Validation of the Vlasov torsion theory for rectangular solid cross-sections and for rectangular closed tube cross-sections
O. Elarras (TU Delft - Civil Engineering & Geosciences)
P.C.J. Hoogenboom – Mentor (TU Delft - Applied Mechanics)
M. Veljkovic – Mentor (TU Delft - Steel & Composite Structures)
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Abstract
To describe the behaviour of beams which are loaded on a torsional force it is possible to make use of the Saint-Venant formula, if the beam is unconstrained on both sides. This theory can be used regardless the cross-sectional dimensions of the beam. If the beam is only constrained at one side and unconstrained at the other side, it is possible to make use of the Vlasov torsion theory to describe the behaviour of the beam, however this theory is proven only for open crosssection. In this report it is attempted to prove the Vlaslov torsion theory for rectangular solid cross-sections and for rectangular closed tube cross-section.
It is important to describe a proper method to validate the Vlasov torsion theory. The beam will be constrained only at one side and a torsional external moment will work at the free end of the beam. During the whole validity process it has been chosen to keep the material properties and the external moment the same in order to compare the results. The length of the beams are kept variable to see what the influence is of the length of the beam on the accuracy of the Vlasov torsion theory. First, the maximum horizontal displacement and the maximum normal stress has been calculated by use of the Vlasov equations. Second, the maximum horizontal displacement and the maximum normal stress have been calculated by use of the FEM software Abaqus. These outcomes have been compared with each other by use of a ratio check, namely if the maximum error is within 15 percent it can be stated that the theory is valid for the tested beam length.
From the obtained results it can be stated that the Vlasov torsion theory seems to be valid regarding the maximum horizontal displacement for the rectangular solid cross-sections and the rectangular closed tube cross-sections. The obtained results for the maximum normal stress exceed the maximum allowable error of 15 percent. Regarding the obtained results for the maximum normal stress, the Vlasov torsion theory can not be declared valid for the mentioned cross-sections.