Module
5
Cables and Arches
Version 2 CE IIT, Kharagpur

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Lesson
33
Two-Hinged Arch
Version 2 CE IIT, Kharagpur

Instructional Objectives:
After reading this chapter the student will be able to
1. Compute horizontal reaction in two-hinged arch by the method of least work.
2. Write strain energy stored in two-hinged arch during deformation.
3. Analyse two-hinged arch for external loading.
4. Compute reactions developed in two hinged arch due to temperature loading.
33.1 Introduction
Mainly three types of arches are used in practice: three-hinged, two-hinged and
hingeless arches. In the early part of the nineteenth century, three-hinged arches
were commonly used for the long span structures as the analysis of such arches
could be done with confidence. However, with the development in structural
analysis, for long span structures starting from late nineteenth century engineers
adopted two-hinged and hingeless arches. Two-hinged arch is the statically
indeterminate structure to degree one. Usually, the horizontal reaction is treated
as the redundant and is evaluated by the method of least work. In this lesson, the
analysis of two-hinged arches is discussed and few problems are solved to
illustrate the procedure for calculating the internal forces.
33.2 Analysis of two-hinged arch
A typical two-hinged arch is shown in Fig. 33.1a. In the case of two-hinged arch,
we have four unknown reactions, but there are only three equations of
equilibrium available. Hence, the degree of statical indeterminacy is one for two-
hinged arch.
Version 2 CE IIT, Kharagpur

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