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 Verification and Expansion of Single-Degree-of-Freedom Transformation Factors for Beams Using a Multi-Degree-of- Freedom Non-Linear Numerical Analysis Method A Thesis Presented to the Faculty of California Polytechnic State University San Luis Obispo, California In partial fulfillment of the Requirements for the Degree Master of Science in Architecture with a Spe cialization in Architectural Engineering  by Takayuki Yokoyama  November 2011
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