Reaming

So you are correct that friction is used in tranferring torque in
wooden props. They also use counterbored drive bushings to transfer
the torque. I'd be willing to bet that the bushings transfer most of
it, but that is only a guess.

Thanks.
--
Jim in NC

I spent some time talking today at lunch with some friends who are
structural engineers, about this issue of friction delivering torque
to the prop. They said that if the strength of the attachment of the
prop to the flange had been determined through experience, then
eliminating the friction load path for the engine torque to be
tranmitted to the prop could result in failure of the junction of the
flange and prop, but that it wasn't likely.

I'll bet that you structural engineer friends are not experienced with wood
props, and their failure modes. It seems to be their own unique circumstance.
It has been found that the props fail, not the bolts.
--
Jim in NC

The big reason for the "drive lugs" is to remove the nuts from the airstream
in back of the prop and reduce the drag the produce. If they are the only
drive mechanism, the recessed holes will quickly be beat out. If they did
do the job, you could have one center bolt. Many props such as used on A-65
don't even have drive lugs but use bolts straight thru.


--
Cy Galley - Chair,
AirVenture Emergency Aircraft Repair
A 46 Year Service Project of Chapter 75
EAA Safety Programs Editor - TC
EAA Sport Pilot


"Morgans" wrote in message
...

So you are correct that friction is used in tranferring torque
in
wooden props. They also use counterbored drive bushings to transfer
the torque. I'd be willing to bet that the bushings transfer most of
it, but that is only a guess.

Thanks.
--
Jim in NC

I spent some time talking today at lunch with some friends who are
structural engineers, about this issue of friction delivering torque
to the prop. They said that if the strength of the attachment of the
prop to the flange had been determined through experience, then
eliminating the friction load path for the engine torque to be
tranmitted to the prop could result in failure of the junction of the
flange and prop, but that it wasn't likely.

I'll bet that you structural engineer friends are not experienced with
wood props, and their failure modes. It seems to be their own unique
circumstance. It has been found that the props fail, not the bolts.
--
Jim in NC

On Aug 22, 4:21 pm, "Cy Galley" wrote:
The big reason for the "drive lugs" is to remove the nuts from the airstream
in back of the prop and reduce the drag the produce. If they are the only
drive mechanism, the recessed holes will quickly be beat out. If they did
do the job, you could have one center bolt. Many props such as used on A-65
don't even have drive lugs but use bolts straight thru.

--
Cy Galley - Chair,
AirVenture Emergency Aircraft Repair
A 46 Year Service Project of Chapter 75
EAA Safety Programs Editor - TC
EAA Sport Pilot

"Morgans" wrote in message

...





So you are correct that friction is used in tranferring torque
in
wooden props. They also use counterbored drive bushings to transfer
the torque. I'd be willing to bet that the bushings transfer most of
it, but that is only a guess.

Thanks.
--
Jim in NC

I spent some time talking today at lunch with some friends who are
structural engineers, about this issue of friction delivering torque
to the prop. They said that if the strength of the attachment of the
prop to the flange had been determined through experience, then
eliminating the friction load path for the engine torque to be
tranmitted to the prop could result in failure of the junction of the
flange and prop, but that it wasn't likely.

I'll bet that you structural engineer friends are not experienced with
wood props, and their failure modes. It seems to be their own unique
circumstance. It has been found that the props fail, not the bolts.
--
Jim in NC- Hide quoted text -

