Application of Probability to Mechanical Design
103
The combined stresses for the shoulder are
where
and
O-rr = O-2xr -t- 32xyr
32Mm
4Fa
32(4500 in lb)
~.~r = K,B~5-+ K~F-~ = 2.025
~d 3
+2.35-axr = ~3 [18,225 + 58.75d]
16Tr 16 [1.65(15,000 in lb)] = 16-(24,750)
"Ccxy r = gtz 7td 3 - gd
3
~td ~
a’r = ~3 [[18,225 + 58.75d] 2 + 3124,75012]
~/2
(2.108)
4(100 lb)
gd 2
,
2 4- 3v 2 1 I/2
Gm ~ [~Yxm ---ixym~
4Fro 16
o’xm -- red2 - ~d 3 [25d]
16Tin 16
(2.109)
red3 gd3 (45,000 in lb)
16V/
a~, = ~ [(25d) + 3(45,000)21
~/2
find the ratio a;/a’ m
or’ r = [(18,225 + 58.75df + 3124,75012]
~/2
(2.110
a~,,
[(25d) 2 + 3(45,000)2]
1/2
neglect the terms with d
’
1
O" r
-- = 0.5976 -- -’
1.67732
Note the a’r/~r’,,, line will be used with no variation assuming the angle vanation is small.
Obtain a solution for Section C.7.
1. Mean Curve
Using mean curve Fig. 2.38 and f.s. = 3 then cry. - 3~s curve
a. mean curve f.s. =3
°’rt = 13,426 psi = 7~ 516 [(18,225)2 + 3(24,750)2]~/2 (2.111)