fatigue factor of safety

huangyhg

fatigue factor of safety
i have been looking at fatigue assessments using the goodman mean stress relationships (aka goodman diagram). the goodman line on my diagram is plotted by taking the uts for the mean stress and 40% of the uts for the alternating stress - a line is then drawn between the two points (standard-ish procedure). i then plot the alternating stress in the component against the mean stress on the goodman diagram - giving a point on the plot, let's say point 'a'. i was told to find the distance from the origin to the point 'a' - call this distance 'l1'. then i found the distance of a line which passes from the origin and through this point 'a' until it intersects with the goodman line - let's say line 'l2'.
the fos then = l2/l1
the problem is this. i came across an equation which gives a fos based on a goodman curve which gives a different value to the method described above. this equation is:
fos = 1/((sa/se)+(sm/suts))
sa = alternating stress
se = endurance (limit) stress) = 40% of uts
sm = mean stress
suts = material ultimate tensile strength (uts)
has anyone come across this discrepancy before, or am i missing something?
cheers,
-- drej --