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3 Analysis of Strain
Fig. 3.3 Two-dimensional geometric strain deformation
ε x =
A
C
− AC
AC
=
[u + (∂u/∂ x) )x + x − u] − x
x
= ∂u/∂ x
(3.2)
Similarly, if v and w are the displacement components in Y and Z directions,
respectively, then the strain components in those directions derived as
ε y = ∂v/∂ y ε z = ∂w/∂ y
(3.3)
In order to determine the angular deformation, let us consider the rotation of side
AC with respect to A from x-axis.
Hence,
tan β =
C
C
A C
tan β =
(v+∂v/∂ x x)−v
(u+∂u/∂ x x)+x−u
tan β =
(∂v/∂ x)
1+(∂u/∂ x)
Considering only infinitesimal deformations, then ∂u/∂ x is very small compared
to unity.
3 Analysis of Strain
Fig. 3.3 Two-dimensional geometric strain deformation
ε x =
A
C
− AC
AC
=
[u + (∂u/∂ x) )x + x − u] − x
x
= ∂u/∂ x
(3.2)
Similarly, if v and w are the displacement components in Y and Z directions,
respectively, then the strain components in those directions derived as
ε y = ∂v/∂ y ε z = ∂w/∂ y
(3.3)
In order to determine the angular deformation, let us consider the rotation of side
AC with respect to A from x-axis.
Hence,
tan β =
C
C
A C
tan β =
(v+∂v/∂ x x)−v
(u+∂u/∂ x x)+x−u
tan β =
(∂v/∂ x)
1+(∂u/∂ x)
Considering only infinitesimal deformations, then ∂u/∂ x is very small compared
to unity.