Anatomy of Computer Response Spectrum Analyses In Other Words What Goes on in the Black

Now that we have learned the fundamentals of dynamic analysis, perhaps it is instructive to study a couple of computer dynamic analysis results. This will enhance our understanding of the modal superposition process that takes place in the computer, in the black box.

The examples presented illustrate the modal analysis method. In the first part of each example, the analysis is performed to determine the base shear for each mode using given building characteristics and ground motion spectra. In the second part, the story forces, accelerations, and displacements are calculated for each mode, and are combined statistically using the SRSS combination. The following equations are used in the analysis procedure.

The base shear is determined from

where

Vm = bease shear contributed by the mth mode am = modal base shear participation factor for the mth mode Sam = spectral acceleration for the mth mode determined from the response spectrum W = total weight of the building including dead loads and applied portions of other loads

The modal base shear participation factor, am, for the mth mode is determined from m in "\2

The story modal participation, PFxm, for the mth mode is determined from

PFxm = modal participation factor at level x for the mth mode wi/g = mass assigned to level i fim = amplitude of the mth mode at level i Qxm = amplitude of the mth mode at level x n = level n under consideration

The modal story lateral displacement, ôxm, is determined from c _ np o m xm xm^am | ^ | 6

,2n, where

8xm = lateral displacement at level x for the mth mode

Sam = spectral acceleration for the mth mode determined from the response spectrum Tm = the period of vibration at the mth mode

2.4.8.1. Example 1: Three-Story Building

Given. The example is illustrated in Fig. 2.50. Weights and Masses

WR = 187 kips 187

Figure 2.50. Three-story building example; dynamic analysis.
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