Buckling analysis of braced and unbraced steel frames exposed to fire Carlos Couto a , Paulo Vila Real a,⇑ , Nuno Lopes a , João Paulo Rodrigues b a LABEST—Civil Engineering Department, University of Aveiro, Campus Universitário de Santiago, 3810-193 Aveiro, Portugal b ISISE—Institute for Sustainability and Innovation in Structural Engineering, University of Coimbra, Rua Luís Reis Santos – Pólo II, 3030-788 Coimbra, Portugal article info Article history: Received 27 June 2012 Revised 13 November 2012 Accepted 14 November 2012 Available online 7 January 2013 Keywords: Fire Steel Column Frame Buckling Critical load abstract This paper presents a buckling analysis of steel frames, taking into account the effect of temperature, in order to evaluate the buckling lengths of the columns in a fire situation. The results obtained for the buck- ling lengths are compared with those suggested in the fire part of the Eurocode 3 (Part 1.2) for the design of columns in braced frames in a fire situation. Part 1.2 of the Eurocode 3 does not provide rules regarding the buckling lengths for unbraced frames used in fire design, so this study offers a proposal for the buck- ling lengths of columns in unbraced steel structures. The results of the calculated mechanical resistance of the frames (using simple calculation models) and the evaluated buckling lengths are compared with the results obtained with advanced calculation models for a number of different cases in a fire situation. Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction At normal temperature, any influence of the deformed geome- try of the structure (second-order effects) in the verification of col- umn stability is accounted for by performing a global analysis that takes into account these non-linear effects and checks the member instability with non-sway buckling lengths, or more simply, con- sidering the system length as the buckling length of the column as suggested in the Part 1.1 of the Eurocode 3 [1]. Most of the com- puter programs available today can perform this type of analysis in a practical and simple way. However, in the fire situation, the tem- perature must be taken into account when performing these sec- ond-order analyses, making them too complex and prohibitive for a daily basis usage and thus justifying the need for simple methods to check column stability in fire design. Assuming that in the fire situation the influence of second-order effects must be taken into account by considering the appropriate buckling lengths in simple calculation methods, the study of the frame buckling and the subsequent buckling of its members in high temperatures is of extreme importance. It is interesting to note that performing a global second-order analysis at normal temperature and calculating the mechanical resistance of members with non-sway buckling lengths (or the sys- tem length for simplicity) in fire design can lead to very unsafe re- sults [2]. The fire part of Eurocode 3 (Part 1.2) [3] states that in the case of a braced frame in which each storey comprises a separate fire com- partment with sufficient fire resistance, the buckling length, l fi , of a continuous column may be taken as 0.5 l in an intermediate storey and 0.7 l in the top storey, where l is the system length in the rel- evant storey. For unbraced frames, no specific guidance is given by the Eurocode. A few studies exist regarding the verification of the stability of columns for the fire situation. Publication No. 159 from the Steel Construction Institute in the UK [4] proposes that in the case of col- umns in sway frames under fire conditions the non-dimensional slenderness ratio (for the fire situation) may conservatively be ta- ken as  k h ¼ 1:25  k, with  k being the non-dimensional slenderness at normal temperature. A publication from the ECCS [5] suggests that if a global analysis of the frame is not performed to take account of instability effects at elevated temperatures, a conservative default critical temperature of 300 °C should be considered. Gomes et al. [6] made an alternative proposal to the buckling lengths suggested in Eurocode 3 for columns in braced frames, but the study did not address unbraced frames. Wang [7] has also studied the effects of frame continuity on the behaviour of steel columns in the fire sit- uation and concluded that buckling lengths are very close to 0.5 and 1.0 for non-sway and sway frames, respectively. Shepherd and Burgess [8] have studied the effects of axial restraint in the buckling of columns in the fire situation and have shown that the axial restraint itself does not influence the magnitude of the buckling load of the column as much as the temperature, as there is an increase on the axial force and the buckling load can be reached more quickly in a highly restrained column. Skowronski 0141-0296/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.engstruct.2012.11.020 ⇑ Tel.: +351 234370049. E-mail address: pvreal@ua.pt (P. Vila Real). Engineering Structures 49 (2013) 541–559 Contents lists available at SciVerse ScienceDirect Engineering Structures journal homepage: www.elsevier.com/locate/engstruct