Acta Mechanica

, Volume 230, Issue 11, pp 3945–3961 | Cite as

Distortional buckling of composite thin-walled columns of a box-type cross section with diaphragms

  • Czesław Szymczak
  • Marcin KujawaEmail author
Open Access
Original Paper


Distortional buckling of axially compressed columns of box-like composite cross sections with and without internal diaphragms is investigated in the framework of one-dimensional theory. The channel members are composed of unidirectional fibre-reinforced laminate. Two approaches to the member orthotropic material are applied: homogenization based on the theory of mixture and periodicity cells, and homogenization based on the Voigt–Reuss hypothesis. The principle of stationary total potential energy is applied to derive the governing differential equation. The obtained buckling stress is valid in the linear elastic range of column material behaviour. Numerical examples address simply supported columns, and analytical critical stress formulas are derived. The analytical and FEM solutions are compared, and sufficient accuracy of the results is observed.

List of symbols


Height of cross section


Fibre volume fraction


Number of half-waves of a buckling mode


Polar radius of gyration


Displacement of cross section corner


Homogenized Poisson’s ratio


Poisson’s ratio in the longitudinal direction


Poisson’s ratio in the transverse direction


Poisson’s ratio of the matrix


Poisson’s ratio of fibres


Cartesian coordinate system


Area of cross section


Elastic modulus in the longitudinal direction


Elastic modulus in the transverse direction


Homogenized Young’s modulus in the longitudinal direction


Homogenized Young’s modulus in the transverse direction


Young’s modulus of the matrix


Young’s modulus of fibres


Homogenized shear modulus


Shear modulus of the matrix


Shear modulus of fibres


Polar moment of inertia


Moment of inertia of wall cross section in the longitudinal direction


Moment of inertia of wall cross section in the transverse direction


Free torsion moment of inertia of wall cross section


Torsional stiffness of cross section


Longitudinal stiffness of cross section

\(K_{\mathrm{\gamma }}\)

Distortional stiffness of cross section

\(\overline{K}_{\mathrm{\gamma }}\)

Diaphragm stiffness


Length of column


Characteristic length of column


Bending moment of walls in the transverse direction


Bending moment of walls in the longitudinal direction


Compressive axial load


Critical distortional buckling load


Potential energy of compressive load due to bending


Potential energy of compressive load due to torsion


Elastic strain energy


Potential energy of elastic bending


Potential energy of cross-sectional distortion


Potential energy of torsion

\(\gamma \)

Distortion angle

\(\delta \)

Wall thickness

\(\eta \)

Coefficient of characteristic length of column

\(\sigma _\mathrm{b}\)

Buckling stress

\(\sigma _{\mathrm{cr}}\)

Critical buckling stress

\(\sigma _{\mathrm{cr},\mathrm{min}}\)

Minimum critical buckling stress

\(\varPi \)

Total potential energy



The calculations presented in this paper were carried out at the TASK Academic Computer Centre in Gdańsk, Poland.

Compliance with ethical standards

Conflict of interest

The author declares that he has no conflict of interest.


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Authors and Affiliations

  1. 1.Department of Structural Engineering, Faculty of Ocean Engineering and Ship TechnologyGdańsk University of TechnologyGdańskPoland
  2. 2.Department of Structural Mechanics, Faculty of Civil and Environmental EngineeringGdańsk University of TechnologyGdańskPoland

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