Buckling and Vibration of Arches and Tied Arches

Abstract

A simple method of computing the planar elastic buckling loads, natural frequencies, and corresponding mode shapes for arches and tied arches has been developed. The proposed method is applicable to arches and tied arches of general shape. Stiffnesses of arch rib and tie (if present) may vary in any manner along the span. The only major limitation in the applicability of the procedure is that the simplifying idealizations that are made can result in significant error for very steep arches. The details of the proposed method of analysis have been developed to be compatible with normal design office practice. The procedure involves linear elastic analysis with multiple loadings to obtain a simplified flexibility matrix, manual development of a stability matrix (for buckling) or mass matrix (for vibration), and solution of an eigenvalue equation. Several examples that are presented indicate that the proposed method is accurate—at least to the degree normally required in structural design—for arches and tied arches that have rise/span ratios within the range customarily encountered in medium‐ and long‐span bridges.