132
Chapter 2
G aus sian-G aus s ian
The material representation is Eqs. (2.186) and (2.187)
~ = 51,250 psi
~s = 7151 psi
A lower value Kc 99.999% greater with 95% confidence from Appendix E
where ~c = ~- KcS with Kc = 4.8 from Fig. E1 for 100 samples.
~c = 51,250 psi - 4.8(7151 psi)
yields
~c = 16,925 psi
(2.206)
Now set Smax Eq. (2.205) equal to 7c Eq. (2.206)
/~3_ 912.037
16,925
(2.207)
/~ = 0.3777 in (0.3813 Example 2.22; Table 2.13)
from Eq. (2.3777)
bmax = (1 + 0.02576)/~
(2.208)
bmax = 0.3874 in (0.3911 Example 2.22; Table 2.13)
and
h = 2b
Now to calculate/~ for
Gaussian- Weibull
The Weibull representation of the material is Eqs. (2.173)-(2.175)
Vs=26,458 psi Eq. (2.173) and setting it equal to Eq. (2.205)
/~3 _ 912.037
26,458
(2.209)
0.3255 in (0.3279 Example 2.22; Table 2.13)
(2.210)
~max ---- 0.3338
(2.211)
Probability of failure and safety factor
Gaussian-Gaussian
The overlap areas of stress and material will give the total failure PU. The PU
material is 1/105 and Pf(smax >)= 1/109
1
1
1
Pf = --~ -~ 109 -- 105
(2.212)