Where, c= critical damping ratio, M = model mass, A =model acceleration
By using these formulas, it was found that vertical forces vary randomly over the span of the bridge. In this bridge, the crowed density was provided 2 people / m2, but it was observed that on average of 1.7 people / m2, there started difficulty in walking over this bridge. It is assumed that these failures for the bridge are significant for the engineering professions but particularly difficult to assimilate in the light of the fact that this kind of phenomenon has not been observed for none other than this occasion (Structural Safety 2000-01). This is concluding that the phenomenon of lateral synchronous excitation is not linked to technical innovations. This kind of phenomenon can be occurred anywhere in future on any design or bridge if the lateral frequency is below 1.3 Hz loaded with sufficient number of pedestrians. This bridge steel structure failed because of the unexpected loading or forces on the bridge, though the estimation and assumption for this bridge were realistic. Therefore, such kind of failures are rare in nature and only occurs due to unexpected factors such as in case of Millennium bridge, the unexpected force exerted from pedestrians on critical spans.
The failures must be taken as an opportunity to learn, thus the key loopholes identified in the structure of London’s Millennium Bridge must not be repeated in the future projects. As stated earlier, the information gathered can be utilized to construct a better and stronger bridge. A crowd–structure interaction model is the best and easiest way to identify any kind of loopholes in the new structures, especially suspension bridges. Moreover, certain precautions can be utilized and incorporated to avoid such kind of problems. The problem of the London’s Millennium Bridge was adequately solved after the fitting of 91 dampers so that the structure can effectively absorb both the vertical and lateral oscillations. The same has been successful ever since, which is clearly evident from the non–occurrence of the similar issue.