# Theory of Arched Structures

## Theory of Arched Structures

In modern engineering, as a basis of construction, arches have a diverse range of
applications. Today the theory of arches has reached a level that is suitable for most
engineering applications. Many methods pertaining to arch analysis can be found in
scientific literature. However, most of this material is published in highly
specialized journals, obscure manuals, and inaccessible books. This is not
surprising, as the intensive development of arch theory, particularly stability and
vibration have mostly occurred in the 1940s to the 1960s. Therefore, most engineers
lack the opportunity to utilize these developments in their practice.
The author has committed to the goal of presenting a book which encompasses
essential and tested methods on fundamental methods of arch analysis and equally
important problems.

This book contains an introduction, four parts (nine chapters), and an appendix.
The first part “Strength” contains three chapters. Chapter 1 is devoted to
fundamental methods of determining displacement of elastic structures in general
accompanied by examples specifically for arches.
Chapter 2 covers the analysis of three-hinged arches, while analysis of redundant
arches is considered in Chap. 3; in these chapters a special attention is dedicated to
the analysis of arched structures using influence lines.
Second part “Stability” contains two chapters. Chapter 4 provides analytical
methods of the stability of arches. These methods are based on the integration of
differential equations.

Chapter 5 presents Smirnov’s matrix method and approximate method. Approx-
imate method is based on the approximation of the arch by straight members with

subsequent application of the precise displacement method in canonical form.

The third part, “Vibration” contains two chapters. Chapter 6 deals with compu-
tation of eigenvalues and eigenfunctions for arches. For analysis of the circular

uniform arch, Lamb’s differential equation is used; for analysis of parabolic
uniform arch the Rabinovich’s model is applied. The frequency of vibration for
arches with different ratio “rise/span” of an arch are presented on the basis of this
model.