The L 80 × 60 × 10 -mm structural angle has the following cross-sectional properties: I x = 0.808 × 10 6 mm 4 , I y = 0.388 × 10 6 mm 4 , and I 2 = 0.213 × 10 6 mm 4 , where I 2 is a principal centroidal moment of inertia. Assuming I x y is negative, compute (a) I 1 (the other principal centroidal moment of inertia); and (b) the principal directions.
The L 80 × 60 × 10 -mm structural angle has the following cross-sectional properties: I x = 0.808 × 10 6 mm 4 , I y = 0.388 × 10 6 mm 4 , and I 2 = 0.213 × 10 6 mm 4 , where I 2 is a principal centroidal moment of inertia. Assuming I x y is negative, compute (a) I 1 (the other principal centroidal moment of inertia); and (b) the principal directions.
Solution Summary: The author calculates the other principal centroidal moment of inertia using the relation I_1.
The
L
80
×
60
×
10
-mm
structural angle has the following cross-sectional properties:
I
x
=
0.808
×
10
6
mm
4
,
I
y
=
0.388
×
10
6
mm
4
,
and
I
2
=
0.213
×
10
6
mm
4
,
where
I
2
is a principal centroidal moment of inertia. Assuming
I
x
y
is negative, compute (a)
I
1
(the other principal centroidal moment of inertia); and (b) the principal directions.
For a beam with the cross-section shown, calculate the moment of inertia about the z axis.
Assume the following dimensions:
by-83mm
h₂ = 15 mm
by 9 mm
b₂-72 mm
by-35 mm
h-24 mm
The centroid of the section is located 65 mm above the bottom surface of the beam.
M₂
H
Answer:
mm
by
The shaded area shown is bounded by x,y axes and the curve y2 = 3.24 − 0.5x m2 , where x is in m. Suppose that a = 6.48 m and h = 1.8 m .
A) Determine the moment of inertia for the shaded area about the y axis.
Iy = ?
Chapter 9 Solutions
International Edition---engineering Mechanics: Statics, 4th Edition
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