The considerable progress in the research and development of thin-walled beam structures responds to their growing use in engineering construction and to their increased need for efficiency in strength and cost. The result is a structure that exhibits large shear strains and important non uniform warping under different loadings, such as non uniform torsion, shear bending and distortion... A unified approach is formulated in this thesis for 3D thin walled beam structures with arbitrary profile geometries, loading cases and boundary conditions. A single warping function, defined by a linear combination of longitudinal displacements at cross sectional nodes (derived from Prokic work), is enhanced and adapted in order to qualitatively and quantitatively reflect and capture the nature of a widest possible range of behaviors. Constraints are prescribed at the kinematics level in order to enable the study of arbitrary cross sections for general loading. This approach, differing from most published theories, has the advantage of enabling the study of arbitrary cross sections (closed/opened or mixed) without any restrictions or distinctions related to the geometry of the profile. It generates automatic data and characteristic computations from a kinematical discretization prescribed by the profile geometry. The amount of shear bending, torsional and distortional warping and the magnitude of the shear correction factor is computed for arbitrary profile geometries with this single formulation. The proposed formulation is compared to existing theories with respect to the main assumptions and restrictions. The variation of the location of the torsional center, distortional centers and distortional rotational ratio of a profile is discussed in terms of their dependency on the loading cases and on the boundary conditions. A 3D beam finite element model is developed and validated with several numerical applications. The displacements, rotations, amount of warping, normal and shear stresses are compared with reference solutions for general loading cases involving stretching, bending, torsion and/or distortion. Some examples concern the case of beam assemblies with different shaped profiles where the connection type determines the nature of the warping transmission. Other analyses –for which the straightness assumption of Timoshenko theory is relaxed– investigate shear deformation effects on the deflection of short and thin beams by varying the aspect ratio of the beam. Further applications identify the cross sectional distortion and highlight the importance of the distortion on the stresses when compared to bending and torsion even in simple loading cases. Finally, a non linear finite element based on the updated lagrangian formulation is developed by including torsional warping degrees of freedom. An incremental iterative method using the arc length and the Newton-Raphson methods is used to solve the non linear problem. Examples are given to study the flexural, torsional, flexural torsional and lateral torsional buckling problems for which a coupling between the variables describing the flexural and the torsional degrees of freedom occurs. The finite element results are compared to analytical solutions based on different warping functions and commonly used in linear stability for elastic structures having insufficient lateral or torsional stiffnesses that cause an out of plane buckling.

Cette thèse s’intéresse à l’étude l’effet de la corrosion sur les propriétés mécaniques des armatures corrodées et les performances mécaniques résiduelles des poutres corrodées. L’étude est basée sur deux poutres corrodées notées B2CL2 et B2CL3, conservées respectivement 26 ans et 28 ans en ambiance saline. Deux poutres non corrodées B2T2 et B2T3 conservées en conditions ambiantes ont également été testés afin d’identifier l'effet de la corrosion indépendamment du vieillissement.Les propriétés mécaniques des armatures corrodées ont été étudiées par des essais de traction.La limite d'élasticité et résistance à la rupture ont été étudiées sur la base de la section transversale résiduelle évaluée par perte de masse. Les résultats ont montré que les effets de la corrosion sur la diminution ductilité étaient très importants. La forme de la section transversale résiduelle apparait comme étant un paramètre essentiel affectant la ductilité de l'armature.Les performances résiduelles en flexion des poutres corrodées ont été étudiées. Les résultats montrent que la corrosion réduit la capacité portante et de façon plus significative, la flèche maximale à rupture en raison d’un changement de mode de rupture. La diminution de la charge de plasticité apparait en relation avec la perte de section d’acier tendu due à la corrosion Des poutres de portées courtes ont été réalisées à partir des poutres corrodées après les essais de flexion. Les tests mécaniques ont été effectués en flexion pour vérifier la réponse des poutres courtes corrodées. Les poutres courtes corrodées ont péri en flexion avec une bonne ductilité tandis que les poutres courtes non corrodées ont péri comme prévu en cisaillement suivant un mode de rupture fragile, qui a montré que la corrosion de l'armature pouvait modifier les modes de défaillance.Les produits de corrosion ont été recueillis à partir de l'armature corrodée de B2Cl3. Des expériences XRD et TG ont été menées afin d'identifier la composition des produits de corrosion. Le coefficient d'expansion des produits de