columns seem to be influenced by temperature gradients, fire protection levels, and load ratios. [PERSON] and [PERSON] [22] investigated the system-level response of braced frames under fire exposure scenarios and later, the same authors, studied the effect of transient creep on fire-induced instability in steel-framed structures [23]. In particular, it was demonstrated that the response of steel frames depends significantly on the location and type of fire exposure, as well as with the number of compartments under fire exposure. Notably, the stability of the structure was identified to be critically affected when the fire occurs in the lower levels of the building. However, the creep effects tend to be higher when the upper stories are subjected to fire, mainly because of the relatively slender members used in the top stories of the building [23]. [PERSON] et al. have developed fire fragility curves for steel frames [24; 25]. [PERSON] et al. [26] have investigated the post-earthquake fire response of steel buildings. A review on the behavior of steel frames made of high strength steels under fire exposure is provided in [27]. This study extends the previous investigation, carried out in [5], by assessing the evolution of the critical load of several steel frames with irregular geometry in fire and for 12 different fire cases corresponding to different heating schemes mostly not covered in the former study. In addition, it was considered a generalized fire in a single isolated story or/and two stories simultaneously. These different assumptions allow to analyze the most suitable buckling lengths for the verification of structures in fire in a wider number of situations than those covered in [5; 7]. Moreover, the present study investigated the fire resistance of steel frames using the simplified method, with the formulations proposed by EN1993-1-2 [15], and then compared those results with the ones yielded by advanced calculation methods, i.e., the finite element method (FEM). The aim of such comparison was to validate the proposed buckling lengths and to show that the recommendations of EN1993-1-1 [2] to use a buckling length equal to the system length when second-order analyses are used to calculate the internal forces leads to results outside of safety in the verification procedure and should not be used in case of fire.