Civil Engineering Reference
In-Depth Information
2
w
x
2
w
y
∂
∂
∂
∂
= −
+
M
D
υ
x
x
y
2
2
2
w
y
2
w
x
∂
∂
∂
∂
= −
+
M
D
υ
y
y
x
2
2
w
x y
2
∂
∂ ∂
= −
2
M
D
z
xy
where:
3
E t
x
D
=
(2.5a)
x
12 (
−
υ υ
)
x y
3
E t
y
D
=
y
12 (
−
υ υ
)
x y
1
2
(
D
=
−
ν ν
)
D D
xy
x y
x
y
As engineers usually deal with stresses, principal stresses and Mohr's circle
of stresses are expressed in Equation 2.5b and illustrated in Figure 2.14.
2
+
−
+
σ
σ
σ
σ
x
y
x
y
=
−
2
(2.5b)
σ
τ
1
xy
2
2
z
1
1
τ
τ
yx
dz
τ
xy
t
/2
σ
y
z
y
σ
x
σ
x
,
τ
xy
M
y
2α
M
yx
0
σ
1
σ
2
M
x
M
xy
t
/2
σ
x
σ
y
,
τ
yx
(a) Moments and stresses in a unit area of
an orthotropic plate
(b) Principle stresses and Mohr's
circle of stresses
Figure 2.14
(a, b) Moment and stress relationships of an orthotropic plate.
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