Application of Probability to Mechanical Design
115
to depth equal to 6 which yields a kt of 2.10. Also from Example 2.16 using
-- = -t-0.02674
(2.127)
with
bh 2
The Monte Carlo simulation is used to solve for a PU = 10 -6 for the beam
cross section. The beam stress 6 is expressed from Gaussian parameters.
The aluminum casting is expressed as a Gaussian and Weibull distribution
from Example 1.4 with
Weibull Averages
Gaussian Averages
/~ (shape) - 1.561
# (mean) - 46,508 psi
6 (scale) - 3766.9
~ (standard deviation) - 2159 psi
7 (threshold) 43,109 psi
The first solution is a Weibull distribution for strength and a Gaussian distribution for the stress.
Weibullformulation. The curve ar - 0"m (Fig. 2.42) is set up like Figs
2.38 and 2.40. The end of the failure line on the O’rn axis is the lowest value
10
2.461
a
41.889
0
Figure 2.42
10
20
30
~rn ksi
~ Weibull aluminum casting parameter.
4O