Theory of Structures II (ENCE 252): Analysis of Indeterminate Arches

An Introduction to the Analysis of Indeterminate Arches

This chapter delves into the Analysis of Indeterminate Arches, a critical topic in structural engineering. Arches are not only aesthetically pleasing but also highly efficient structural forms capable of spanning large distances by primarily transferring loads through axial compression. This makes them ideal for bridges, long-span roofs, and other iconic structures.

In this section, we will focus on indeterminate arches, specifically two-hinged and fixed arches. Unlike three-hinged arches, these structures have redundant reactions, requiring compatibility equations based on deformation for their analysis. We will explore methods to calculate the horizontal thrust, which is key to their behavior, considering effects like support yielding, temperature changes, and rib shortening. For a two-hinged arch, the horizontal thrust (H) is given by the formula: $H = \frac{\int \frac{M_s y}{EI} ds}{\int \frac{y^2}{EI} ds}$, where $M_s$ is the bending moment of the simply supported base structure.

Furthermore, this chapter covers the creation of bending moment, shear force, and normal thrust diagrams, providing a complete picture of the internal forces. Finally, we will construct Influence Line Diagrams (ILDs) for various parameters, an essential tool for analyzing structures under moving loads.