Exact approach for evaluating the buckling load of multilayered orthotropic elastic columns : application to timber columns

Kočman, Peter (avtor), Planinc, Igor (avtor), Huč, Sabina (avtor)

This paper presents an exact analytical method for evaluating the buckling load of three-dimensional multi-layered orthotropic elastic columns. While classical Euler-based approaches remain widely used in design, there is a lack of exact analytical formulations capable of capturing both orthotropy and multi-layered configurations with arbitrary fiber orientations. The proposed method, based on the Simo–Reissner beam model, addresses this gap by enabling precise determination of critical buckling loads, while allowing each layer to have its own constitutive model and orthotropic orientation. Two characteristic orthotropic orientations are examined: cross-sectional orthotropy and longitudinal orthotropy. The results show that cross-sectional orthotropy has a negligible influence on the buckling load (variations within approximately 0.01%), whereas longitudinal orthotropy leads to significant reductions, exceeding 10%–20% depending on fiber orientation and slenderness. The reduction becomes more pronounced at higher slenderness ratios. The analytical results are validated against finite element simulations, showing a difference of approximately 3.6%, and compared with the Eurocode 5 (EC5) method, which may differ by about 1% depending on assumptions. A parametric analysis reveals that a 20% variation in the elastic modulus in the loading direction results in up to approximately 25% change in the buckling load, while variations in shear moduli and Poisson’s ratios generally affect the results by less than 1%. Application to multilayered timber columns, such as cross-laminated timber (CLT), indicates that configurations with fewer, thicker layers and an odd number of layers can increase the buckling load by up to 13–30% compared to equivalent even-layered configurations. Overall, the proposed approach provides both theoretical insight and practical guidance for the design of orthotropic timber columns.

• Jezik: Angleški jezik
• Ključne besede: buckling load, analytical solution, elastic column, orthotropy, wood, timber, Simo-Reissner beam model
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FGG - Fakulteta za gradbeništvo in geodezijo
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2026
• Št. strani: 11 str.
• Številčenje: Vol. 89, art. 112064
• PID: 20.500.12556/RUL-182519
• UDK: 624.011.1
• ISSN pri članku: 2352-0124
• DOI: 10.1016/j.istruc.2026.112064
• COBISS.SI-ID: 278131971
• Datum objave v RUL: 14.05.2026

Gradivo je del revije

• Naslov: Structures
• Založnik: Elsevier
• ISSN: 2352-0124
• COBISS.SI-ID: 525573145

Licence

• Licenca: CC BY-NC-ND 4.0, Creative Commons Priznanje avtorstva-Nekomercialno-Brez predelav 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by-nc-nd/4.0/deed.sl
• Opis: Najbolj omejujoča licenca Creative Commons. Uporabniki lahko prenesejo in delijo delo v nekomercialne namene in ga ne smejo uporabiti za nobene druge namene.

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: uklonska obremenitev, analitična rešitev, elastični steber, ortotropija, les, Simo-Reissnerjev model nosilca

Projekti

• Financer: MVZI - Ministry of Higher Education, Science and Innovation of the Republic of Slovenia
• Program financ.: CRESTIMB
• Številka projekta: C3360-24-452017

• Financer: EC - European Commission
• Številka projekta: 101094340
• Naslov: ForestValue2 - Innovating forest-based bioeconomy
• Akronim: ForestValue2