Application of Probability to Mechanical Design
123
with h = 2b
with
6PmaxL [K~2 + 1]~/2
s-~
s= 0.75
+ 11
~=-4-0.01163
-=-=~0.01
~=+0.01
~=+0.01
Kt
p
L
b
~=2.10
~b=301bs
L=15" /~=unknown
(2.165)
Equation (2.165) is the Gaussian formulation to use with the Weibull and
Gaussian curves for the titanium in separate Monte Carlo simulations
to solve for/~ These are shown in Table 2.13 for/~, bmax, , hmax, and the
safety factors. The material representation by Gaussian and Weibull curve
are developed next.
Weibull
The development follows that in Example 2.21 and Eq. (2.128) except
~z is 141,000 and from Fig. 2.26
Sult __ ~L
(2.166)
O-’e
2 2
~
Suit ~L
(2.167)
Z~ -- 30 -- ~-~
~L
-- :4-]~ = 4-0.0667
(2.168)
and km is for 1 × 106 cycles and the values are the same now substitute into
Eqs. (2.128) and (2.129)
~r e -~ ~a~b . , . km~r’
e
~’e = (0.8)(0.85)(0.88)
(2.169)
?re = 42,187 psi
Substituting into Eq. (2.130)
~re = ~’e[(0-0667) 2 q-(0.11) 2 q- (0.06) 2 q- (0.0455)2]
1/2
(2.170)
~oe = 4-0.1491 ~’e
Note Eq. (2.168) Cvo,,=-4-0.0667 and Cw, -- +0.1491. Now using Eq.