Timoshenko beam formulation for in-plane behaviour of tapered monosymmetric I-beams: Analytical solution and exact stiffness matrix
The presence of curved centroidal axis in tapered monosymmetric I-beams results in coupling between the axial and flexural behaviours. In this paper, an extended Timoshenko beam formulation that incorporates the axial–flexure coupling in the governing differential equations is presented. The propose...
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Veröffentlicht in: | Thin-walled structures 2021-05, Vol.162, p.107604, Article 107604 |
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Sprache: | eng |
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Zusammenfassung: | The presence of curved centroidal axis in tapered monosymmetric I-beams results in coupling between the axial and flexural behaviours. In this paper, an extended Timoshenko beam formulation that incorporates the axial–flexure coupling in the governing differential equations is presented. The proposed formulation is applicable to generic 3D tapered I-beam, with monosymmetric/ bisymmetric cross-section, under in-plane loading. The governing equations are solved analytically and the results are validated with 3D finite element model for a range of tapered I-beams under distributed axial and transverse loadings. Further, the analytical solutions are used to develop an exact 1D tapered beam element (TBE) that can be used within the finite element framework. The main advantage of the proposed approach is that it allows tapered I-beam with monosymmetric section to be modelled as a straight-line segment along its web-centreline. The analytical solutions are also used to develop the exact shape functions for interpolating nodal variables and stress resultants within the element. The proposed beam element is validated by considering a statically indeterminate beam subjected to distributed axial and transverse loads. The displacements, rotations, stress resultants, normal and shear stresses obtained from the proposed beam element show good agreement with 3D FE model.
•Extended Timoshenko beam formulation for tapered monosymmetric I-beams.•Differential equations incorporate coupling between axial and flexural behaviours.•Analytical solution is derived for in-plane behaviour under distributed loads.•Exact stiffness matrix and shape functions are developed for a 1D tapered beam element. |
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ISSN: | 0263-8231 1879-3223 |
DOI: | 10.1016/j.tws.2021.107604 |