Browsing by Subject "Buckling"

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    Constrained Buckling of Variable Length Elastica
    (2017-10) Liakou, Anna
    The physical understanding of the response of slender elastic bodies restrained inside constraints under various loading and boundary conditions is of a great importance in engineering and medical applications. The research work presented in this thesis is especially concerned with the buckling response of an elastic rod (the elastica) subjected to unilateral constraints under axial compression. It seeks to address two main issues: (i) the conditions that lead to the onset of instability, and (ii) the factors that define the bifurcation diagram. Two distinct classes of problems are analyzed; (i) the classical buckling problem of a constant length elastica and (ii) the insertion buckling problem of a variable length elastica. Their main difference is the generation of a configurational force at the insertion point of the sliding sleeve in the insertion problem, which is not present in the classical problem. The thesis describes two distinct methodologies that can solve these constrained buckling problems; (1) a geometry-based method, and (2) an optimal control method. The geometry-based method is used to analyze the post-buckling response of a weightless planar elastica subjected to unilateral constraints. The method rests on assuming a deformed shape of the elastica and on uniquely segmenting the elastica consistent with a single canonical segment (clamped-pinned). An asymptotic solution of the canonical problem is then derived and the complete solution of the constrained elastica is constructed by assembling the solution for each segment. Nevertheless, the application of the optimal control method is more generic. It can be used to solve any constrained buckling problem under general boundary and loading conditions. Based on Hamiltonian mechanics, the optimality conditions, which constitute the Pontryagin’s minimum principle, involve the minimization of the Hamiltonian with respect to the control variables, the canonical equations and the transversality conditions. The main advantage of the optimal control method is the assumption of strong rather than weak variation of the involved variables, which leads to the additional Weierstrass necessary condition (“optimal” equilibrium state). Based on it, several factors such as the effect of the self-weight of the elastica and the clearance of the walls are investigated.
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    Performance of Full-Scale Reinforced Concrete Columns Subjected to Extreme Earthquake Loading
    (2015-12) Nojavan, Alireza
    Seven full-scale reinforced concrete (RC) columns were tested at the Multi-Axial Subassemblage Testing (MAST) Laboratory of the University of Minnesota to investigate their performance under extreme seismic events that would produce near-collapse conditions. One of the goals of the tests was to investigate any potential differences in performance with column size, thus, the test specimens were larger than nearly all of the columns tested previously. In order to investigate the adequacy of current provisions, the specimens were designed according to seismic provisions of ACI 318-11 and featured two different cross sections (36×28 in. and 28×28 in.). Another goal of the program was to investigate the influence of loading history, thus the column specimens were subjected to several large displacement loading protocols, including monotonic and uniaxial and biaxial cyclic loading protocols. The last overall goal of the program was to investigate the post-peak behavior of the specimens at near-collapse conditions, hence loading on the specimens continued beyond the stopping criteria in previous tests until the specimens exhibited severe strength loss and stiffness degradation. Results from these tests were combined with the available dataset of RC column tests to study the effects of cross-sectional size on parameters representing seismic performance of columns including moment capacity, effective stiffness, drift capacity, displacement ductility, and reinforcing bar buckling. It was revealed that unlike the other parameters, specimens featuring larger cross-sectional depths are more prone to in-plane bar buckling, a failure mechanism that has never been reported during previous tests of RC columns. Unlike outward buckling of bars, in-plane bar buckling is not generally controlled by confining reinforcement; rather it is the concrete surrounding the bars that restrain them from in-plane buckling. To better understand this phenomenon, finite element (FE) models of isolated bars as well as a three-dimensional (3D) FE model of the lower portion of the tested specimens were analyzed. A parametric study indicates that concrete compressive strength, bar size and overall cross-sectional size of the columns can affect bar buckling while the effects of longitudinal bar and tie spacing are minor. The evolution of damage during application of the various loading protocols was quantified using several cumulative and noncumulative damage index models. In addition, observed visual damage to the specimens was used to assess calculated damage indices based on different models. Calculated and measured damage quantities were considered in combination with the lateral force-deformation cyclic envelope, strength loss, stiffness reduction, and hysteretic energy dissipation of the specimens to study the effects of applied loading protocols on the performance of tested column specimens.