Chapter 1
Kinematical Analysis of Structures
Kinematical analysis of a structure is necessary for evaluation of ability of the
structure to resist external load. Kinematical analysis is based on the concept of
rigid disc, which is an unchangeable (or rigid) part of a structure. Rigid discs may
be separate members of a structure, suchas straight members, curvilinear, polygonal
(Fig.1.1), as well as their special combination.
Any structure consists of separate rigid discs. Two rigid discs may be connected
by means of link, hinge, and fixed joint. These types of connections and their static
and kinematical characteristics are presented in Table1.1.
The members of a structure may be connected together by a hinge in various
ways. Types of connection are chosen and justified by an engineer as follows:
1.Simple hinge. One hinge connectstwoelements in the joint.
2.Multiple hinge. One hinge connectsthree or moreelements in the joint. The mul-
tiple hinge is equivalent ton– 1 simple hinges, wherenis a number of members
connected in the joint. Hinged joints cantransmit axial and shear forces from one
part of the structure to the other; the bending moment at the hinge joint is zero.
1.1 Classification of Structures by Kinematical Viewpoint
All structures may be classified as follows:
Geometrically unchangeable structure. For this type of structure, any distortion
of the structure occurs only with deformation of its members. It means that this
type of structure with absolutely rigid members cannot change its form. The
simplest geometrically unchangeable structure is triangle, which contains the
pin-joined members (Fig.1.2a).
Geometrically changeable structure. For this type of structure, any finite dis-
tortion of the structure occurs without deformation of its members. The sim-
plest geometrically changeable system is formed as hinged four-bar linkage
(Fig.1.2b, c). In Fig.1.2c, the fourth bar is presented as ground. In both cases,
even if the system would be made with absolutely rigid members, it still can
change its form.
I.A. Karnovsky and O. Lebed,Advanced Methods of Structural Analysis,
DOI 10.1007/978-1-4419-1047-91,cSpringer Science+Business Media, LLC 2010
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