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

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

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.

• Language: English
• Keywords: buckling load, analytical solution, elastic column, orthotropy, wood, timber, Simo-Reissner beam model
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FGG - Faculty of Civil and Geodetic Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2026
• Number of pages: 11 str.
• Numbering: Vol. 89, art. 112064
• PID: 20.500.12556/RUL-182519
• UDC: 624.011.1
• ISSN on article: 2352-0124
• DOI: 10.1016/j.istruc.2026.112064
• COBISS.SI-ID: 278131971
• Publication date in RUL: 14.05.2026

Record is a part of a journal

• Title: Structures
• Publisher: Elsevier
• ISSN: 2352-0124
• COBISS.SI-ID: 525573145

Licences

• License: CC BY-NC-ND 4.0, Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
• Link: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Description: The most restrictive Creative Commons license. This only allows people to download and share the work for no commercial gain and for no other purposes.

Secondary language

• Language: Slovenian
• Keywords: uklonska obremenitev, analitična rešitev, elastični steber, ortotropija, les, Simo-Reissnerjev model nosilca

Projects

• Funder: MVZI - Ministry of Higher Education, Science and Innovation of the Republic of Slovenia
• Funding programme: CRESTIMB
• Project number: C3360-24-452017

• Funder: EC - European Commission
• Project number: 101094340
• Name: ForestValue2 - Innovating forest-based bioeconomy
• Acronym: ForestValue2