This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
,
Faculty of Civil Engineering, University of Belgrade, Belgrade, Serbia
Faculty of Civil Engineering, University of Belgrade, Belgrade, Serbia
In practice, consideration of fire protection for structural elements mainly occurs after the adopted dimensions of sections. However, this procedure leads to not the most cost-effective solution in general. To find the optimal solution, it is necessary to apply one of the optimization methods. The presented optimization of purlins RHS cross-section is performed with nonlinear programming available in widely used program Excel. The objective function is defined as producing the purlin at a minimal price, considering the price of steel, work, and fire-resistant paint. Limits are introduced to ensure the cross-section satisfies the ultimate limit state for permanent and transient load situations, as well as in case of fire. Besides the ultimate limit states, the limits are defined for serviceability limit states and for cross-sectional geometry. Optimization analysis for different ISO 834 fire durations is followed by a result comparison. It provides an overview of cross-sectional parameters that most influence the bearing capacity in case of fire. It is concluded that by increasing the exposure time to fire, the optimal solution becomes a section with a smaller perimeter, larger surface area, and a thicker layer of fire-resistant coating.
The first author thanks the Ministry of Science, Technological Development and Innovation of the Republic of Serbia for financial support via a Ph.D. student stipend. The second author thanks the Ministry of Education, Science, and Technological Development, Republic of Serbia, through Project 200092.
[{"id":138,"citationNumber":null,"type":"journal-article","title":"Topology optimization for simplified structural fire safety","DOI":"10.1016\/j.engstruct.2016.06.018","author":[{"given":"S\u00f8ren","family":"Madsen"},{"given":"Nis P.","family":"Lange"},{"given":"Luisa","family":"Giuliani"},{"given":"Grunde","family":"Jomaas"},{"given":"Boyan S.","family":"Lazarov"},{"given":"Ole","family":"Sigmund"}],"issued":{"date-parts":["2016"]},"container-title":"Engineering Structures","volume":"124","issue":null,"page":"333-343"}]
[{"id":139,"citationNumber":null,"type":"journal-article","title":"Protected steel columns vs partially encased columns: Fire resistance and economic considerations","DOI":"10.1016\/j.jcsr.2016.05.011","author":[{"given":"A.","family":"Piquer"},{"given":"D.","family":"Hern\u00e1ndez-Figueirido"}],"issued":{"date-parts":["2016"]},"container-title":"Journal of Constructional Steel Research","volume":"124","issue":null,"page":"47-56"}]
[{"id":140,"citationNumber":null,"type":"journal-article","title":"Investigating the behaviour of steel framed-tube and moment-resisting frame systems exposed to fire","DOI":"10.1016\/j.istruc.2021.05.053","author":[{"given":"Mahsa","family":"Chaboki"},{"given":"Mahdi","family":"Heshmati"},{"given":"Ali Akbar","family":"Aghakouchak"}],"issued":{"date-parts":["2021"]},"container-title":"Structures","volume":"33","issue":null,"page":"1802-1818"}]
[{"id":141,"citationNumber":null,"type":"journal-article","title":"Mechanical properties of conventional structural steel and fire-resistant steel at elevated temperatures","DOI":"10.1016\/j.jcsr.2021.106615","author":[{"given":"Waibhaw","family":"Kumar"},{"given":"Umesh Kumar","family":"Sharma"},{"given":"Mahadev","family":"Shome"}],"issued":{"date-parts":["2021"]},"container-title":"Journal of Constructional Steel Research","volume":"181","issue":null,"page":"106615"}]
[{"id":142,"citationNumber":null,"type":"journal-article","title":"Approximate optimal design of fire-resisting beams and columns","DOI":"10.1016\/s0143-974x(03)00052-x","author":[{"given":"Andrea","family":"Benedetti"}],"issued":{"date-parts":["2003"]},"container-title":"Journal of Constructional Steel Research","volume":"59","issue":"10","page":"1251-1266"}]
[{"id":143,"citationNumber":null,"type":"book-chapter","title":"Optimal steel frame design for fire resistance","DOI":"10.1007\/1-4020-5370-3_782","author":[{"given":"K.","family":"J\u00e1rmai"},{"given":"J. P. C.","family":"Rodrigues"}],"issued":{"date-parts":[null]},"container-title":"III European Conference on Computational Mechanics","volume":null,"issue":null,"page":"782-782"}]
[{"id":144,"citationNumber":null,"type":"journal-article","title":"Adequate fire safety for structural steel elements based upon life-time cost optimization","DOI":"10.1016\/j.firesaf.2020.103095","author":[{"given":"Danny","family":"Hopkin"},{"given":"Ian","family":"Fu"},{"given":"Ruben","family":"Van Coile"}],"issued":{"date-parts":["2021"]},"container-title":"Fire Safety Journal","volume":"120","issue":null,"page":"103095"}]
[{"id":145,"citationNumber":null,"type":"journal-article","title":"Optimal design of prestressed concrete hollow core slabs taking into account its fire resistance","DOI":"10.1016\/j.advengsoft.2018.05.001","author":[{"given":"V.","family":"Albero"},{"given":"H.","family":"Saura"},{"given":"A.","family":"Hospitaler"},{"given":"J.M.","family":"Montalv\u00e0"},{"given":"Manuel L.","family":"Romero"}],"issued":{"date-parts":["2018"]},"container-title":"Advances in Engineering Software","volume":"122","issue":null,"page":"81-92"}]
