Page 965 - MiSUMi FA Mechanical Components Economy Series

[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
bh 2 12 6 Qab a ba 0.7854ba 3 ba 0.7854ba 2
3
2
e 4 4
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 2r e 2 0.1098r 4
h e 0.5756r
e 1
e h 4 2 e 2 0.4244r Z 10.1296r 3
3
h 2 2 2 h 12 0.11793h  h 3 r Q 2 0.055r 4
r
4
12
h h 1 e 2 Z 20.0956r 3
e r 0.5756r
b
e bh bh 3 bh 2 H
h 2 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
4
4
2
h 1 3b2b1 6b 6bb 1b 1 2 6b 6bb 1b 1 2 a A A A a 4 1 A a 4
2
2
e (2bb1) 2 3 M h 36(2 bb 1) h 3 12(3 b2b1) h 2 A a 2 2 12 6 A
h 2bb1
b1 1 b A
2 b 2
a A -a 4 4
e A a 4 12A 2
4
3 2
r
2
e r 0.866r 5 3 A a 2 A 12
4
4 8 2 0.1179(A a ) 4
A A 
r A
3 3 r 2 5 3
4
2 r 0.5413r 4
16
2.598r 2 r 4 4
Q 4 4 32( d 2 )
Q d d 1
2
e 5 3 Q 64 (d d ) 1
2
3
2
r r r 0.5413r 3 d1 Re 4 (d d ) 1 2 d 2 2
2
16 Q 4 4
4
 (R r ) 4 Q R r
4  × R
4
d2
d
12 2 4 r Qd 2 a 1 1
4 3Q 4
4 3Q 4
d
2
d
r 2.828r 2 0.924r 2 6 0.6906r 3 e a  12( a  ) 6a( a  16 )
e 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
1 3 Q
1 3 Q
4
4
r 64  4 32  4 d1 d 2b(hd) 12 { 16 (d 1 d ) 4 6h { 16 (d 1 d ) 4
Qr 2 Qd 2 d 0.0491d 4 0.0982d 3 e h b (h d 1) 3 b (h d 1) 3

3

3
e  4 2 Q 2 2 2
≈0.05d 4 ≈0.1d 3 b h 4 (d d ) b (hd 1) } b (hd 1) }
3
3
1
d 0.7854r 4 0.7854r 3
r A : Sectional area e : Distance of Center of Gravity I : Geometrical
0.0075r 4 Moment of Inertia ZI/e : Cross Section Coeffi cient
Q
r ( 1 ) e 1 e 2
2
e1 4 0.2234r 0.0075r 4 0.00966r 3
2 90o r 0.2146r 2 e 2 ≈0.01r 3
e 0.7766r
962