Date of Award
Doctor of Philosophy
In this study, methods for the geometric nonlinear analysis and the material nonlinear analysis of plane frames subjected to elevated temperatures are presented. The method of analysis is based on a Eulerian (co-rotational) formulation, which was developed initially for static loads, and is extended herein to include geometric and material nonlinearities. Local element force-deformation relationships are derived using the beam-column theory, taking into consideration the effect of curvature due to temperature gradient across the element cross-section. The changes in element chord lengths due to thermal axial strain and bowing due to the temperature gradient are also taken into account. This "beam-column" approach, using stability and bowing functions, requires significantly fewer elements per member (i.e. beam/column) for the analysis of a framed structure than the "finite-element" approach. A computational technique, utilizing Newton-Raphson iterations, is developed to determine the nonlinear response of structures. The inclusion of the reduction factors for the coefficient of thermal expansion, modulus of elasticity and yield strength is introduced and implemented with the use of temperature-dependent formulas. A comparison of the AISC reduction factor equations to the Eurocode reduction factor equations were found to be in close agreement. Numerical solutions derived from geometric and material analyses are presented for a number of benchmark structures to demonstrate the feasibility of the proposed method of analysis. The solutions generated for the geometrical analysis of a cantilever beam and an axially restrained column yield results that were close in proximity to the exact, theoretical solution. The geometric nonlinear analysis of the one-story frame exhibited typical behavior that was relatively close to the experimental results, thereby indicating that the proposed method is accurate. The feasibility of extending the method of analysis to include the effects of material nonlinearity is also explored, and some preliminary results are presented for an experimentally tested simply supported beam and the aforementioned one-story frame. The solutions generated for these structures indicate that the present analysis accurately predicts the deflections at lower temperatures but overestimates the failure temperature and final deflection. This may be in part due to a post-buckling reaction after the first plastic hinge is formed. Additional research is, therefore, needed before this method can be used to analyze the materially nonlinear response of structures.
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