356. In a bridge formed of curved ribs, when the rise is limited, whether by the height of the roadway or other local circumstance, the span is also limited; for if the rise does not bear a certain proportion to the span, the bridge will not be sufficiently strong to support its own weight and that of the loads passing over it. This proportion depends upon the radius of the curve of equilibrium. The largest span of a bridge executed with timber of which there is any reliable record, is that over the Limmat, near Wettingen, of which the span was 390 feet, the whole rise about 43 feet, and the radius of the curve of equilibrium about 600 feet.*

* ' Essay on the Strength of Timber.'

† ' Traite' contenant une Partie essentielle.

Wiebeking, in his work on Bridges, gives some proportions for the rise in relation to the span, founded upon observation. He states that one-tenth of the span, as far as regards appearance, is the best general proportion for the rise of an arch, but as in most cases it is desirable to keep bridges low, he gives the following: -

Wiebeking's experience had convinced him that large spans require a greater rise in proportion than small ones.† His practice, however, did not extend beyond spans of about 300 feet: it is probable that greater spans require even more rise than he has assigned to them. The proportions given in the following Table are much safer to adopt, particularly as wooden bridges, however well they may be executed, will always settle a little immediately after being erected, which will increase with time, though in a lesser degree. Wiebeking made some observations on this subject, and found that the settlement in the middle may be expressed in inches by '806 r/s , where r is the rise and s the span, both in feet.‡

* Gauthey, ' Construction des Ponts.'

† Wiebeking, ' Traite d'une Partie essentielle.'

‡ ' Traite' contenant une Partie essentielle.'

Table of the Least Rise for Arches of Different Spans.