Module
5
Cables and Arches
Version 2 CE IIT, Kharagpur

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Lesson
34
Symmetrical Hingeless
Arch
Version 2 CE IIT, Kharagpur

Instructional Objectives:
After reading this chapter the student will be able to
1. Analyse hingeless arch by the method of least work.
2. Analyse the fixed-fixed arch by the elastic-centre method.
3. Compute reactions and stresses in hingeless arch due to temperature
change.
34.1 Introduction
As stated in the previous lesson, two-hinged and three-hinged arches are
commonly used in practice. The deflection and the moment at the center of the
hingeless arch are somewhat smaller than that of the two-hinged arch. However,
the hingeless arch has to be designed for support moment. A hingeless arch
(fixed–fixed arch) is a statically redundant structure having three redundant
reactions. In the case of fixed–fixed arch there are six reaction components;
three at each fixed end. Apart from three equilibrium equations three more
equations are required to calculate bending moment, shear force and horizontal
thrust at any cross section of the arch. These three extra equations may be set
up from the geometry deformation of the arch.
34.2 Analysis of Symmetrical Hingeless Arch
Consider a symmetrical arch of span
L
and central rise of
Let the loading on
the arch is also symmetrical as shown in Fig 34.1. Consider reaction components
c
h
Version 2 CE IIT, Kharagpur

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