[{"id":146,"citationNumber":null,"type":"journal-article","title":"Design optimization of hybrid steel\/timber structures for minimal environmental impact and financial cost: A case study","DOI":"10.1016\/j.enbuild.2021.111600","author":[{"given":"D.","family":"Van Cauteren"},{"given":"D.","family":"Ramon"},{"given":"J.","family":"Stroeckx"},{"given":"K.","family":"Allacker"},{"given":"M.","family":"Schevenels"}],"issued":{"date-parts":["2022"]},"container-title":"Energy and Buildings","volume":"254","issue":null,"page":"111600"}]
[{"id":147,"citationNumber":null,"type":"journal-article","title":"Multi-objective optimization of cross laminated timber-concrete composite floor using NSGA-II","DOI":"10.1016\/j.jobe.2022.104285","author":[{"given":"Minh","family":"Van Thai"},{"given":"Philippe","family":"Galimard"},{"given":"Sidi Mohammed","family":"Elachachi"},{"given":"Sylvain","family":"M\u00e9nard"}],"issued":{"date-parts":["2022"]},"container-title":"Journal of Building Engineering","volume":"52","issue":null,"page":"104285"}]
[{"id":148,"citationNumber":null,"type":"article-journal","title":"Evrokod 3 \u2013 Projektovanje \u010deli\u010dnih konstrukcija \u2013 Deo 1-1: op\u0161ta pravila i pravila za zgrade","DOI":null,"author":[{"given":"E.N.","family":"SRPS"}],"issued":{"date-parts":["1993"]},"container-title":"Institut za standardizaciju Srbije","volume":null,"issue":null,"page":null}]
[{"id":149,"citationNumber":null,"type":"article-journal","title":"Evrokod 3 \u2013 Projektovanje \u010deli\u010dnih kontrukcija \u2013 Deo 1-1: Op\u0161ta pravila i pravila za zgrade \u2013 Nacionalni prilog","DOI":null,"author":[{"given":"E.N.","family":"SRPS"}],"issued":{"date-parts":["1993-1-1\/NA"]},"container-title":"Institut za standardizaciju Srbije","volume":null,"issue":null,"page":null}]
[{"id":150,"citationNumber":null,"type":"article-journal","title":"Eurocode 1 \u2013 Design of steel structures \u2013 Part 1-2: General rules \u2013 Structural fire design","DOI":null,"author":[{"given":"E.N.","family":"SRPS"}],"issued":{"date-parts":["1993"]},"container-title":"Institute for standardization of Serbia","volume":null,"issue":null,"page":null}]
[{"id":151,"citationNumber":null,"type":"journal-article","title":"Approach for modelling thermal properties of intumescent coating applied on steel members","DOI":"10.1016\/j.firesaf.2020.103200","author":[{"given":"Donatella","family":"de Silva"},{"given":"Antonio","family":"Bilotta"},{"given":"Emidio","family":"Nigro"}],"issued":{"date-parts":["2020"]},"container-title":"Fire Safety Journal","volume":"116","issue":null,"page":"103200"}]
[{"id":152,"citationNumber":null,"type":"journal-article","title":"Thermal characterization of intumescent fire retardant paints","DOI":"10.1088\/1742-6596\/547\/1\/012005","author":[{"given":"L","family":"Calabrese"},{"given":"F","family":"Bozzoli"},{"given":"G","family":"Bochicchio"},{"given":"B","family":"Tessadri"},{"given":"S","family":"Rainieri"},{"given":"G","family":"Pagliarini"}],"issued":{"date-parts":["2014"]},"container-title":"Journal of Physics: Conference Series","volume":"547","issue":null,"page":"012005"}]
[{"id":153,"citationNumber":null,"type":"journal-article","title":"Performance-based fire modelling of intumescent painted steel structures and comparison to EC3","DOI":"10.1016\/j.jcsr.2014.10.008","author":[{"given":"J.","family":"Kol\u0161ek"},{"given":"P.","family":"\u010ce\u0161arek"}],"issued":{"date-parts":["2015"]},"container-title":"Journal of Constructional Steel Research","volume":"104","issue":null,"page":"91-103"}]
[{"id":154,"citationNumber":null,"type":"article-journal","title":"Eurocode 1 \u2013 Action on structures \u2013 Part 1-2: General actions \u2013 Action on structures exposed to fire","DOI":null,"author":[{"given":"E.N.","family":"SRPS"}],"issued":{"date-parts":["1991"]},"container-title":"Institute for standardization of Serbia","volume":null,"issue":null,"page":null}]
[{"id":155,"citationNumber":null,"type":"journal-article","title":"A Generalized Reduced Gradient Algorithm for Solving Large-Scale Discrete-Time Nonlinear Optimal Control Problems","DOI":"10.1016\/b978-0-08-037869-5.50011-x","author":[{"given":"J.L.D.","family":"Fac\u00f3"}],"issued":{"date-parts":["1989"]},"container-title":"IFAC Proceedings Volumes","volume":"22","issue":"2","page":"45-50"}]
[{"id":156,"citationNumber":null,"type":"journal-article","title":"Nonlinear optimization using the generalized reduced gradient method","DOI":"10.1051\/ro\/197408v300731","author":[{"given":"Leon S.","family":"Lasdon"},{"given":"Richard L.","family":"Fox"},{"given":"Margery W.","family":"Ratner"}],"issued":{"date-parts":["1974"]},"container-title":"Revue fran\u00e7aise d'automatique, informatique, recherche op\u00e9rationnelle. Recherche op\u00e9rationnelle","volume":"8","issue":"V3","page":"73-103"}]
The statements, opinions and data contained in the journal are solely those of the individual authors and contributors and not of the publisher and the editor(s). We stay neutral with regard to jurisdictional claims in published maps and institutional affiliations.
