PSI - Issue 14

Angitha Vijayan et al. / Procedia Structural Integrity 14 (2019) 696–704 Angitha Vijayan et al. / Structural Integrity Procedia 00 (2018) 000 – 000

702

7

The vertical frequency range for different activities as specified by Bachmann et al (1995) is listed in Table 5. Modal analysis is performed for the empty structure. The obtained modal properties are listed in Table 6 and the corresponding mode shapes are shown in Fig. 5. A natural frequency of 3.356 Hz was obtained for the first vertical (dominant) mode. This mode is considered for further analysis.

Fig. 5. (a) First vertical mode shape at 3.356 Hz; (b) Second vertical mode shape at 9.492 Hz.

The modal parameters of the occupied system for different crowd size are obtained by plotting FRF curves. Natural frequency is determined from the peak of FRF curves whereas damping ratio is calculated from the curves using half-power band width method. The peak acceleration response of the structure is found and is expressed as percentage of acceleration due to gravity ( g ). The comfort level of an individual to the corresponding vibration level is estimated using the specifications listed in Table 7 as given by Ellis and Littler (2004) for structures like grandstands with frequency less than 10 Hz. Analysis is carried out by varying parameters such as crowd size, crowd location and crowd activity.

Table 7. Crowd comfort level for various peak accelerations (Ellis and Littler, 2004). Vibration level Comfort level <5% g Reasonable <18% g Disturbing <35% g Unacceptable >35% g Probably cause panic

Fig. 6. FRF curves for crowd activity (a) along the structure; (b) in a circle at midspan; (c) in a circle at both 1/4 th and 3/4th of span.