| Abstract: | This dissertation presents two methods for analyzing the elastic stability of planar structures with prismatic members whose deformations are primarily due to bending and axial loads, and whose deformations due to shearing forces may be disregarded. These two methods are the traditional finite element nonlinear analysis and an eigenvalue analysis using a Laguerre Solution Method for obtaining buckling loads. The structures may be subjected to buckling displacements due to imperfections, support settlements or primary loadings. Primary loadings may include distributed and/or concentrated loads. Each of the two methods presented has four formulations resulting from four different strain energy expressions. Three of these strain energy expressions are derived using different curvature expressions in the strain displacement relations. They differ by the inclusion of terms which take into account bending effects not previously considered in eigenvalue and nonlinear stability analyses. The fourth strain energy expression utilizes a linear beam curvature which is most frequently found in the literature. Critical buckling loads are determined for several examples such as beam columns and bents. A comparison of the results with solutions found in the literature indicates that some formulations yield favorable results while others do not. ... |
|---|