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Interactive Buckling and Post-Buckling Studies of Thin-Walled Structural Members with Generalized Beam Theory

dc.contributor.authorCai, Junleen
dc.contributor.committeechairMoen, Cristopher D.en
dc.contributor.committeememberBorggaard, Jeffrey T.en
dc.contributor.committeememberEatherton, Matthew R.en
dc.contributor.committeememberKoutromanos, Ioannisen
dc.contributor.committeememberRoberts-Wollmann, Carin L.en
dc.contributor.departmentCivil and Environmental Engineeringen
dc.date.accessioned2017-02-17T09:00:28Zen
dc.date.available2017-02-17T09:00:28Zen
dc.date.issued2017-02-16en
dc.description.abstractMost thin-walled metallic structural members experience some extent of interactive buckling that corrodes the load carrying capacity. Current design methods predict the strength of thin-walled metallic structural members based on individual buckling limit-states and limited case of interactive buckling limit state. In order to develop design methods for most coupled buckling limit states, the interaction of buckling modes needs to be studied. This dissertation first introduces a generally applicable methodology for Generalized Beam Theory (GBT) elastic buckling analysis on members with holes, where the buckling modes of gross cross-section interact with those of net cross-section. The approach treats member with holes as a structural system consisting of prismatic sub-members. These sub-members are connected by enforcing nodal compatibility conditions for the GBT discretization points at the interfaces. To represent the shear lag effect and nonlinear normal stress distribution in the vicinity of a hole, GBT shear modes with nonlinear warping are included. Modifications are made to the GBT geometric stiffness because of the influence from shear lag effect caused by holes. In the following sections, the GBT formulation for a prismatic bar is reviewed and the GBT formulation for members with holes is introduced. Special aspects of analyzing members with holes are defined, namely the compatibility conditions to connect sub-members and the geometric stiffness for members with holes. Validation and three examples are provided. The second topic of this dissertation involves a buckling mode decomposition method of normalized displacement field, bending stresses and strain energy for thin-walled member displacement field (point clouds or finite element results) based on generalized beam theory (GBT). The method provides quantitative modal participation information regarding eigen-buckling displacement fields, stress components and elastic strain energy, that can be used to inform future design approaches. In the method, GBT modal amplitudes are retrieved at discrete cross-sections, and the modal amplitude field is reconstructed assuming it can be piece-wisely approximated by polynomials. The unit displacement field, stress components and strain energy are all retrieved by using reconstructed GBT modal amplitude field and GBT constitutive laws. Theory and examples are provided, and potential applications are discussed including cold-formed steel member design and post-disaster evaluation of thin-walled structural members. In the third part, post-buckling modal decomposition is made possible by development of a geometrically nonlinear GBT software. This tool can be used to assist understanding couple-buckling limit-states. Lastly, the load-deformation response considering any one GBT mode is derived analytically for fast computation and interpretation of structural post-buckling behavior.en
dc.description.abstractgeneralHere I present novel analytical methods to quantitatively decompose interactive buckling in the thin-walled structures. Interactive buckling, where multiple buckling modes are present to initiate structure failure, often controls the load-carrying capacity of thin-walled structures, e.g., the amount of load a column can withstand or the maximum acceleration a space shuttle can experience. In this research, based on Generalized Beam Theory, I describe in detail the analytical methods revealing how buckling modes are coupled and contribute to key quantities related to the structural failure, namely, displacement, stress, and strain energy. I obtain the algorithms by performing rigorous mathematical derivations based on thin-walled mechanics. The research not only facilitates better building design according to the simplified method in the current design standard, but also enables advanced, nonlinear modal decomposition analysis using the custom-made Finite Element program. These studies aim to provide the quantitative understanding of the coupled buckling mechanism and further the development of more powerful strength prediction methods for thin-walled structures.en
dc.description.degreePh. D.en
dc.format.mediumETDen
dc.identifier.othervt_gsexam:9099en
dc.identifier.urihttp://hdl.handle.net/10919/75055en
dc.publisherVirginia Techen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectThin-walled structuresen
dc.subjectElastic bucklingen
dc.subjectPerforationsen
dc.subjectHolesen
dc.subjectGeneralized beam theoryen
dc.subjectBuckling mode decompositionen
dc.subjectPost-bucklingen
dc.titleInteractive Buckling and Post-Buckling Studies of Thin-Walled Structural Members with Generalized Beam Theoryen
dc.typeDissertationen
thesis.degree.disciplineCivil Engineeringen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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