## 5 Discussion of Test Results
### Human Comfort and Vibration Serviceability Assessment Based on Existing Technical Documents
#### 5.3.3 Aisc Design Guide 11  
The North American AISC document was finally taken into account. The document is based on a simplified approach that was specifically calibrated for framed steel floors of 20-30 years ago  
Figure 12: Vibration serviceability assessment of the examined system, based on the SETRA guideline document. Experimental acceleration peaks (average values, vertical direction), as a function of (**a**) number of occupants and (**b**) frequency. (with typical vertical frequency in the range from 5 Hz to 8 Hz). As a result, the method is not able to correctly reproduce the dynamic performance of recent systems (i.e., lightweight concrete, etc. ), or structures with frequencies below 5 Hz or above 8 Hz. For pedestrian structures with frequency higher than 9-10 Hz, moreover, the AISC document recommends an additional \"stiffness verification\", to ensure appropriate performances under concentrated loads [24]. The vibration verification can be conventionally carried out by comparing the expected acceleration (\(100\times a_{max}\)/g):  
\[100.\frac{a_{max}}{g}=\frac{P_{o}exp(-0.35\cdot f)}{\beta W}\leq 100.\frac{a_{lim} }{g} \tag{10}\]  
with the corresponding limit value, given as a function of the class of use of the system (\(a_{lim}\) = 5%g for \"outdoor\" footbridges; \(a_{lim}\) = 1.5%g for \"indoor structures\" and \(a_{lim}\) = 0.5%g for \"churches\"). In Equation (10), \(P_{0}\) is a constant force representing the walking excitation (0.41 kN for indoor footbridges and 0.29 kN for churches), \(f\) is the fundamental frequency (in Hz), \(\beta\) the modal damping ratio (0.01 for indoor footbridges, 0.02 for churches) and \(W\) the effective weight (in kN) sustained by steel beams, joists of girder panes (as applicable). For the examined walkway, given \(f\) = \(f_{cs}\) = 15.1 Hz and W = \(M_{glass}\), it is possible to notice that the inequality of Equation (10) clearly results in unsatisfactory vibration performances, with a maximum acceleration up to 4.59%g \(>\) 1.5%g (\"indoor footbridges\", that is \(\approx\)3.15 the exceedance ratio). Even considering that the pedestrian system is realized in a church, Equation (10) would provide unpleasant acceleration ratios (1.62%g \(>\) 0.5%g, \(\approx\)3.24 the exceedance ratio), see Figure 13a,b. Figure 13: Vibration serviceability assessment of the examined system, based on the AISC technical guide. Expected acceleration peaks, based on Equation (10), for (**a**) indoor footbridges and (**b**) church systems, with (**c,d**) assessment of experimental acceleration peaks (average values, vertical direction), as a function of the number of occupants or frequency. Besides the intrinsic uncertainty that derives from the application of the AISC methodology to a glass pedestrian system with dynamic features that do not match the original criterion, it is interesting to notice in Figure 13a,b that the \"design\" performance of the glazed structure would be still able to satisfy the vibration serviceability requirements (with 1.06%g \(<\) 1.5% for \"indoor footbridges\" and 0.37%g \(<\) 0.5%g for \"church\" structures). Otherwise, as far as the PVB stiffness decreases, the vertical frequency of the walkway also decreases and results in unfavorable comfort estimates, hence emphasizing the key role of continuous maintenance interventions and monitoring programs for glass structures. In Figure 13c,d, it is also worth mentioning the actual comfort classification of the system, with respect to the AISC recommended limits. The distinction is made in terms of acceleration peaks (%g), as a function of \(p\) and \(f_{\text{os}}\). As shown, in both the cases, for nine of the tested scenarios (\(\approx\)1/3 rd the experimental campaign) the measured accelerations are \"unacceptable\" and do not satisfy the \"indoor footbridge\" threshold value (1.5%g). Up to 14 loading configurations (\(\approx\)1/2 nd the experimental study) are above the acceleration limit for \"churches\".