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PROBLEM 9.112
Using the invariance property established in the preceding problem,
express the product of inertia
xy
I
of an area
A
with respect to a pair of
rectangular axes through
O
in terms of the moments of inertia
x
I
and
y
I
of
A
and the principal moments of inertia
min
I
and
max
I
of
A
about
O
.
Use the formula obtained to calculate the product of inertia
xy
I
of the 76
×
51
×
6.4mm angle cross section shown in Fig. 9.13B knowing that its
maximum moment of inertia is
34
524
10 mm .
×
SOLUTION
(
a
)
(
b
)
From Problem 9.111 have,
constant
xy
x
y
II
I
′′
′
′
−=
Now consider the following two cases
Case
1
:
,
x
yx
y
x
y
I
I
′′′
′
==
=
Case
2
:
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 Spring '08
 Jenkins
 Statics

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