Assessment of the Bill Emerson Memorial Bridge - FTP Directory ...

Measured frequency (Hz)141210864200 2 4 6 8 10 12 14Calculated frequency (Hz)Figure 5.39 Comparison of calculated and measured frequencies5.4.2. Mode shape verificationThe validation of the FE model was evaluated by comparing the graphical representationof the corresponding calculated and identified mode shapes as shown in Figures 5.40 to5.45. It can be visually seen that a good correlation between the calculated and theidentified mode shapes of several vibration modes has been demonstrated. Tosystematically evaluate the correlation of all calculated and identified mode shapes, themodal assurance criterion (MAC) index (Friswell and Mottershead, 1995) is computedfor each mode as follows:th({φ } T )j{φ k} 2MAC jk= (5.6)({φ j} T {φ })({ } Tjφ k{φ k})where { φj} is the j mode shape from the FE model and{φ k}is the k mode shapeidentified from the measured accelerations. In this study, the mode shapes are extractedfrom the seismic records during the May 1, 2005 earthquake. Due to insufficient numberof accelerometers installed on the approach span, only the cable-stayed main span of thebridge is considered. In addition, the exact locations of accelerometers are unknown. Themode shapes identified from the acceleration records are only rough estimates. Thisestimation may cause some uncertainties in the measured mode shapes. The MAC valuesof the bridge are graphically shown in Figure 5.46. It is clearly seen that the calculatedmode shapes correlate rather well with the identified mode shapes. These results furtherensure the reliability of the FE model.th72