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ME 307 FORMULAS
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( ) ( )
x
yz
x
2
E1
E
12
⋅ε ⋅ −υ +υ⋅ ⋅ ε +ε
σ=
−υ− υ
VQ
Ib
⋅
τ=
⋅
o
c
y
Q
ydA
=
∫
( ) ( )
y
xz
y
2
E
4
d
I
64
π⋅
=
3
bh
I
12
⋅
=
4
d
J
32
=
( ) ( )
z
xy
z
2
E
( )
( )
n
My
y
Ae r y
⋅
⋅⋅ −
n
A
r
dA
r
=
∫
1,2
max
2
σ +σ
σ =
±τ
2
2
max
xy
2
σ −σ
τ
=
+τ
( ) ( ) ( )
32
1
23
I
I
I0
σ −
σ +
σ−
=
1
xyz
I
σσσ
=++
222
2
x
y
x
z
y
z
xy
yz
zx
I
σσ
τ
=
+
+
−−−
3
2
x
y
z
xy yz zx
x yz
y zx
z xy
I
τττ
στ
=
+
3
1
3
3
2
2
2
9
27
cos3
2(
3
)
I
II
I
θ
−+
=
−
1
cos
3
ii
I
r
σθ
=
⋅+
2
2
3
3
r
=
⋅−
( )
22
io
o i
oo
2
t
oi
r
rr p p
pr pr
for
r
rr
for
⋅−⋅±
−σ
−
+σ
( )( )
( )
2
2
22 2
r
RRr
E
p
R
2R r
r
−−
⋅δ
=
⋅
−
2
cr
2
C
EA
P
k
⋅π ⋅ ⋅
=
I
k
A
=
3
i
0.45
D 0.001 D
=
⋅
D DD
=
⋅
(
)
ITn IT6
K 10 1.6
−
=
⋅
T Ki
=
( ) ( ) ( )
( ) ( ) ( ) ( )
2 22
1/2
2
31
x
y
y
z
z
x
xy
yz
zx
1
6
2
2
+ σ −σ
′
=
+
τ
b
bm
k
C
kk
=
+
bi
F F CP
= +⋅
mi
F
F
(1 C) P
=
−+− ⋅
for
m
F0
<
i
n
2
1
TA r
F
Ar
⋅⋅
′′
=
⋅
∑
Tr
J
⋅
2
n
2
i
1
L
JA
r
12
=
∑
3
8FD
K
d
⋅
s
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This note was uploaded on 10/25/2010 for the course MECHINCAL 2010 taught by Professor علاءحجازي during the Spring '10 term at Hashemite University.
 Spring '10
 علاءحجازي

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