fundamentals of engineering supplied-reference handbook - Ventech!

28
y
y
y
Figure Area & Centroid Area Moment of Inertia (Radius of Gyration) 2 Product of Inertia
C
a
a
C
y = (h/b n )x n
b
b
b
C
b
x
y y = (h/b 1/n )x 1/n
b
C
h
x
h
x
x
A = 4ab/3
xc = 3a/5
= 4ab
= 16a
b 175
yc = 0 I = 4a
b 7
A = 2ab/3
xc = 3a/5
yc = 3b/8
A = bh
n + 1
x = b
n + 2
h n + 1
yc
=
2 2n
+ 1
I
I
xc
yc
y
= I
x
3
3
Ix = 2ab 3 /15
Iy = 2ba 3 /7
( n + 1)
3
bh
I x =
c ( 3n
+ 1)
n
A = bh
n + 1
n + 1
xc
= b
2n
+ 1
n + 1
yc
=
2
( ) h
n + 2
I
I
I
y
x
y
3 3
hb
=
n + 3
3
n
= bh
3(
n + 3)
n 3
= b h
3n
+ 1
3
15
2
xc
2
yc
2
y
r
r
r
2
x
2
y
r
r
2
x
r
2
y
r
2
x
r
2
y
r
= r
2
x
= 12a
= 3a
2
= b
2
2
7
= b 5
2
= 3a
7
2
5
175
2(
n + 1)
( 3n
+ 1)
h
=
3
n + 1
= b
n + 3
2
n + 1
= h
3(
n + 1)
n + 1 2
= b
3n
+ 1
Housner, George W. & Donald E. Hudson, Applied Mechanics Dynamics, D. Van Nostrand Company, Inc., Princeton, NJ, 1959. Table reprinted by permission of G.W. Housner & D.E. Hudson.
2
I
I
xc
y
xy
= 0
c
= 0
Ixy = Aab/4 = a 2 b 2
STATICS (continued)