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Reduced basis techniques and the method of mode-acceleration are applied to transient analysis of simple beam and truss structures. It is noted that the method of mode-acceleration effectively recovers the first Ritz vector used in Ritz procedures. The theoretical basis for Lanczos algorithms that generate Ritz vectors is explained. Both mode-acceleration and Ritz procedures are found, generally, to be more accurate than mode-displacement in calculation of transient shear stresses, moments and normal stresses. Reanalysis using Ritz vectors is discussed following Kitis and Pilkey [9] and Noor and Lowder [10].