Vibration Characteristics and Earthquake Forces in a Fifteen Story Building

This paper is an abridgement of a classical mathematical solution of twelve of fifteen translational modes of vibration of a fifteen story building. This work was done just prior to the advent of the digital computer, by Edward C. Robison (C) in the period 1948-1950. He used seven place logarithms! The solution is in terms of lateral forces in each of twelve modes at each of fifteen floors coming out of admissible solutions for eigenvalues from the characteristic equation. These forces, when “normalized” by a constant multiplying factor for each mode, add algebraically to the weight of each floor, and in the over-all to the weight of the building—a principle illustrated by Robison's work and by Figure 9 of the Joint Committee's report (a) for which figure Milton Ludwig (D) was responsible, independently, about the same time.