Civil Engineering Reference
In-Depth Information
Figure 4.6
Graphical expression of principal stresses
and the unit length are in the positive
-direction. For the same reason, the strain
ε
t
is positive
in the
t
-direction.
For the shear strain
γ
t
in Figure 4.7(b), the first subscript
indicates the original unit length
in the
-direction, and the second subscript
t
indicates the displacement in the
t
-direction. Since
both the unit length and the displacement are in their positive directions, the shear strains
γ
t
indicated is positive. Similarly,
γ
t
indicated is also positive.
To find the three strain components in various directions, we introduce a rotating 1-2 coordi-
nate system as shown in Figure 4.7(c). The 1-2 coordinate have been rotated counter-clockwise
by an angle of
α
1
with respect to the stationary
−
t
axes. The three strain components in this
rotating coordinate system are
ε
1
,
ε
2
and
γ
12
(or
γ
21
). The relationship between the rotating
Figure 4.7
Definitions of strains and transformation geometry
