On Aug 25, 8:35 pm, Fred the Red Shirt
wrote:
As to the statement that I clearly don't understand the factors
involved, you clearly do not understand what I said, the nature of
preloaded bolts, or even the S-n curves themselves. Improved fatigue
life due to preloading has nothing to do with friction. Friction may
improve fatigue life in the real world by spreading load over a larger
area, but the benefit of preloading on fatigue life is due primarily
to an effect that exists even if no friction is present at all.

Could you please elaborate on the theory of that effect?
E.g. is this a result of the superposition of stresses?


....and...

If we now begin to subject both bolts to the same cyclic
loading of 1500 lbs, where the applied load is increased from 0 up to
1500 and then reduced to zero again, the bolt with the 2000 lb preload
will see a cyclic load of only about 150 lbs, whereas the un-preloaded
bolt will see a cyclic load of 1500 lbs, and will obviously fail much
sooner.

Here you temporarily lost me because you have not told us
HOW the bolt is loaded. If the load consists of additional
tension, then plainly the bolt will see cyclical stress over the
range of 3500 lb to 2000. That is clearly the type of loading Matt
was discussing. If I make the unremarkable assumption that y
ou are familiar with addition then clearly you are NOT assuming
that the load is applied in the form of additional tension.

When a joint is pre-loaded, two important things happen. The bolt
stretches. AND The plates or whatever are being fastened are
compressed. When you add load that induces additional axial tensile
stress in the bolt, you have to consider that the compression in the
plates is being relaxed at the same time. So the stress increase is
not a 1:1 correlation to the additional applied load. The slope will
actually be something less than 1:1 until the point where all the
compression has been removed, after which it will be 1:1. As you can
imagine, the actual slope to the left of the knee is a function of the
modulus of elasticity of the bolts, the MoE of the plates, and the
effective area being compressed (where thickness comes into play).

However, the clamping force will still cause the shear to be
distributed over the surface area being clamped and not just
through the bolts. The superposition of stresses is not
the total story.

That is a completely separate effect and loading situation than what
Bud is talking about. My understanding has always been that what Bud
is talking about is only effective for additional tensile loading of
the fastener. But I agree with you, the clamping can be very important
for shear of the bolt, even if we ignore that effect in practice.

As for S-n curves, there are more than one type. The one
relating to what I am talking about are the ones that show S vs N for
different stress ratios. The stress ratio is the fraction equivalent
of the maximum to minimum load. For example, something that is loaded
in tension to 25000 psi, followed by being loaded in compression to
25000 psi back and forth, will have a ratio of -1.0 ( +25000 tension/
-25000 compression). Something loaded to 25000 psi tension that is
reduced to 10000 psi tension and back and forth will have a stress
ratio of .4 (10000 tension/ 25000 tension). The S-n curves show that
the amount of cyclic load that structure loaded with a ratio of -1
will fail far sooner than one with a ratio of .4, even though the
maximum stress level is the same. You can look in Mil-Hnbk-5 or
elsewhere for S-n curves to verify that.

The peak-to-peak stress difference in the first case, (ratio -1)
is 5,000psi, for the second case (.4) it is 1500 psi. So it is
no surprise that the first case fails earlier!

Now suppose two cases in which the magnitudes of
the stress cycles are equal:

Yes, that is exactly what I'm talking about.

In the first case the bolt is pre-loaded to 2500 psi then
subjected to an alternating load of an additional +/- 1500 psi,
(e.g. from 4000 to 1000 both in tension) while a second,
otherwise identical but not prestressed bolt is cycled
from 1500 psi in tension to 1500 psi in compression.
Both bolts see the same peak-to-peak stress difference.
The ration in the first case (preloaded bolt) is 4, in the
second case it is -1. Which bolt fails first?

Actually case 1 R=0.25, but otherwise your example illustrates my
point pretty well.

Cheers,
Matt