In presentations of results in terms of structural response, it is considered useful to employ the ratio: ( ) ( ) e o R R m e m 2 2 = (6) which basically is a normalisation of rms-values obtained for the structure carrying a stationary crowd of people with the result obtained for the empty structure. For values of e smaller than 1, the presence of the stationary crowd has attenuated the structural vibrations. The load model introduced in this section is a simplification of jumping loads, but it is not all that unreasonable, in that it models the dynamic load factor with a maximum value of 2.0 (for the first dynamic load factor), and superharmonic dynamic load factors are modelled to be lower that this value. 3. RESULTS The response ratio e was computed for different values of m2 smaller than 250 kg. Hence quite small stationary crowds of people are considered, as 250 kg might correspond to a group of 3 people. The response ratio was computed for 3 different assumptions for the damping ratio of the empty structural system (systems A1, A2, A3), and results are shown in Fig. 2. Fig. 2 Response ratio e as function of mass of the stationary crowd of people ζ1= 0.5 % (o), ζ1= 1.0 % (x), ζ1= 2.0 % ( ) As can be seen, a stationary crowd is found to attenuate the structural response, as all values of e are below 1. There is the tendency that the response reduces as the size of the crowd increases (m2 increases). Another item to notice is that as the damping ratio of the empty structure ( ζ1) decreases the attenuating effect of the stationary crowd increases (in that e decreases with decreases in ζ1 for fixed values of m2). In fact the results suggest that the attenuating effect of the stationary crowd is quite sensitive the damping ratio of the empty structure. It is quite obvious that the results shown in Fig. 1 deviate a lot from that would be expected had the stationary crowd been modelled as a mass rigidly attached to the structural mass. It should be noted that realistic values of m2 might be 75 kg, 150 kg and 225 kg if the group of people (one person, two persons, and three persons, respectively) is located at the point of maximum structural displacement, but if the group of people is located at any other location on the structure these values would reduce. 448
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