Editing Bridge (section)

== Bridge vibration ==
Bridges vibrate under load and this contributes, to a greater or lesser extent, to the stresses.<ref name=":2">{{Cite book |title=Bridge deck analysis |last1=O'Brien |first1=Eugene J. |last2=Keogh |first2=Damien L. |last3=O'Connor |first3=Alan J. |isbn=978-1-4822-2724-6 |edition=Second |location=Boca Raton |oclc=892094185|date=6 October 2014 |publisher=CRC Press }}</ref> Vibration and dynamics are generally more significant for slender structures such as pedestrian bridges and long-span road or rail bridges. One of the most famous examples is the [[Tacoma Narrows Bridge]] that collapsed shortly after being constructed due to excessive vibration. More recently, the [[Millennium Bridge, London|Millennium Bridge]] in London vibrated excessively under pedestrian loading and was closed and retrofitted with a system of dampers. For smaller bridges, dynamics is not catastrophic but can contribute an added amplification to the stresses due to static effects. For example, the Eurocode for bridge loading specifies amplifications of between 10% and 70%, depending on the span, the number of traffic lanes and the type of stress (bending moment or shear force).<ref>{{Cite book |title=Research perspectives: traffic loading on highway bridges |first=Peter |last=Dawe |date=2003 |publisher=Thomas Telford |isbn=0-7277-3241-2 |location=London |oclc=53389159}}</ref>

=== Vehicle–bridge dynamic interaction ===
There have been many studies of the dynamic interaction between vehicles and bridges during vehicle crossing events. Fryba<ref>{{Cite book |title=Dynamics of railway bridges |last=Fryba |first=L. |date=2009 |publisher=Thomas Telford |isbn=978-0-7277-3956-8 |oclc=608572498}}</ref> did pioneering work on the interaction of a moving load and an Euler–Bernoulli beam. With increased computing power, vehicle-bridge interaction (VBI) models have become ever more sophisticated.<ref>{{Cite journal|last1=Li|first1=Yingyan|last2=OBrien|first2=Eugene|last3=González|first3=Arturo|date=May 2006|title=The development of a dynamic amplification estimator for bridges with good road profiles|journal=Journal of Sound and Vibration|volume=293|issue=1–2|pages=125–137|doi=10.1016/j.jsv.2005.09.015|bibcode=2006JSV...293..125L|hdl=10197/2529|s2cid=53678242 |hdl-access=free}}</ref><ref>{{Cite journal|last1=Cantero|first1=D.|last2=González|first2=A.|last3=OBrien|first3=E. J.|date=June 2009|title=Maximum dynamic stress on bridges traversed by moving loads|journal=Proceedings of the Institution of Civil Engineers - Bridge Engineering|volume=162|issue=2|pages=75–85|doi=10.1680/bren.2009.162.2.75|issn=1478-4637|hdl=10197/2553|s2cid=53057484 |hdl-access=free}}</ref><ref>{{Cite journal|last1=Cantero|first1=D|last2=O'Brien|first2=E J|last3=González|first3=A|date=June 2010|title=Modelling the vehicle in vehicle—infrastructure dynamic interaction studies|journal=Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-Body Dynamics|volume=224|issue=2|pages=243–248|doi=10.1243/14644193JMBD228|issn=1464-4193|hdl=10197/2551|s2cid=59583241|hdl-access=free}}</ref><ref>{{Cite journal|last1=González|first1=A.|last2=Cantero|first2=D.|last3=OBrien|first3=E.J.|date=December 2011|title=Dynamic increment for shear force due to heavy vehicles crossing a highway bridge|journal=Computers & Structures|volume=89|issue=23–24|pages=2261–2272|doi=10.1016/j.compstruc.2011.08.009|hdl=10197/3426|s2cid=53367765 |hdl-access=free}}</ref> The concern is that one of the many natural frequencies associated with the vehicle will resonate with the bridge's first natural frequency.<ref>{{Cite journal|last1=González|first1=Arturo|last2=OBrien|first2=Eugene J.|last3=Cantero|first3=Daniel|last4=Li|first4=Yingyan|last5=Dowling|first5=Jason|last6=Žnidarič|first6=Ales|date=May 2010|title=Critical speed for the dynamics of truck events on bridges with a smooth road surface|journal=Journal of Sound and Vibration|volume=329|issue=11|pages=2127–2146|doi=10.1016/j.jsv.2010.01.002|bibcode=2010JSV...329.2127G|hdl=10197/2138|s2cid=56078933 |hdl-access=free}}</ref> The vehicle-related frequencies include body bounce and axle hop but there are also pseudo-frequencies associated with the vehicle's speed of crossing<ref>{{Cite journal|last1=Brady Sean P.|last2=O'Brien Eugene J.|last3=Žnidarič Aleš|date=1 March 2006|title=Effect of Vehicle Velocity on the Dynamic Amplification of a Vehicle Crossing a Simply Supported Bridge|journal=Journal of Bridge Engineering|volume=11|issue=2|pages=241–249|doi=10.1061/(ASCE)1084-0702(2006)11:2(241)|hdl=10197/2327|s2cid=53417698 |hdl-access=free}}</ref> and there are many frequencies associated with the surface profile.<ref name="engineer. 2015"/> Given the wide variety of heavy vehicles on road bridges, a statistical approach has been suggested, with VBI analyses carried out for many statically extreme loading events.<ref>{{Cite journal|last1=OBrien|first1=Eugene J.|last2=Cantero|first2=Daniel|last3=Enright|first3=Bernard|last4=González|first4=Arturo|date=December 2010|title=Characteristic Dynamic Increment for extreme traffic loading events on short and medium span highway bridges|journal=Engineering Structures|volume=32|issue=12|pages=3827–3835|doi=10.1016/j.engstruct.2010.08.018|bibcode=2010EngSt..32.3827O |url=https://arrow.dit.ie/engschcivart/40|hdl=10197/4045|s2cid=52250745 |hdl-access=free}}</ref>