Page 1651 - MiSUMi 2025

[Technical Data]
Calculation of Area, Center of Gravity and Geometrical Moment of Inertia

Cross Section A e I Z＝I/e Cross Section A e I Z＝I/e

h h bh 3 bh 2 a Q Q
3
2
e bh 2 12 6 Qab a 4 ba ＝0.7854ba 3 4 ba ＝0.7854ba 2
b b
e 1
2 Q 8
h h h 4 h 3 e r ＝0.4244r ( 8 － 9Q) r 4 Z 1＝0.2587r 3
r
e h 2 2 12 6 Q 2 Z 2＝0.1908r 3
2
1 e 2r e 2 ＝0.1098r 4
h ＝0.5756r
e 1
e h 4 e 2 ＝0.4244r Z 1＝0.1296r 3
2
3
h 2 2 2 h 12 0.11793h ＝ h 3 r Q 2 0.055r 4
r
h 1
h 12 4 e 2 Z 2＝0.0956r 3
e r ＝0.5756r
b
e bh 3 2
h 2 bh bh H b b
3
3
2 3 h 36 24 e b(H－h) 2 12 (H －h ) 3 6H (H －h ) 3
b h H
b
e A 4 4 4 4
a
2
2
2
2
12
e h (2b＋b1) h 2 1 3 M 3b＋2b1 h 6b ＋6bb 1＋b 1 2 h 3 6b ＋6bb 1＋b 1 h 2 A －a 2 A 2 A －a 1 A －a
36(2 b＋b 1)
12(3 b＋2b1)
6
A
2b＋b1
b1 1 b A
2 b 2
a A -a 4 4
e 4 4 12A 2
3 5 3 2 2 2 A －a
e 4 r ＝0.866r 8 r A －a 2 A 12 0.1179(A －a ) 4
4
r A A ＝ A
3 3 r 2 5 3
4
2 16 r ＝0.5413r 4
＝2.598r 2 r 4 4
Q 4 4 32( d 2 )
2
Q d －d 1
e 5 3 e Q 64 (d －d ) 1
2
r r ＝0.5413r 3 d1 2 2 d 2
3
r 16 R 4 (d －d ) 1 2 ＝ (R －r ) 4 ＝ × 4 4
2
Q R －r
Q
4
d2 4 4 R
d
1＋2 2 4 r Qd 2 a 1 1 4 3Q 4
4 3Q 4
d
2
r 2.828r 2 0.924r 2 0.6906r 3 e a － 12( a － ) d 6a( a － 16 )
e 6 4 a 4 2 16
＝0.6381r
a
a
b
2 2 d
1 3Q
1 3Q
a 2b(h－d) h 12{ 16 d 4 6h{ 16 d 4
0.8284a 2 b＝ 1＋ 2 0.0547a 4 0.1095a 3 e Q 2 2 ＋b(h －d ) 3 ＋b(h －d ) 3
3
3
e ＝0.4142a b h ＋ 4 d ＋b (h－d) } ＋b (h－d) }
3
3
b
b 2 b 2
Qd 4 Qr 4 Qd 3 Qr 3 d1
1 3 Q
1 3 Q
4
4
r 64 ＝ 4 32 ＝ 4 d 2b(h－d)＋ 12 { 16 (d 1 －d ) 4 6h { 16 (d 1 －d ) 4
3
Qr 2 Qd 2 d ＝0.0491d 4 ＝0.0982d 3 h ＋b (h －d 1) 3 ＋b (h －d 1) 3
3

e ＝ 4 2 ≈0.05d 4 ≈0.1d 3 b e h Q 4 (d －d ) 2 2 ＋b (h－d 1) } ＋b (h－d 1) }
2
3
3
1
d ＝0.7854r 4 ＝0.7854r 3
r 4 A : Sectional area e : Distance of Center of Gravity I : Geometrical
r ( 1－ ) e 1 0.0075r Moment of Inertia Z＝I/e : Cross Section Coefficient
Q
2
e 2
e1 4 ＝0.2234r 0.0075r 4 ＝0.00966r 3
2 90° r ＝0.2146r 2 e 2 ≈0.01r 3
e ＝0.7766r
B-006