24 Finite Element Model Updating Accounting for Modeling Uncertainty 215 0 E s f y b E s R 0 Strain (−) Stress (MPa) b) Fig. 24.3 (a) Model of the SAC-LA3 steel moment resisting frame building; (b) Modified Giuffre-Menegotto-Pinto steel constitutive model model parameters are assumed for the MGMP of beams and columns, because these elements are made of different type of steel. Then, θ is defined by θ = Ecol s ,f col y ,Rcol 0 ,b col,Ebeam s ,f beam y ,Rbeam 0 ,b beam ∈ R8×1. ϕincorporates different sources of modeling uncertainty, including gravity loads, geometry variables, damping properties, and mass properties (nodal masses). The response of the frame is simulated numerically considering defined values of modeling uncertainty parameter values and different sets of ϕparameter values are considered to mimic diverse cases of modeling uncertainty. 24.3.1 Cases of Modeling Uncertainty The cases of modeling uncertainty are taken from [11], and they were chosen to have large discrepancies between the measured and FE-predicted responses when a parameter-only estimation approach is used. Vector ϕanalyzed in this study is shown below and the levels (magnitudes) of modeling uncertainty are summarized in Table 24.1 (see Fig. 24.3 for notation). A total of 28 cases are studied (Table 24.2), then j =1, 2, . . . , 28 for Mj. ϕ= ⎡ ⎢⎢ ⎢⎢ ⎣ H0 H1 H2 H3 V1 V2 V3 T NM11 NM12 NM13 NM14 NM21 NM22 NM23 NM24 NM31 NM32 NM33 NM34 T DGL1 DGL2 DGL3 T αM βK T ⎤ ⎥⎥ ⎥⎥ ⎦ ∈R24×1 Note that geometry parameters Ha (a =0, 1, 2, 3) and Vb (b =1, 2, 3) define the location of vertical and horizontal axes of the FE model; terms NMik denote the nodal mass at floor i and column k (i =1, 2, 3 and k =1, 2, 3, 4); DGLc denotes
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