Advanced Methods of Structural Analysis

Chapter 4

Three-Hinged Arches

The arches are widely used in modern engineering. Arches permit to cover a larger
span. The greater is the span than an arch becomes more economical than a truss.
From esthetic point of view the arches are more attractive than trusses. Materials of
the modern arches are concrete, steel, and wood. The body of the arch may be solid
or consist of separate members.
The arches are classified as three-hinged, two-hinged, and arch with fixed sup-
ports. A three-hinged arch is geometrically unchangeable statically determinate
structure which consists of two curvilinear members, connected together by means
of a hinge, with two-hinged supports resting on the abutment. This chapter is de-
voted to analyze only three-hinged arches. Two-hinged arch and arch with fixed
supports will be considered in Part 2.

4.1 Preliminary Remarks...................................................

4.1.1 Design Diagram of Three-Hinged Arch.....................

The arch with overarched members is shown in Fig.4.1a. The arch contains three
hinges. Two of them are located at the supports and third is placed at the crown.
These hinges are distinguishing features of the three-hinged arch. Design diagram
also contains information about the shape of the neutral line of the arch. Usually this
shape is given by the expression,yDf.x/.

A x

C

l

f

B

y

HA HB

RA RB

y=f(x)

j

l

f

a b

Fig. 4.1 (a)Design diagrams for deck-arch bridge;(b)Design diagram of three-hinged arch

I.A. Karnovsky and O. Lebed,Advanced Methods of Structural Analysis,
DOI 10.1007/978-1-4419-1047-94,cSpringer Science+Business Media, LLC 2010

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