corrosion a été déduit, ce qui pourrait être utile pour les recherches futures concernant le mécanisme de fissuration du béton d'enrobage. / The thesis aims to study the influence of chloride corrosion on the mechanical properties ofthe reinforcement and RC beams. The experiments were based on two corroded beams named B2Cl2 and B2Cl3, with a corroded age of 26 years and 28 years respectively. Two noncorroded beams B2T2 and B2T3 which were cast in the same condition and same time were also tested in order to make clear the corrosion effect.The mechanical properties of the corroded reinforcement were investigated by the tensiontests. The yield strength and ultimate strength were studied based on the residual gravimetrical cross-section. The results found that the impact of corrosion on the ductility was more significant than that of the strength. The shape of residual cross-section was considered to be in deep relationships with the ductility of the reinforcement.The flexural performances of the beams were studied. The results showed that the corrosion deteriorated the capacity and the ductility of the corroded beams. The corrosion degree of reinforcement was found in linear with the residual yield capacity of the corroded beams.The short-span beams were formed from the corroded beams after bending tests. Mechanical tests were carried out directly to check the response of the corroded beams. The corroded short-span beams failed in bending mode with good ductility while the non-corroded beams performed a brittle shear failure mode, which showed that the corrosion of reinforcement could change the failure modes.The corrosion products were collected from the corroded reinforcement of B2Cl3. XRD andTG experiments were conducted so as to identify the composition of the corrosion products.The expansive coefficient of the corrosion products was deduced, which could be helpful forthe further research on the cracking mechanism of the concrete cover

The considerable progress in the research and development of thin-walled beam structures responds to their growing use in engineering construction and to their increased need for efficiency in strength and cost. The result is a structure that exhibits large shear strains and important non uniform warping under different loadings, such as non uniform torsion, shear bending and distortion.<p><p>A unified approach is formulated in this thesis for 3D thin walled beam structures with arbitrary profile geometries, loading cases and boundary conditions. A single warping function, defined by a linear combination of longitudinal displacements at cross sectional nodes (derived from Prokic work), is enhanced and adapted in order to qualitatively and quantitatively reflect and capture the nature of a widest possible range of behaviors. Constraints are prescribed at the kinematics level in order to enable the study of arbitrary cross sections for general loading. This approach, differing from most published theories, has the advantage of enabling the study of arbitrary cross sections (closed/opened or mixed) without any restrictions or distinctions related to the geometry of the profile. It generates automatic data and characteristic computations from a kinematical discretization prescribed by the profile geometry. The amount of shear bending, torsional and distortional warping and the magnitude of the shear correction factor is computed for arbitrary profile geometries with this single formulation.<p><p>The proposed formulation is compared to existing theories with respect to the main assumptions and restrictions. The variation of the location of the torsional center, distortional centers and distortional rotational ratio of a profile is discussed in terms of their dependency on the loading cases and on the boundary conditions.<p><p>A 3D beam finite element model is developed and validated with several numerical applications. The displacements, rotations, amount of warping, normal and shear stresses are compared with reference solutions for general loading cases involving stretching, bending, torsion and/or distortion. Some examples concern the case of beam assemblies with different shaped profiles where the connection type determines the nature of the warping transmission. Other analyses –for which the straightness assumption of Timoshenko theory is relaxed– investigate shear deformation effects on the deflection of short and thin beams by varying the aspect ratio of the beam. Further applications identify the cross sectional distortion and highlight the importance of the distortion on the stresses when compared to bending and torsion even in simple loading cases. <p><p>Finally, a non linear finite element based on the updated lagrangian formulation is developed by including torsional warping degrees of freedom. An incremental iterative method using the arc length and the Newton-Raphson methods is used to solve the non linear problem. Examples are given to study the flexural, torsional, flexural torsional and lateral torsional buckling problems for which a coupling between the variables describing the flexural and the torsional degrees of freedom occurs. The finite element results are compared to analytical solutions based on different warping functions and commonly used in linear stability for elastic structures having insufficient lateral or torsional stiffnesses that cause an out of plane buckling. <p> / Doctorat en sciences appliquées / info:eu-repo/semantics/nonPublished