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PROBLEM 9.46
Determine the polar moment of inertia of the area shown with respect to
(a) Point O, (b) the centroid of the area.
PROBLEM 9.47
Determine the polar moment of inertia of the area shown with respect
to (a) Point O, (b) the centroid of the area.
Determination of centroid C of entire section
233
(4000 mm ) 122.67 10 mm
30.667 mm
YA yA
Y
Y
Area mm2 ,mmy 3
,mmyA
1 1(160)(80) 6400
2 80
3 3
170.67 10
2 1(80)(60) 2400
2
20 3
48 10
4000 3
122.67 10
(a) Polar moment of inertia :
O
J
Section
: 364
1(160)(80) 6.8267 10 mm
12
x
I
For Iy consider the following two triangles
364
664
1
2 (80)(80) 6.8267 10 mm
12
(6.8267 6.8267)10 13.653 10 mm
y
Oxy
I
JII
PROBLEM 9.47 (Continued)
PROBLEM 9.48
Determine the polar moment of inertia of the area shown with respect
to (a) Point O, (b) the centroid of the area.
PROBLEM 9.48 (Continued)
PROBLEM 9.49
Two channels and two plates are used to form the column
section shown. For b 200 mm, determine the moments of
inertia and the radii of gyration of the combined section with
respect to the centroidal x and y axes.
For C250 22.8
2
64
64
2890 mm
28.0 10 mm
0.945 10 mm
x
y
A
I
I
Total area 432
2[2890 mm (10 mm)(375 mm)] 13.28 10 mmA
Given b 200 mm:
64 3 2
1
2[28.0 10 mm ] 2 (375 mm)(10 mm) (375 mm)(10 mm)(132 mm)
12
x
I
6
186.743 10
64
186.7 10 mm
x
I
6
232
3
186.743 10 14.0620 10 mm
13.28 10
x
xI
kA
118.6 mm
x
k
PROBLEM 9.49 (Continued)
PROBLEM 9.50
Two L6 4 2
1-in. angles are welded together to form the section shown.
Determine the moments of inertia and the radii of gyration of the combined
section with respect to the centroidal x and y axes.
From Figure 9.13A: Area A 4.75 in2
4
4
17.3 in
6.22 in
x
y
I
I
2422 4
2[ ] 2[17.3 in (4.75 in )(1.02 in.) ] 44.484 in
xxO
IIAy
4
44.5 in
x
I
Total area 2(4.75) 9.50 in2
4
22
2
44.484 in 4.6825 in
area 9.50 in
x
xI
k 2.16 in.
x
k
2422
2[ ] 2[6.22 in (4.75 in )(1.269 in.) ]
yyO
IIAx
4
27.738 in 4
27.7 in
y
I
Total area 2(4.75) 9.50 in2
4
22
27.738 in 2.9198
area 9.50 in
y
y
I
k 1.709 in
y
k
PROBLEM 9.51
Two L6 4 2
1-in. angles are welded together to form the section
shown. Determine the moments of inertia and the radii of gyration
of the combined section with respect to the centroidal x and y axes.
Copyright © McGraw-Hill Education. Permission required for reproduction or display.
PROBLEM 9.52
Two 20-mm steel plates are welded to a rolled S section as shown. Determine
the moments of inertia and the radii of gyration of the combined section with
respect to the centroidal x and y axes.
