In-Plane Bending and Buckling of Arches

The state of knowledge of the in-plane bending and buckling of arches is summarized herein. There is a remarkable correlation between the critical thrusts for arches and columns. The buckling strength of nonprismatic arches can be accurately estimated by using prismatic arch equations with an average flexural stiffness which is easily determined. The buckling strength of symmetric prismatic and nonprismatic arch ribs of any shape and any symmetric loading can be estimated with good accuracy for any of the common support conditions. A review is given of methods for the bending analysis of slender arches and of simple, approximate methods for estimating the maximum effects. The approximate methods may be useful for the preliminary design of very slender arches and for the final design of less slender arches where the axial thrust is small compared with the critical value. In general, an accurate deflection theory analysis is recommended for the final design of very slender arches. The presentation is concerned with the available experimental and analytical data and with useful design concepts rather than with the various mathematical theories. The information is presented in a way which will make it helpful for design purposes. The review does not include shallow arches.