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A study aimed at determining the thermal deformation response and thermal buckling loads of rectangular grid-stiffened composite panels is presented. Two edge conditions are considered for the panel, one in which all panel edges are free to deform, and another when all the edges are restrained. In the first case panel deformations due to a uniformly distributed thermal load are analyzed. In the latter case, thermal loads causing buckling failure due to the suppressed in-plane deformations are determined. The panel is composed of a skin and a network of stiffeners, which are all made of the same graphite-epoxy composite material. Kirchhoff's Theory is used to determine the pre-buckling deformations and load distributions of the composite laminates for a panel with free to deform edges. To illustrate both the in-plane and out-of-plane deformations of plate structures under uniform thermal loads, two thermal coefficient vectors, thermal expansion and thermal bending coefficient vectors are introduced. Linear panel buckling analysis performed by assuming a linear undeformed prebuckling state. Rayleigh-Ritz Method, which utilizes minimization of the total energy of a structure to determine the buckling loads, is used to govern the buckling analysis of composite laminates forming the panel. Lagrange Multiplier Method is used along with the Rayleigh-Ritz Method to enforce the deformation continuity constraints at discrete locations along the skin and stiffener interface. As a result, graphical and numerical presentations of the effects of skin and stiffener laminate stacking sequences on the thermal deformations and on the thermal buckling load of the grid-stiffened panel are given. / Master of Science

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Most 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. / Ph. D. / Here 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.

Pultruded, fibre reinforced, polymeric composites are now being used in a wide range of structural engineering applications, due to their high strength to weight ratios and resistance to environmental conditions. However, such materials posses a relatively low shear modulus in relation to their axial and flexural moduli. This can result in shear deformation constituting a significant proportion of the total deformation and a reduction in buckling loads for various modes of instability. An experimental and theoretical study of the influence of shear deformation on the flexural and torsional stiffnesses and various modes of instability of pultruded polymeric bars of open cross-section is therefore presented. Theories for the bending and warping torsional response of pultruded, fibre reinforced polymeric bars of open cross-section, excluding and including the influence of shear deformation, are presented. Full section bending mechanical properties of several pultruded beams are determined using a static testing apparatus and a wide variety of span configurations. Full section warping torsional mechanical properties of several pultruded bars are determined using a new testing apparatus, capable of applying a torque to any cross-section along a bar, whilst maintaining the bars lateral position. Theories for the flexural, torsional and lateral instability of pultruded, fibre reinforced polymeric bars of open cross-section, excluding and including the influence of shear deformation, are developed and presented. Parametric studies of the influence of shear deformation in the flexural, torsional and lateral instability of various pultruded bars of open cross-section are also presented. The experimental and theoretical studies indicate that shear deformation reduces significantly the non-uniform bending stiffness of pultruded polymeric bars, but that its influence on the non-uniform and restrained warping torsional stiffness is practically negligible. Shear deformation has also been found to result in a significant reduction in flexural, torsional and coupled flexural-torsional or lateral buckling loads.

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AN ABSTRACT OF THE THESIS OF TARUN KUMAR DONGA, for the Master of Science degree in Civil Engineering, Presented on August 29th 2017, at Southern Illinois University Carbondale. TITLE: EFFECT OF TEMPERATURE INCREASE ON BUCKLING OF AXIALLY RESTRAINED BEAM-COLUMNS WITH DOUBLE CURVATURE MAJOR PROFESSOR: Dr. Aslam Kassimali, Ph.D. The main objective of this research was to study the buckling and post-buckling response of axially restrained beam-columns under thermal loading. Also the effects of slenderness ratios on pre-buckling and post-buckling behavior which is neglected in (AISC 2010 specification) for Structural Steel Buildings, was examined. The results of this study indicate that: a) The deflection and end moment amplification factors are significantly smaller for the restrained beam-columns under temperature increase than the corresponding unrestrained beam-columns under mechanical axial loads. - b) The deflection amplification and moment amplification factors tend to increase with increasing ratio of end moments. c) Thermal amplification factors, even in the pre buckling range, were found to be smaller than the AISC (2010) specification values, the difference was more significant for longer beam columns as compared to shorter ones.