For Hingeless Arches:

These four formulae are based on the author's published designing specifications, which treat reversing stresses by adding one-half of the smaller stress to the larger stress and proportioning for the sum; but if the effect of reversion is entirely ignored, as some engineers deem proper, those formulae will reduce to the following:

For Three-Hinged Arches:

For Two-Hinged Arches:

For Combined Two-Hinged and Three-Hinged Arches:

For Hingeless Arches:

In Equations (4) to (11) inclusive, Wa or W'a, is the weight of metal, in pounds per lineal foot of span, in the arches of the structure; D is the dead load, in pounds per lineal foot of span; L is the live load plus impact, in pounds per lineal foot, used in making the calculations; and l is the span length, in feet. These eight equations will give fairly accurate results (slightly on the side of safety) for ordinary conditions which do not vary greatly from the theoretically economic ones.

In computing the value of L for insertion in Equations (4) to (11), inclusive, the equivalent uniform live load and the impact should be determined for the half-span-length.

Fourth. From the formulae given above for weights of arch ribs, some interesting deductions may be drawn. For instance, in Equation (4), viz.,

the dead load, D, is composed of the rib weight, Wa, plus the weight of floor, columns, lateral system, etc., all of which may be grouped under the symbol, W', making the equation

Solving this gives

In order that Wa may be infinitely great, the divisor of the second term must be equal to zero, or