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3 Analysis of Strain
Fig. 3.1 Displacement and strain of a body
Generally, the symbols u, v and w are used to represent displacement components
in x, y and z directions, respectively.
3.3 Concept of Strain
As stated earlier, deformations occur due to relative displacements between points
in a body. However, if the shape and size of the body remain unaltered, then this type
of deformation is known as rigid body motion. But if the shape and size of the body
are altered, then a state of strain has been set up in the body. Generally, the strain
will not be constant or homogeneous with in a body but will be different at different
points due to the variation in the displacements from particle to particle. But if the
region of the material of the body considered is sufficiently small, then the strain
within it may be treated as constant or homogeneous. Thus, the strain along P
Q
in
Fig. 3.1 may be defined as
ε =
L 1 − L o
L o
=
L 1
L o
− 1
(3.1)
The change in length (L 1 − L o ) with the original length L o is known as strain.