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

5040Frequency (Hz)30201000 1000 2000 3000 4000ModeFigure 5.1Natural frequency and mode numberThe natural frequencies of the first 31 modes with significant modal mass-participantfactors are listed in Table 5.1 along with a brief description of each dominant motion andits respective modal participating mass ratios (MPMR). Here, the significant modes aredefined as those with an MPMR of 2% or higher in any single direction. In Table 5.1,UX, UY, and UZ represent the motions in traffic or longitudinal direction, lateral ortransverse direction, and vertical direction, respectively. In addition to translationalmotions, the rotations about the global X, Y, and Z axes are also included in the table andnoted as RX, RY, and RZ, respectively. The MPMR value provides a measure of howimportant a particular mode of vibration is for the overall response to the accelerationloads in each of the three global directions. It helps ensure a significant and requirednumber of vibration modes are included in seismic response analysis. It can be seen fromTable 5.1 that the accumulated MPMR exceeds 70% in all directions. In particular, theMPMR value is higher than 90% in transverse direction and in its associated rotation inthe transverse-vertical plane or about the longitudinal axis. Additionally, the MPMRvalue also exceeds 90% for the rotational component in the plane of deck or about thevertical axis. The fact that a less mass participation is observed in longitudinal directionis likely attributable to the presence of expansion joints in the bridge, where some parts ofthe structure vibrate independently of the remaining structure. This speculation issupported by the existence of so many local and insignificant modes excluded from Table5.1.The first 30 mode shapes of vibration are presented in Figures 5.2 to 5.31. Additionalmode shapes with significant participating mass ratios are plotted in Figures 5.32 to 5.35.It can be seen that many modes of low frequencies correspond to the coupled motion invertical and longitudinal directions. This observation indicates that the bridge structure ismost flexible in the vertical direction. Indeed, the fundamental frequency of 0.339 Hz54