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Title
Non-prismatic Beams: a Simple and Effective Timoshenko-like Model
AuthorBalduzzi, Giuseppe ; Aminbaghai, Mehdi ; Sacco, Elio ; Füssl, Josef ; Eberhardsteiner, Josef ; Auricchio, Ferdinando
Published in
International Journal of Solids and Structures, 2016, Vol. 90, Issue July, page 236-250
PublishedElsevier, 2016
LanguageEnglish
Document typeJournal Article
Keywords (EN)Non-prismatic Timoshenko beam / beam modeling / analytical solution / tapered beam / arches
Project-/ReportnumberCariplo Foundation: iCardioCloud 20131779
Project-/ReportnumberCariplo Foundation: SICURA 20131351
Project-/ReportnumberFoundation Banca del Monte di Lombardia Progetto Professionalitá Ivano Benchi: Enhancing Competences in Wooden Structure Design 1056
ISSN0020-7683
URNurn:nbn:at:at-ubtuw:3-3584 Persistent Identifier (URN)
DOI10.1016/j.ijsolstr.2016.02.017 
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 The work is publicly available
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Abstract (English)

The present paper discusses simple compatibility, equilibrium, and constitutive equations for a non-prismatic planar beam. Specifically, the proposed model is based on standard Timoshenko kinematics (i.e., planar cross-section remain planar in consequence of a deformation, but can rotate with respect to the beam centerline). An initial discussion of a 2D elastic problem highlights that the boundary equilibrium deeply influences the cross-section stress distribution and all unknown fields are represented with respect to global Cartesian coordinates. A simple beam model (i.e. a set of Ordinary Differential Equations (ODEs)) is derived, describing accurately the effects of non-prismatic geometry on the beam behavior and motivating equations terms with both physical and mathematical arguments. Finally, several analytical and numerical solutions are compared with results existing in literature. The main conclusions can be summarized as follows. (i) The stress distribution within the cross-section is not trivial as in prismatic beams, in particular the shear stress distribution depends on all generalized stresses and on the beam geometry. (ii) The derivation of simplified constitutive relations highlights a strong dependence of each generalized deformation on all the generalized stresses. (iii) Axial and shear-bending problems are strictly coupled. (iv) The beam model is naturally expressed as an explicit system of six first order ODEs. (v) The ODEs solution can be obtained through the iterative integration of the right hand side term of each equation. (vi) The proposed simple model predicts the real behavior of non-prismatic beams with a good accuracy, reasonable for the most of practical applications.

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