Question 2.9
: A thin rectangular plate a=20 mm and b=12 mm is acted upon by a stress
distribution
resulting in the uniform strains,
m
g
m
e
m
e
200
,
500
,
300
xy
y
=
=
=
x
.
Determine the changes in length of diagonals QB and AC.
Solution:
Y
A
B
b
Q
C
a
Since the diagonals are in a direction different from the X, Yaxes, We will have to first
evaluate the strains in those directions which when multiplied with the original length of
the diagonal will give us the change in the length of the diagonal.
From the equations of stress transformation as given by
eq.(2.11a) and (2.10b)
)
2
sin(
2
)
2
cos(
2
2
'
q
g
q
e
e
e
e
e
×
+
×

+
+
=
xy
y
x
y
x
x
)
sin

cos
(
cos
.
sin
)

(
2
2
2
xy
x
y
'
q
q
g
q
q
e
e
g
+
=
xy
Now, for diagonal QB
:
b
a
QB
AC
2
2
+
=
=
mm
QB
AC
32
.
23
)
12
(
)
20
(
2
2
=
+
=
=
∴
=
=
=


)
20
12
(
tan
)
(
tan
1
1
a
b
q
0.5404
m
e
17
.
441
'
=
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