20.500.12556/DKUM-100524 Lateral-torsional buckling of sustainable timber, steel, and reinforced concrete beams using MINLP cost optimization and sensitivity to material and CO2 price variations 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. 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 trajnostno načrtovanje konstrukcij bočna zvrnitev lesene konstrukcije jeklene konstrukcije optimizacija stroškov stroški emisij CO2 true false true MDPI Angleški jezik Slovenski jezik https://www.mdpi.com/journal/sustainability Članek v reviji 2026-09-22 12:16:54 2026-09-22 12:16:54 2026-09-23 03:08:38 0000-00-00 00:00:00 2026 0 0 34 str. issue 18, [article no.] 9567 Vol. 18 Sep. 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 2026-08-19 2026-09-14 2026-09-17 624.04:502.131.1 291991811 10.3390/su18189567 2071-1050 sustainability-18-09567.pdf sustainability-18-09567.pdf 1 F383DCD7673FFB5209A3CF33F57591E9 11816f5b1736cb9b9572af93b942bfdeeaab35e9ba2c8667704eedaecc38e577 e2814016-b66e-11f1-9ea3-00155d0001be https://dk.um.si/Dokument.php?lang=slv&id=213144 https://www.mdpi.com/2071-1050/18/18/9567 1 bcba85d4-b66e-11f1-9ea3-00155d0001be https://dk.um.si/Dokument.php?lang=slv&id=213143 Fakulteta za gradbeništvo, prometno inženirstvo in arhitekturo 0 0 0