## 02545 05777 07756 05449 05769 06085 07989 05775 01680

For horizontal ground motion input, the participation factors are

where {In} = - [1 1 1]T. Since the structure is located on medium firm soil, the prevailing frequency is pg = 15.6 rad/s and the damping factor is pg = 0.60. From Equations 3.121b, 3.121c and 3.124b and 3.124c

 [ Nqi Nq2 N,] = [0.2318 [ Dqi Dq2 Dq3 ] = [0.0303 [ Nq 1 Nq2 Nq 3] = [1.8146 [ Dq 1 Dq 2 Dq 3] = [0.0369

For the ground acceleration RMS value assumed as c^ = 0.1g, Equation 3.120 yields S0 = 9.6 x 10 -3 m2/s3. Then, from Equations 3.122 and 3.125, the RMS values for each floor's displacement and velocity are calculated as

For the third-floor displacement, the range of safety is D = [3cx -3cx] = [0.097 - 0.097] m, then the probability of safety can be determined from Equation 3.129b with m = 0, cx = 0.0325 m, and ci = 0.4150 m/s as

{95.6% for duration t = 1s 79.8% for duration t = 5 s 63.6% for duration t = 10 s which implies that the probability of safety for the third-floor displacement within ±0.097 m is 95.6% in 1 s, 79.8% in 5 s, and 63.6% in 10 s.

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