{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:35:33Z","timestamp":1760236533173,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2021,12,5]],"date-time":"2021-12-05T00:00:00Z","timestamp":1638662400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["52178143","51578120"],"award-info":[{"award-number":["52178143","51578120"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005046","name":"Natural Science Foundation of Heilongjiang Province","doi-asserted-by":"publisher","award":["LH2020E018"],"award-info":[{"award-number":["LH2020E018"]}],"id":[{"id":"10.13039\/501100005046","id-type":"DOI","asserted-by":"publisher"}]},{"name":"2021 Social Science Development Research Project of Hebei Province","award":["20210301135"],"award-info":[{"award-number":["20210301135"]}]},{"name":"Humanities and Social Science Research Project of Higher Education institutions of Hebei Province","award":["SQ2021115"],"award-info":[{"award-number":["SQ2021115"]}]},{"name":"Northeast Petroleum University Guided Innovation Fund","award":["2020YDL-02"],"award-info":[{"award-number":["2020YDL-02"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Tubular flange composite beams are increasingly applied in modern bridge structures. In order to investigate the overall stability behavior of doubly symmetric tubular flange composite beams with lateral bracing under concentrated load, the analysis of elastic lateral-torsional buckling is conducted by the energy variation method. The analytical solution of critical moment of doubly symmetric tubular flange composite beams with lateral bracing is obtained. Meanwhile, the simplified calculation formula of critical moment is fitted by 1stOpt software based on 26,000 groups of data, and the accuracy is verified by the finite element method. It is found that, the critical moment rises obviously with increasing lateral bracing stiffness, and adding lateral bracing to doubly symmetric tubular flange composite beams is beneficial to improve the overall stability in engineering practice. Finally, the influence of several parameters including concrete strength, span, steel ratio of flange and height-thickness ratio of web are studied. The results show that the concrete strength and the web height-thickness ratio have a weak influence on critical moment of elastic lateral-torsional buckling, while the influence of span-depth ratio and flange steel ratio is very significant.<\/jats:p>","DOI":"10.3390\/sym13122328","type":"journal-article","created":{"date-parts":[[2021,12,7]],"date-time":"2021-12-07T02:48:13Z","timestamp":1638845293000},"page":"2328","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Lateral-Torsional Buckling Analysis for Doubly Symmetric Tubular Flange Composite Beams with Lateral Bracing under Concentrated Load"],"prefix":"10.3390","volume":"13","author":[{"given":"Yingchun","family":"Liu","sequence":"first","affiliation":[{"name":"Heilongjiang Key Lab of Disaster Prevention, Mitigation and Protection Engineering, Northeast Petroleum University, Daqing 163318, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ziwen","family":"He","sequence":"additional","affiliation":[{"name":"Heilongjiang Key Lab of Disaster Prevention, Mitigation and Protection Engineering, Northeast Petroleum University, Daqing 163318, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenfu","family":"Zhang","sequence":"additional","affiliation":[{"name":"Heilongjiang Key Lab of Disaster Prevention, Mitigation and Protection Engineering, Northeast Petroleum University, Daqing 163318, China"},{"name":"School of Architecture Engineering, Nanjing Institute of Technology, Nanjing 211167, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jing","family":"Ji","sequence":"additional","affiliation":[{"name":"Heilongjiang Key Lab of Disaster Prevention, Mitigation and Protection Engineering, Northeast Petroleum University, Daqing 163318, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuchen","family":"Liu","sequence":"additional","affiliation":[{"name":"Handan Key Laboratory of Building Physical Environment and Regional Building Protection Technology, School of Architecture and Art, Hebei University of Engineering, Handan 056038, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zizhen","family":"Wang","sequence":"additional","affiliation":[{"name":"Handan Key Laboratory of Building Physical Environment and Regional Building Protection Technology, School of Architecture and Art, Hebei University of Engineering, Handan 056038, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ruili","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Management Engineering and Business, Hebei University of Engineering, Handan 056038, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kailin","family":"Yang","sequence":"additional","affiliation":[{"name":"Heilongjiang Key Lab of Disaster Prevention, Mitigation and Protection Engineering, Northeast Petroleum University, Daqing 163318, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhichao","family":"Zhang","sequence":"additional","affiliation":[{"name":"Heilongjiang Key Lab of Disaster Prevention, Mitigation and Protection Engineering, Northeast Petroleum University, Daqing 163318, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,12,5]]},"reference":[{"key":"ref_1","unstructured":"Smith, A. 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