We were disappointed to read Robert Benaim describing again his personal theories, acknowledged to be based on instinct and not on calculation, on the causes of the Millennium Bridge sway (NCE 21 June).
These theories are misleading and liable to distract the profession from understanding and accepting the real causes and their implications.
The proposition made is that the Millennium Bridge is particularly susceptible to pedestrian induced sway because of the lack of plan bracing under the deck and because of the vertical-lateral coupling of motion in some of the spans.
But it is easily shown that the large cable tensions provide significantly more lateral stiffness than would lateral bracing under the deck. The instinctive desire for lateral bracing is misplaced.
On vertical-lateral coupling, the instinctive static understanding ignores the fact that vertical footfall forces are applied at twice the frequency of the lateral footfall forces and of the lateral response of the bridge. Simple structural dynamics show that vertical forces applied at twice the response frequency cannot cause the large resonant lateral response observed.
Evidence from the other instances of synchronous sway clearly shows that bridges with the normal amount of plan bracing and of highly conventional truss or girder construction with no cables at all have also swayed.
Plan bracing and inclined cables are not relevant factors to any of these instances. The only two common factors are that the bridges all have lateral natural frequencies below 1.3Hz and they were loaded by large crowds of pedestrians. To deny this is to fly in the face of both mathematics and evidence.
We feel it is our duty to state unambiguously that any bridge with these two factors in common is potentially susceptible. The bridge design codes should acknowledge this fact.
When a bridge is designed for the conventional live load the expectation is that it will be safe and serviceable when loaded with as many pedestrians as can literally fit on the bridge. Our research shows that this will not be the case for a significant number of bridges when loaded heavily with pedestrians for special events. The industry must recognise this.
Tony Fitzpatrick, Michael Willford, Ove Arup Partnership, 13 Fitzroy Street, London W1T 4BQ