{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:14:49Z","timestamp":1760145289951,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"13","license":[{"start":{"date-parts":[[2024,6,29]],"date-time":"2024-06-29T00:00:00Z","timestamp":1719619200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001871","name":"FCT\u2014Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["CEECINST\/00026\/2018"],"award-info":[{"award-number":["CEECINST\/00026\/2018"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Applied Sciences"],"abstract":"<jats:p>A parametric investigation of several unbraced steel frames with regular and irregular geometry subjected to elevated temperatures is carried out in this study to determine the most accurate procedure and buckling lengths to be considered during the structural design under a fire situation. In such conditions, the stiffness and strength of steel decrease considerably due to high temperatures, and uncertainty remains in the application of the fire design rules of Eurocode 3 Part 1-2 (EN 1993-1-2) for unbraced frames as no information is given regarding the treatment of the deformed geometry (the so-called second-order effects). More precisely, it is unclear in the norm whether the verification based on the buckling length concept could be used or if a second-order analysis to calculate the internal forces is sufficient to ensure the stability of the frame in case of fire. Based on the linear buckling analysis of the steel frames accounting for the temperature development during a fire, recommendations for the appropriate buckling lengths to be used are given. Finally, it is demonstrated that using the recommended buckling lengths together with the design rules of EN 1993-1-2 leads to results in favor of safety when compared to the results obtained with the finite element method. On the other hand, it is concluded that using second-order internal forces and the real length of the columns as the buckling length, as suggested for room temperature design, yielded results outside safety when compared with the finite element method, and this analysis and verification procedure should not be used for the case of fire.<\/jats:p>","DOI":"10.3390\/app14135709","type":"journal-article","created":{"date-parts":[[2024,7,2]],"date-time":"2024-07-02T11:23:55Z","timestamp":1719919435000},"page":"5709","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Parametric Study on the Buckling of Unbraced Steel Frames under Fire Situation"],"prefix":"10.3390","volume":"14","author":[{"given":"Thiago","family":"Silva","sequence":"first","affiliation":[{"name":"Instituto Federal do Tocantins (IFTO)\u2014Civil Engineering Department, Campus Palmas, Palmas 77.021.090, TO, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0865-2225","authenticated-orcid":false,"given":"Carlos","family":"Couto","sequence":"additional","affiliation":[{"name":"RISCO\u2014Civil Engineering Department, University of Aveiro, Campus Universit\u00e1rio de Santiago, 3810-193 Aveiro, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7221-410X","authenticated-orcid":false,"given":"Paulo","family":"Vila Real","sequence":"additional","affiliation":[{"name":"RISCO\u2014Civil Engineering Department, University of Aveiro, Campus Universit\u00e1rio de Santiago, 3810-193 Aveiro, Portugal"}]},{"given":"Nuno","family":"Lopes","sequence":"additional","affiliation":[{"name":"RISCO\u2014Civil Engineering Department, University of Aveiro, Campus Universit\u00e1rio de Santiago, 3810-193 Aveiro, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2024,6,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Franssen, J.-M., and Vila Real, P. 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