Shigley's Centroide e Momento de Inercia

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1044 Mechanical Engineering Design
Part 1 Properties of Sections
 A 5 area
 G 5 location of centroid
 Ix 5 # y2 dA 5 second moment of area about x axis
 Iy 5 # x2 dA 5 second moment of area about y axis
 Ixy 5 # xy dA 5 mixed moment of area about x and y axes
 JG 5 # r 2 dA 5 # (x2 1 y2) dA 5 Ix 1 Iy
 5 second polar moment of area about axis through G
 k2x 5 IxyA 5 squared radius of gyration about x axis
Rectangle
A 5 bh  Ix 5
bh3
12
  Iy 5
b3h
12
  Ixy 5 0
Circle
A 5
pD2
4
  Ix 5 Iy 5
pD4
64
  Ixy 5 0  JG 5
pD4
32
Hollow circle
A 5
p
4
 (D2 2 d 2)  Ix 5 Iy 5
p
64
 (D4 2 d 4)  Ixy 5 0  JG 5
p
32
 (D4 2 d 4)
b
h x
y
b
2
h
2
G
x
y
G
D
x
y
G
Dd
Table A–18
Geometric Properties
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Useful Tables 1045
Table A–18
Geometric Properties
(Continued)
Right triangles
A 5
bh
2
  Ix 5
bh3
36
  Iy 5
b3h
36
  Ixy 5
2b2h2
72
Right triangles
A 5
bh
2
  Ix 5
bh3
36
  Iy 5
b3h
36
  Ixy 5
b2h2
72
Quarter-circles
A 5
pr2
4
  Ix 5 Iy 5 r
4 ap
16
2
4
9p
b  Ixy 5 r4 a18 2 49pb
Quarter-circles
A 5
pr 2
4
  Ix 5 Iy 5 r
4 ap
16
2
4
9p
b  Ixy 5 r4 a 49p 2 18b
x
x
G
Gh h
b
b
y y
h
3
b
3
b
3
h
3
h
x
x
h
b
b
y y
h
3
b
3
b
3
h
3
G
G
r
y
x
4r
3"
4r
3"
r
y
x
4r
3"
4r
3"
G
G
r
y
x
4r
3"
4r
3"
r
y
x
4r
3"
4r
3"
G
G
(Continued)
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