ABSTRACT
The catenary occupies a central place in the development of differential equations. In a catenary, uniform mass is distributed along the length of the hanging chain. Inglis showed in 1863 that the optimum shape of a stone arch bridge is in the form of an inverted catenary. A related problem is the cable suspension bridge for which a uniform mass is distributed along the horizontal distance of the span. Collapse caused by vibrations induced by marching of soldiers was reported for little Broughton Bridge in England in 1831 and Ostrawitza River Bridge in Austria in 1886. The complete mathematical solution of an arch bridge with a level ground was found by Inglis in 1863. In the formulation of a suspension bridge, the weight of cable is negligible when comparing the weight of the bridge deck and its live loads. In 1784-1824, a number of cable-stay bridges were built in Europe.
