PSI - Issue 5

C.A. Prato et al. / Procedia Structural Integrity 5 (2017) 332–339 C.A. Prato/ Structural Integrity Procedia 00 (2017) 000 – 000

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No signs of permanent geometric distortion of the bridge were evident before and after the tests. The mean value for sensor 1 at 60 km/h was 0.64 m/s 2 and 1.06 m/s 2 for sensor 2, with a ratio of 1.06 / 0.64 = 1.7.

3. Natural frequencies by numerical model

The numerical model for SAP2000 Program [2] shown in Figure 2 yields the natural modes and frequencies given in Table 3. The fundamental mode with a frequency of 2.03 Hz involves flexural deformations in the central span without rotations (torsion) about the longitudinal axis. The modal shapes for the 2nd through 5th modes are associated with transverse vibrations of the pillars, and do not significantly involve vertical displacements the bridge deck, thus are not expected to be excited by the reference truck. The 6 th mode, however, with a natural frequency of 3.15 Hz involving torsion of the bridge deck, can be associated to an observed peak at around 3.10 Hz generated by passage of the truck. The 7 th through 12 th modes (5.00 to 5.30 Hz) are associated to vibrations of the deck, but with negligible contributions to vertical movements at the center of the span. These modes involve symmetric and anti-symmetric flexural and torsional vibrations of the central and lateral spans. The 13 th and 14 th modes (7.08 and 7.50 Hz, respectively) are flexural and torsional, respectively, deformations of the central spans, involving vertical displacements at the center.

Table 3. Natural frequencies and modal shapes of the modeled bridge. Modal Shape

Frequency [Hz]

f 1 = 2.03 Hz

f 2-3-4-5 = 2.96, 2.98, 3.08 and 3.13 Hz

f 6 = 3.15 Hz

f 7-8-9-10-11-12 = 5.00, 5.13, 5.19, 5.20, 5.25 and 5.30 Hz

f 13 = 7.08 Hz

f 14 = 7.50 Hz

4. Numerical results for the code-prescribed reference vehicle

On account of the experimental results showing the significant participation of the torsional effects, the numerical analysis of the response of the bridge for a reference vehicle was carried out for two scenarios: i) Truck path centered