Exam 2 Equation Sheet - Classes
Exam 2 Equation Sheet - Classes
Exam 2 Equation Sheet - Classes
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
! = Mc<br />
I<br />
! = Tr<br />
J<br />
$<br />
" ! = " 1<br />
#"<br />
&<br />
2<br />
%<br />
! = P A<br />
( ) 2 + (" 1<br />
#" 3 ) 2 + (" 2<br />
#" 3 ) 2<br />
2<br />
direct shear: ! = P A<br />
rectangular section: A = bh , I = bh3<br />
12 , ! = 3V<br />
2A<br />
round section: A = !d 2<br />
1<br />
'<br />
2<br />
) "!<br />
= " 2 2<br />
x<br />
+ 3# xy<br />
(<br />
( ) 1 2<br />
4 , I = !d4<br />
64 , J = !d 4<br />
32 , ! = 32M<br />
"d 3 , ! = 16T<br />
"d 3 , ! = 4V<br />
3A<br />
Mohr’s circle: center : c = ! x + ! y<br />
2<br />
R =<br />
#<br />
%<br />
$<br />
! x<br />
"! y<br />
2<br />
&<br />
(<br />
'<br />
2<br />
2<br />
+ ) xy<br />
S e<br />
= k a<br />
k b<br />
k c<br />
k d<br />
k e<br />
k f<br />
S e<br />
! S e<br />
! = 0.504S u<br />
for steels<br />
stress concentration: K f<br />
= 1 + q( K t<br />
!1)<br />
normal stresses: n = S e<br />
! a<br />
normal stresses: Goodman: 1 n = ! a<br />
S e<br />
+ ! m<br />
S u<br />
finite life: S= aN b or N =<br />
S 1<br />
! $ bwhere (0.9S<br />
# & a = u<br />
) 2<br />
and b = ! 1 " a%<br />
S e<br />
3 log " 0.9S %<br />
u<br />
$ '<br />
# S e &<br />
shear stresses: Goodman: 1 n = ! a<br />
+ ! m<br />
, S su = 0.67S u S sy = 0.577S y , S se = S e with k c =.59<br />
S se<br />
S su<br />
surface finish factor: k a<br />
= aS ut<br />
b<br />
Surface<br />
Factor a<br />
Exponent<br />
Finish<br />
S ut , kpsi S ut , MPa b<br />
Ground 1.34 1.58 -0.085<br />
Machined or cold drawn 2.70 4.51 -0.265<br />
Hot-rolled 14.4 57.7 -0.718<br />
As-forged 39.9 272 -0.995<br />
size factor: Rotating shaft, bending and torsion: k b<br />
=<br />
( d 0.3) 0.11 " d " 2in<br />
0.91d !0.157 2 < d "10in<br />
( d 7.62) 2.8 " d " 51mm<br />
1.51d !0.157 51 < d " 254mm<br />
axial: k b =1<br />
For a rectangular cross section: d e = 0.808 (h b) 1/2<br />
1.0 bending<br />
load factor: k c<br />
= 0.85 axial<br />
0.59 torsion
GEARS:<br />
HP = T ! rpm<br />
5252<br />
(T: ft-lbs) V =<br />
!dn<br />
12<br />
HP =<br />
W t V<br />
33000<br />
W t<br />
=<br />
T<br />
d 2<br />
d = N P<br />
d = mN<br />
(P=pitch)<br />
! 1<br />
! 2<br />
= N 2<br />
N 1<br />
T 1<br />
T 2<br />
= N 1<br />
N 2<br />
T 1<br />
! 1<br />
= T 2<br />
! 2<br />
W r<br />
= W t<br />
tan!<br />
! = K v<br />
W t<br />
P<br />
FY<br />
K v<br />
= 1200 + V<br />
1200<br />
W a<br />
= W t<br />
tan!<br />
(V: ft/min)<br />
Table 14-2<br />
Values of Lewis Form Factor Y<br />
Number of Y Number of Y<br />
Teeth<br />
Teeth<br />
12 0.245 28 0.353<br />
13 0.261 30 0.359<br />
14 0.277 34 0.371<br />
15 0.290 38 0.384<br />
16 0.296 43 0.397<br />
17 0.303 50 0.409<br />
18 0.309 60 0.422<br />
19 0.314 75 0.435<br />
20 0.322 100 0.447<br />
21 0.328 150 0.460<br />
22 0.331 300 0.472<br />
24 0.337 400 0.480<br />
26 0.346 rack 0.485<br />
SPRINGS:<br />
D = OD ! d k = F ! = d 4 G<br />
8D 3 N a<br />
C = D K B<br />
= 4C + 2<br />
d<br />
4C ! 3<br />
n = S sy<br />
!<br />
1<br />
n =<br />
! a<br />
S se<br />
+ ! m<br />
S su<br />
! = K B<br />
8FD<br />
"d 3<br />
8F<br />
! a<br />
= K a<br />
D<br />
B<br />
"d ! = K 8F m<br />
D<br />
3 m B<br />
!<br />
"d 3 a<br />
= ! " ! max min<br />
2<br />
! m<br />
= ! max + ! min<br />
2
Change language