100
Chapter 2
2O
10
Copper-based alloy
~
÷3~
~s
t~u, = 80,000 psi
10 20 30 40 50 60
70 80 90
G~ ksi
Figure 2.36 Coupling diagram for or - a,, plot.
1 1
1
set Pf -- 10 3 10 6 or (~,z = -6)
or some selected value from Table 2.3
then
. 2-~ 1/2
Remember as and ~s have the unknown dimension, a m can be scaled
from Fig. 2.36 as well as ~s. This is now an algebra problem with
Cv on each of the variables in the as equation.
6. Monte Carlo
This is a computer solution where as, ~s are known and as is
known with a distribution on the variables be it Gaussian or
Weibull. (as can also be a Weibull distribution).
The computer
picks values on all known and unknown variables according to
their distributions, finds all values of as > as which is a failure,
and does enough calculations to find
1
Pf = maximum calculations 103, 106, 109
should it find more than one failure in the first calculations the
unknown dimension is made larger and the calculations repeated
until a suitable answer is found.
7. Established method with a factor of safety N. Pick the as - 3~s line
as design line and if N= 4 and take 1/4 as along the at/am line and
this becomes a design point for as. When the average value for the