Natural Frequencies of Uniform Cantilever Beams of Symmetrical Cross Section

Abstract

Abstract During the last ten years numerous observations of vibrational periods of buildings have been made, especially by the Seismological Division of the United States Coast and Geodetic Survey in California. Even before the results of these observations were available it was recognized that the factors influencing the periods of buildings are many and involved, and that a rational approach to the problem must necessarily ignore a number of the factors. The debatable question has been, and perhaps still is: Which of the factors must not be ignored? If the discussion be restricted to apply to multistory buildings of relatively symmetrical plan, there is a temptation to consider the buildings cantilever beams planted in or on an elastic ground. However, a multistory building is not necessarily a slender structure. For this reason the degree to which flexural and shearing distortions of the cantilever beam representing the building assume importance for the period determinations is not obvious quantitatively. Similarly, the type of ground deformation or elastic yielding that must be considered varies with the slenderness of the building as well as with the type of foundation and ground. The present study attempts to show that a rational treatment of the problem becomes greatly involved and therefore impractical if too many factors have to be taken into account. Moreover, the study enables the investigator to form an intelligent estimate of the relative importance of the influence on the periods of the factors that he is forced to neglect.