Editing Catenary (section)

===Suspension bridge curve===
[[File:Golden Gate Bridge, SF.jpg|thumb|right|480px|[[Golden Gate Bridge]]. Most [[suspension bridge]] cables follow a parabolic, not a catenary curve, because the roadway is much heavier than the cable.]]

A similar analysis can be done to find the curve followed by the cable supporting a [[suspension bridge]] with a horizontal roadway.<ref>Following [[#Routh|Routh]] Art. 452</ref> If the weight of the roadway per unit length is {{mvar|w}} and the weight of the cable and the wire supporting the bridge is negligible in comparison, then the weight on the cable (see the figure in [[Catenary#Model of chains and arches]]) from {{math|'''c'''}} to {{math|'''r'''}} is {{mvar|wx}} where {{mvar|x}} is the horizontal distance between {{math|'''c'''}} and {{math|'''r'''}}. Proceeding as before gives the differential equation

<math display=block>\frac{dy}{dx}=\tan \varphi = \frac{w}{T_0}x\,. </math>

This is solved by simple integration to get

<math display=block>y=\frac{w}{2T_0}x^2 + \beta</math>

and so the cable follows a parabola. If the weight of the cable and supporting wires is not negligible then the analysis is more complex.<ref>Ira Freeman investigated the case where only the cable and roadway are significant, see the External links section. [[#Routh|Routh]] gives the case where only the supporting wires have significant weight as an exercise.</ref>