Moments in Flexible Two-Hinged Arches

The research described in this paper was planned to furnish information to assist in the design of arch ribs sufficiently flexible to sustain appreciable deflections before becoming overstressed. Experience has shown that the classic elastic theory, when applied to such arches, yields calculated stresses which are considerably less than existing stresses unless extended by successive approximations which consider the effect of the rib deflections on the moments. The work consisted of experimental observations of the behavior of loaded circular two-hinged steel arch models of constant section. The results of these observations are presented graphically and have been treated analytically to provide: (a) Practical limits of flexibility for the design of two-hinged arch ribs by straight elastic theory; (b) material assistance in the preliminary design of arches; and (c) actual design methods for certain two-hinged arch ribs which are too flexible for analysis by elastic theory. Within reasonable limits, the results may be applied to noncircular profiles and to varying sections by use of proper relative dimensions.