Asymmetric Folded Plate with Parallel Edges in Validation of their Static Behavior by Combining Vlasov Torsion Theory with Bernoulli Bending Theory

Triantafyllos K. Makarios1, *, Athanasios P. Bakalis1, Asimina Athanatopoulou1
1 Institute of Structural Analysis and Dynamics of Structures, School of Civil Engineering, Aristotle University of Thessaloniki, Thessaloniki, Greece

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© 2023 Makarios 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 Institute of Structural Analysis and Dynamics of Structures, School of Civil Engineering, Aristotle University of Thessaloniki, Thessaloniki, Greece; E-mail:



A new hybrid procedure that combines the Vlasov torsion theory with the Bernoulli bending theory is presented herein, to demonstrate qualitatively and quantitatively the operation of asymmetric folded plates with parallel edges, which are loaded with gravity static loads.


A recently proposed technique based on Vlasov torsion theory is used for the exact calculation of the Principal Elastic Reference System in a reinforced concrete folded plate having an asymmetric thin-walled open cross-section with parallel edges. Moreover, the warping moment (or bi-moment) concept of the Vlasov theory is combined with the pure-bending around two axes, according to the Bernoulli bending theory, to determine the normal stresses along the longitudinal dimension of the folded plate.


Τhe warping properties of a thin-walled open cross-section are determined by calculating: (a) the elastic characteristics (elastic center, principal axes) of the section, (b) the principal start point, the sectorial coordinates, the wrapping moment of inertia and the wrapping stiffness of the section. Finally, the normal stresses along the longitudinal dimension are calculated considering the bi-axes flexure with the bi-moment phenomenon.


Τhe exact solution of normal stresses at the middle section of an examined folded plate along the longitudinal dimension is found by combining the Bernoulli bending theory for prismatic beams and the Vlasov torsion theory for thin-walled open sections.


The current procedure can be used as a benchmark analysis method of asymmetric folded plates in order to evaluate the reliability of the results of various analysis F.E.M. software, covering an open issue of the structural analysis of special structures.

Keywords: Folded plate, Principal elastic reference system, Principal start point, Vlasov torsion theory, Sectorial coordinates, Warping moment of inertia.