Simplified and Accurate Stiffness of a Prismatic Anisotropic Thin-Walled Box

Giacomo Canale1, *, Felice Rubino2, Paul M. Weaver3, Roberto Citarella2, Angelo Maligno4
1 Rolls-Royce plc, Moor Lane, Derby, UK
2 Department of Industrial Engineering, University of Salerno, Giovanni Paolo II 132, 84084 Fisciano (SA), Italy
3 Department of Aerospace Engineering, University of Bristol, Queens Building, University Walk, Bristol BS8 1TR, UK
4 Institute for Innovation in Sustainable Engineering, University of Derby, Quaker Way, Derby DE1 3EE, UK

© 2018 Canale et al.

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: ( This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Rolls-Royce plc, Department of Aerospace Engineering, Moor Lane, Derby, DE24 8BJ, UK, Tel: +44 (0) 1332 2 49885; E-mail:



Beam models have been proven effective in the preliminary analysis and design of aerospace structures. Accurate cross sectional stiffness constants are however needed, especially when dealing with bending, torsion and bend-twist coupling deformations. Several models have been proposed in the literature, even recently, but a lack of precision may be found when dealing with a high level of anisotropy and different lay-ups.


A simplified analytical model is proposed to evaluate bending and torsional stiffness of a prismatic, anisotropic, thin-walled box. The proposed model is an extension of the model proposed by Lemanski and Weaver for the evaluation of the bend-twist coupling constant.


Bending and torsional stiffness are derived analytically by using physical reasoning and by applying bending and torsional stiffness mathematic definition. Unitary deformations have been applied when evaluation forces and moments arising on the cross section.


Good accuracy has been obtained for structures with different geometries and lay-ups. The model has been validated with respect to finite element analysis. Numerical results are commented upon and compared with other models presented in literature.


For cross sections with a high level of anisotropy, the accuracy of the proposed formulation is within 2% for bending stiffness and 6% for torsional stiffness. The percentage of error is further reduced for more realistic geometries and lay-ups.

The proposed formulation gives accurate results for different dimensions and length rations of horizontal and vertical walls.

Keywords: Thin-walled beams, Composite box, Bending stiffness, Torsional stiffness, Composite beam, Bend-twist coupling.