fundamentals of engineering supplied-reference handbook - Ventech!

26
y
y
y
y
y
y
C
Figure Area & Centroid Area Moment of Inertia (Radius of Gyration) 2 Product of Inertia
b
a
b
C
b
C
b
C
C
b
b
a
C
h
x
h
x
x
h
x
h
x
h
x
a
A = bh/2
xc = 2b/3
yc = h/3
A = bh/2
xc = b/3
yc = h/3
A = bh/2
xc = (a + b)/3
yc = h/3
A = bh
xc = b/2
yc = h/2
A = h
y
c
=
( a + b)
2
h(
2a
+ b)
3(
a + b)
A = ab sin θ
xc = (b + a cos θ)/2
yc = (a sin θ)/2
I
x c
I
yc
= bh
3
3
/36
= b h/36
Ix = bh 3 /12
Iy = b 3 h/4
I
x c
I
yc
= bh
3
3
/36
= b h/36
Ix = bh 3 /12
Iy = b 3 h/12
I x
I y
I
I
c
c
x
y
= bh
=
= bh
=
3
36
2
2
[ bh(
b − ab + a ) ]
3
12
36
2
2
[ bh(
b + ab + a ) ]12
3
I xc
= b h 12
I yc
3
= b h 12
3
I x = bh 3
3
I y = b h 3
J =
I
x c
I
x
I x
I y
I
I
c
x
y
2 2 [ bh(
b + h ) ]12
h
=
h
=
=
=
=
=
3
3
2
2
( a + 4ab
+ b )
36(
a + b)
( 3a
+ b)
12
3 3 ( a b sin θ)
12
2 2 2
[ ab sinθ(
b + a cos θ)
] 12
3 3 ( a b sin θ)
3
2
[ ab sinθ(
b + a cosθ)
] 3
2 2
− ( a b sinθcosθ)
6
2
xc
2
yc
2
x
2
y
r
r
r
r
2
xc
2
yc
2
x
2
y
r
r
r
r
2
xc
2
yc
2
x
2
y
r
r
r
r
2
xc
2
yc
2
x
2
y
2
p
r
r
r
r
r
r
2
x
r
2
x c
= h
= b
= h
= b
= h
= b
2
2
2
2
= h
= b
= h
2
2
2
2
= h
=
=
2
18
18
6
2
18
18
6
6
18
2
2
( b − ab + a )
2
6
18
2
2
( b + ab + a ) 6
= h
= b
= h
2
2
2
2
12
12
3
= b 3
2 2
= ( b + h )12
h
=
2
2
h
=
6
2
2
( a + 4ab
+ b )
18(
a + b)
( 3a
+ b)
( a + b)
2
c r = ( a sinθ)
xc
2
yc
2
x
2
y
r
r
r
=
=
=
2
12
2 2 2 ( b + a cos θ)
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.
12
2 ( a sinθ)
3
2
( b + a cosθ)
3
− ( ab cosθ)
6
I
I
I
I
I
I
I
I
I
xc yc
xy
xc yc
xy
xc yc
xy
xc yc
xy
c c y x
= Abh 36 = b h
2
2
= Abh 4 = b h
= Abh 12 = b h
2
2
2
2
8
2
72
= − Abh 36 = − b h
=
=
=
=
[ Ah(
2a
− b)
]
2
bh ( 2a
− b)
[ Ah(
2a
+ b)
]
2
bh ( 2a
+ b)
= 0
[ ]
36
72
12
[ ] 24
= Abh 4 = b
2 2
h
4
2
24
3 2 ( a b sin θ θ)
12
= cos
72
STATICS (continued)