2

+oo considered with pi and pi. Finally, the probability of safety can be calculated from Equation 3.129b after the response variance is determined.

3.6.5.2 Numerical Example

Consider the three-story shear building shown in Figure 3.31 with mass M1 = M2 = M3 = 12,304 N s2/m; l = 4.2672 m; 11 = 1.98168 x 10-4 m4, 12 = 1.4601 x 10-4 m4, and 13 = 9.9229 x 10-5 m4; E = 206842.8 x 106 N/m2. Let the structure be located on the medium firm soil and the ground acceleration be a zero mean stationary process with RMS c^ = 0.1g. Assume the damping factor Pi = 0.02 for each mode, find the RMS of the floor response and the probability of safety of the third-floor displacement within three times of its RMS. After performing eigensolution calculation, the structural frequencies are

[p1 p2 p3 ] = [12.82 32.11 48.79 ] rad/s and the normalized modal matrix is

0 0

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