Editing Catenary (section)

==Catenary bridges==
[[File:Soderskar-bridge.jpg|thumb|right|250px|[[Simple suspension bridge]]s are essentially thickened cables, and follow a catenary curve.]]
[[File:Puentedelabarra(below).jpg|thumb|right|250px|[[Stressed ribbon bridge]]s, like the [[Leonel Viera Bridge]] in [[Maldonado, Uruguay]], also follow a catenary curve, with cables embedded in a rigid deck.]]

In free-hanging chains, the force exerted is uniform with respect to length of the chain, and so the chain follows the catenary curve.<ref>{{cite book| first1=Owen |last1=Byer |first2=Felix |last2=Lazebnik |first3=Deirdre L. |last3=Smeltzer |author3-link=Deirdre Smeltzer |title=Methods for Euclidean Geometry |url=https://books.google.com/books?id=QkuVb672dWgC&pg=PA210 |date=2010-09-02 | publisher=MAA | isbn=978-0-88385-763-2 |page=210}}</ref> The same is true of a [[simple suspension bridge]] or "catenary bridge," where the roadway follows the cable.<ref>{{cite book| first=Leonardo| last=Fernández Troyano| title=Bridge Engineering: A Global Perspective| url=https://books.google.com/books?id=0u5G8E3uPUAC&pg=PA514| year=2003| publisher=Thomas Telford| isbn = 978-0-7277-3215-6| page = 514 }}</ref><ref>{{cite book| first1= W. |last1=Trinks|first2=M. H. |last2=Mawhinney|first3=R. A. |last3=Shannon|first4=R. J. |last4=Reed| first5=J. R.| last5=Garvey| title=Industrial Furnaces| url=https://books.google.com/books?id=EqRTAAAAMAAJ&pg=PA132| date=2003-12-05| publisher=Wiley| isbn=978-0-471-38706-0| page=132 }}</ref>

A [[stressed ribbon bridge]] is a more sophisticated structure with the same catenary shape.<ref>{{cite book| first= John S. |last=Scott| title=Dictionary Of Civil Engineering| date=1992-10-31| publisher=Springer| isbn=978-0-412-98421-1| page=433}}</ref><ref>{{cite journal| title=Cranked stress ribbon design to span Medway| url=https://www.architectsjournal.co.uk/archive/cranked-stress-ribbon-design-to-span-medway| first=Paul| last=Finch| journal=[[Architects' Journal]] |volume=207 |date=19 March 1998 |page=51}}</ref>

However, in a [[suspension bridge]] with a suspended roadway, the chains or cables support the weight of the bridge, and so do not hang freely. In most cases the roadway is flat, so when the weight of the cable is negligible compared with the weight being supported, the force exerted is uniform with respect to horizontal distance, and the result is a [[parabola]], as discussed below (although the term "catenary" is often still used, in an informal sense). If the cable is heavy then the resulting curve is between a catenary and a parabola.<ref name="Lockwood122">[[#Lockwood|Lockwood]] p. 122</ref><ref>
{{cite web
|title=Hanging With Galileo
|date=June 30, 2006
|first=Paul
|last=Kunkel
|publisher=Whistler Alley Mathematics
|url=http://whistleralley.com/hanging/hanging.htm
|access-date=March 27, 2009
}}</ref>
[[File:Comparison catenary parabola.svg|thumb|none|400px|Comparison of a [[catenary arch]] (black dotted curve) and a [[parabolic arch]] (red solid curve) with the same span and sag. The catenary represents the profile of a simple suspension bridge, or the cable of a suspended-deck suspension bridge on which its deck and hangers have negligible weight compared to its cable. The parabola represents the profile of the cable of a suspended-deck suspension bridge on which its cable and hangers have negligible weight compared to its deck. The profile of the cable of a real suspension bridge with the same span and sag lies between the two curves. The catenary and parabola equations are respectively, <math>y = \text{cosh } x </math> and <math>y = x ^ 2 [(\text{cosh }1) - 1] + 1</math> ]]