216 R. Astroza et al. Table 24.1 Types and magnitudes of errors considered for the modeling uncertainty parameters Parameter type Parameters Variation magnitude Error Geometry H0, H1, H2, H3 Low ±3% of bay-width (0.27 [m]) V1, V2, V3 Low ±3% of story-height (0.12 [m]) Nodal Masses NMik Low +5% High +30% Distributed Gravity Loads DGL1, DGL2, DGL3 Low +5% High +30% Damping Coefficients αM, βK Low +15% High +50% Table 24.2 Cases of modeling uncertainty considered for the frame (defined by coefficients applied to the modeling uncertainty parameters) Case ID H0 H1 H2 H3 V1 V2 V3 NM1 NM2 NM3 DGL1 DGL2 DGL3 αM βK 1 1.00 1.00 1.00 1.00 1.03 0.97 1.03 1.00 1.05 1.05 1.00 1.00 1.00 1.00 1.00 2 1.00 0.97 1.03 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.05 1.05 1.05 1.00 1.00 3 1.00 1.00 1.00 1.00 1.03 0.97 1.03 1.00 1.00 1.00 1.00 1.05 1.05 1.00 1.00 4 1.00 1.00 1.00 1.00 1.03 0.97 1.30 1.00 1.00 1.00 1.00 1.00 1.00 1.15 1.15 5 1.00 0.97 1.03 1.00 1.03 1.00 1.03 1.00 1.00 1.00 1.05 1.05 1.05 1.00 1.00 6 1.00 1.03 0.97 1.00 1.03 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.15 1.15 7 1.00 1.03 0.97 1.00 1.03 1.00 1.03 1.00 1.00 1.00 1.00 1.00 1.00 1.15 1.15 8 1.00 0.97 1.03 1.00 1.03 1.00 1.03 1.00 1.00 1.00 1.00 1.00 1.00 1.15 1.15 9 1.00 0.97 1.03 1.00 1.03 1.00 1.03 1.05 1.05 1.05 1.05 1.05 1.05 1.00 1.00 10 1.00 1.03 0.97 1.00 1.03 1.00 1.00 1.00 1.05 1.05 1.00 1.00 1.00 1.15 1.15 11 1.00 0.97 1.03 1.00 1.03 1.00 1.03 1.05 1.05 1.05 1.00 1.00 1.00 1.15 1.15 12 1.00 1.00 1.00 1.00 1.00 1.00 1.03 1.00 1.30 1.30 1.00 1.00 1.00 1.00 1.00 13 1.00 1.00 1.00 1.00 1.03 0.97 1.03 1.00 1.30 1.30 1.00 1.00 1.00 1.00 1.00 14 1.00 1.00 1.00 1.00 1.00 1.00 1.03 1.00 1.00 1.00 1.00 1.30 1.30 1.00 1.00 15 1.00 1.00 1.00 1.03 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.50 1.50 16 1.00 1.03 0.97 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.50 1.50 17 1.00 1.00 1.00 1.00 1.03 1.03 0.97 1.00 1.00 1.00 1.00 1.00 1.00 1.50 1.50 18 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.30 1.00 1.00 1.30 1.00 1.00 1.00 1.00 19 1.00 1.03 0.97 1.00 1.03 1.00 1.00 1.00 1.30 1.30 1.00 1.00 1.00 1.00 1.00 20 1.00 0.97 1.03 1.00 1.03 1.00 1.03 1.30 1.30 1.30 1.00 1.00 1.00 1.00 1.00 21 1.03 1.00 1.00 1.00 1.03 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.50 1.50 22 1.00 0.97 1.03 1.00 1.03 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.50 1.50 23 1.00 1.03 1.00 1.00 1.03 1.00 1.00 1.00 1.30 1.30 1.00 1.30 1.30 1.00 1.00 24 1.00 1.03 0.97 1.00 1.03 1.00 1.00 1.00 1.30 1.30 1.00 1.30 1.30 1.00 1.00 25 1.00 1.03 1.00 1.00 1.03 1.00 1.00 1.00 1.30 1.30 1.00 1.00 1.00 1.50 1.50 26 1.00 0.97 1.03 1.00 1.03 1.00 1.00 1.00 1.30 1.30 1.00 1.00 1.00 1.50 1.50 27 1.03 1.00 1.00 1.00 1.03 1.00 1.00 1.00 1.30 1.30 1.00 1.30 1.30 1.50 1.50 28 1.00 1.03 1.00 1.00 1.03 1.00 1.00 1.00 1.30 1.30 1.00 1.30 1.30 1.50 1.50 the gravity load acting on the beams at levels c =1, 2, 3; and αMand βK are the mass and stiffness proportional coefficients defining the Rayleigh damping. The true structure does not consider any variation in ϕ. Error related to geometry variables are defined as a percentage (%) of the bay-width and story-height. For example, a coefficient of 0.97 considered for V3 means that roof coordinate is modified as (V3 – 0.03×story height). Coefficients related to nodal masses are evenly modified for a given level. Earthquake Input Motions The 360◦ component of the ground motion recorded at Los Gatos station during the 1989 Loma Prieta earthquake (see Fig. 24.4) is used as base excitation. Model class M0 of the frame is subjected to this record to numerically simulate the seismic response of the actual structure (y). Then, the estimation using this information and both estimation approaches
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