| Title: | Lateral-torsional buckling of sustainable timber, steel, and reinforced concrete beams using MINLP cost optimization and sensitivity to material and CO2 price variations |
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| Authors: | ID Kravanja, Stojan (Author)
ID Žula, Tomaž (Author) |
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| Files: |  sustainability-18-09567.pdf (1,36 MB)
MD5: F383DCD7673FFB5209A3CF33F57591E9
 https://www.mdpi.com/2071-1050/18/18/9567
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| Language: | English |
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| Work type: | Article |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | FGPA - Faculty of Civil Engineering, Transportation Engineering and Architecture
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| Abstract: | Advancing structural sustainability requires a rigorous evaluation of the economic and environmental trade-offs inherent in engineering design and material selection. To address this in sustainable construction, this paper presents a comparative study of the lateral-torsional buckling (LTB) resistance of glulam timber, structural steel, and reinforced concrete beams under fluctuations in material and labor costs and environmental carbon impacts. Two parallel series of multi-parameter cost optimizations are performed using discrete mixed-integer non-linear programming (MINLP) via the outer-approximation/equality-relaxation algorithm to analyze configurations with active LTB controls (laterally unrestrained beams) and without LTB controls (laterally restrained beams) across various discrete spans and imposed loads. The objective functions define the production-dependent material, power, labor, and CO2 emission costs of the beams. The optimization results show that active LTB constraints force steel and concrete elements into sturdier profiles. Conversely, timber demonstrates a unique geometric behavior reversal under medium-to-high loads, shifting into tall, narrow sections. In the projected near future, when the global warming price CGW increases to a tenfold threshold, the combined self-manufacturing and production-induced CO2 emission costs of beams on average could increase by 15.2% for timber, 35.8% for steel, and 50.2% for reinforced concrete. In this case, LTB-unrestrained configurations, compared to restrained beams, will cause total production costs to increase by up to nearly one-third for timber, more than double for steel, and by one-half for reinforced concrete. At higher CGW increases, the total costs expand further, reaching up to 38.1% for timber, 144.8% for steel, and 62.5% for reinforced concrete at a hundredfold escalation. Similar cost increases can likely be expected across the construction industry at large. The sector will have to adapt. |
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| Keywords: | sustainable structural design, lateral-torsional buckling, timber beams, steel beams, reinforced concrete beams, cost optimization, discrete optimization, mixed-integer non-linear programming, sensitivity analysis, CO2 emission costs |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Submitted for review: | 19.08.2026 |
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| Article acceptance date: | 14.09.2026 |
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| Publication date: | 17.09.2026 |
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| Publisher: | MDPI |
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| Year of publishing: | 2026 |
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| Number of pages: | 34 str. |
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| Numbering: | Vol. 18, issue 18, [article no.] 9567 |
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| PID: | 20.500.12556/DKUM-100524  |
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| UDC: | 624.04:502.131.1 |
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| ISSN on article: | 2071-1050 |
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| COBISS.SI-ID: | 291991811 |
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| DOI: | 10.3390/su18189567 |
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| Publication date in DKUM: | 22.09.2026 |
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| Views: | 55 |
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| Downloads: | 1 |
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| Metadata: |    |
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| Categories: | Misc.
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