Civil Engineering Reference
In-Depth Information
The components of traction vector
t
acting on a general plane defined by a normal
vector
n {
n
x
,n
y
,n
z
} that is not parallel to one of the axis planes can be expressed in terms
of stress components by (Figure 4.6)
t
n
V
n
W
n
W
x
x
x
y
xy
z
xz
t
n
V
n
W
n
W
(4.28)
y
y
y
x
xy
z
yz
t
n
V
n
W
n
W
z
z
z
x
zx
y
zy
Figure 4.6
Definition of traction vector acting on a general plane
Infinitesimal strains are defined in terms of displacement components in the
x, y, z
directions (
u
x
,
u
y
,
u
z
) by
w
u
x
H
x
w
x
w
u
y
H
y
w
y
w
u
z
H
z
w
z
w
u
w
u
(4.29)
y
x
J
xy
w
y
w
x
w
u
w
u
y
z
J
yz
w
z
w
y
w
u
w
u
z
x
J
zx
w
x
w
z
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