Simplified Analysis of Vertical Vibrations

Interactions of vertical vibrations among building systems, consisting of slabs, beams, girders, and columns are rather complex. Finite element dynamic analysis for the vertical direction is not only costly in modeling and computer time but also subjected to the limitation of available computer core sizes. The importance and benefit of using simplified analyses of vertical vibration become obvious. In this paper, simplified equations of vertical motion are derived in a general manner to include n modes of all subsystems. Theoretically, n is from 1 to infinity. Two examples are included. The first example illustrates procedures used to set up the simplified equations of vertical motion, according to the general expressions derived in this paper. The second example shows the validity of the simplified analysis by comparing the results with the results from the finite element analysis.