In finding the line of pressure some principle such as the principle of least action must be used in determining the reactions at the crown and springings, and some assumptions must be made of not certain validity.
But if hinges are introduced at crown and springings, the calculation of the stresses in the arch ring becomes simple, as the line of pressures must pass through the hinges.
Three cases therefore arise: (a) The arch is rigid at crown and springings; (b) the arch is two-hinged (hinges at springings); (c) the arch is three-hinged (hinges at crown and springings).
The St Louis bridge is not hinged, but later bridges have been constructed with hinges at the springings and sometimes with hinges at the crown also.
Bridge over the Seine has fifteen steel ribs hinged at crown and springings with a span of 353 ft.