Natural Periods of Uniform Cantilever Beams

An attempt has been made to give a quantitative answer to the question of the relative influence of different types of distortions on the natural periods of uniform cantilever beams elastically fixed at their bases. Very few buildings approximate the uniform and symmetrical beam dealt with in the theory, so that close agreement with actuality cannot be expected if the theory is applied to buildings. However, it is felt that the study enables the designer of earthquake resistant structures to put his finger on the most important factors entering into a determination of periods. The order or magnitude of errors committed by neglecting either flexure or shear in the building and by neglecting elastic yielding of the ground may be inferred from the tables, curves, and approximate formulas of the paper. Quantitative data relating to ground rigidities are as yet rather speculative, but it is hoped that the theory presented will help investigators to form reasonable estimates of the magnitudes of the ground rigidities from field data of natural vibrational periods of buildings.