- Show quoted text -

I talked some more to my structures friends. They said that wood
reacts to cyclic stress in much the same manner as metal. It is also
an elastic material (unless overloaded) and it also will fatigue more
quickly when cycled back and forth from tension to compression than it
will from repeated tension or compression alone. So the same
preloading to improve the fatigue life applies to wood as it does to
metal. Lower preload results in a lower fatigue life.
So the "drive" lugs are really low drag lugs? I doubt it very
much. I've read alot about airplanes, and this is the first I've heard
on that one. The most highly stressed part on the whole airplane is
the propellar attachment. Any design utilized here must take care of
that issue first and foremost. The drive lugs are better than plain
nuts and bolts for at least two reasons. First, counterboring the back
of the wooden prop hub to allow the insertion of the lugs results in a
larger diameter hole in the wood, therefore a larger bearing surface
which improves the load capacity. Second, it utilizes the fact that
for elastic materials, the bearing strength is usually about 3 times
as much as the shear strength, and the drive lugs use the bearing
strength and any friction between the crankshaft flange and the back
face of the prop will test the shear strength of the wood. A
crankshaft flange 6" in diameter will have a little more than 28 sq in
of contact area. For a prop this size, the hub should be at least 4 in
thick. with a 3/4" dia drive lug, this will give you about 18 to 20 sq
in of bearing area. Given that the only place where friction will be
great due to bolt tension will be close to the bolts, as the slight
warping of both flange and wood, comparing the two scenarios easily
shows that using the bearing strength of the wood with the drive
bushings is far stronger, and much more reliable.
As to some props such as C-65 cont having no drive lugs, this is
not surprising on old, low powered engines. I have installed a prop on
an old Cub, and one of the things that you had to be careful about,
was making sure the bolts had a slight drive fit to them through the
wood. This is really the same setup as as bushings, just that the
bolts bear against the wood instead of the bushings. More modern
designs with higher horsepower (Katana, etc) use drive bushings to
make the holes larger and and a more precise fit. All higher
horsepower modern props use drive bushings. There is a reason for
that. It is because it is a better way of doing a very critical joint.
One of the people I talked to is a Boeing Technical Fellow, the
highest level an engineer can achieve there. He said that in all his
years, he has only heard of one instance where friction was used to
qualify a structural joint. It was for some trivial thing like an
adjustment slot for a secondary structure part (like the slot for
adjusting the belt tension on some alternators).
I hope that homebuilders that read RAH seeking help will take
Fortunat1's advice from the building manuals he quoted, and realize
that thinking that you can rely on friction to hold the wing joint
together may get you killed. This is even more true of propellars,
where the cyclic loads are severe and constant.

Regards,
Bud

On Aug 12, 11:09 am, Fortunat1 wrote:
...
I'll just have to get a good
quality reamer and prepare each hole carefully. I'll see if I can get a
drill bit that brings he holes a little closer to the final size.

May I suggest you get more than one drill bit, for the same
reason you need more than one reamer?

..What is the annealing temperature for 4130? You can drill through
a bandsaw blade by spot annealing it, that is you chuck a blunt rod
like a nail with the point ground off into a drill press bring that to
bear
on the spot to be drilled until it gets good and hot, then let it
cool
slowly. Now the spot is annealed and a hole can be drilled with
an ordinary bit.

So I wonder if re-drilling the holes will heat them to the annealing
temperature? Or would it be feasible to spin a rod in the holes
to heat them by friction to soften them? Or would that just
work-harden the surface....

---

FF

On Aug 17, 2:50 am, Charles Vincent wrote:
Fortunat1 wrote:
"Rich S." wrote in
:

"Fortunat1" wrote in message
...
Well, obviously I'd protect it, but I'm not going to rely on epoxy to
bear a load. If I can't get the holes 100% I'll bush them....

...So I guess I'l just be as careful as I can cutting the holes. Just
looking through Bengelis' book, I see he recommends using a twist drill to
cut the holes, presumably to their final size,...

I would test that theory first. Reamers may or may not give a good
finish on wood. That was one of the reasons I quoted the study I did.
The twist drill gave the best hole finish.


Bits made for wood, high quality brad-point or forstner bits,
may give you a cleaner hole than a twist drill made for metal.
Cheap bits are crap-they'll burn their way through the wood.

As a rule of thumb, when working wood, use tools made for
woodworking. Duh!

Wood expands and contracts with changes in humidity and
it does so anisotropically. E.g. a flat-sawn board will
have the highest expansion rate accross it's width, less through
its thickness, and minimal along it's length. Quarter sawn or
vertically grained wood, which is what you usually want for
a spar cap, will have those first two rates reversed.

What this means is that if you drill a perfectly circular hole
in a piece of wood, as soon as the humidity changes it
becomes an oval hole. The same is true of a wooden dowel.

Wood finishes slow the rate at which wood absorbs or
releases moisture to the air so as to prevent moisture
gradients through the interior of the wood, which minimizes
e warpage. But all wood finishes are permeable to some
degree to water vapor.

So don't get too crazy about making the hole perfect. I think
the epoxy approach is a good idea.

--

FF

On Aug 22, 2:55 am, "Morgans" wrote:

I'll bet that you structural engineer friends are not experienced with wood
props, and their failure modes. It seems to be their own unique circumstance.
It has been found that the props fail, not the bolts.
--
Jim in NC

Jim,

I share your skepticism. As a structural engineer, I am also curious
about the statement that friction is only considered when it works
against you. It's not clear to me whether these were aircraft
structural engineers or otherwise, so I'll have to give Bud the
benefit of the doubt. However, Chris Heintz, designer of the Zenith
aircraft, that has stated that the reason fatigue isn't much of a
problem for the rivets in the aircraft skin is because the friction
between the joined surfaces typically carries the cyclic loads from
engine vibration (See "Riveted Joints", Chris Heintz, P.E.). I won't
speak to use in aircraft, but in general construction friction is
often considered a working part of the structure.

In fact, there are many instances in steel structures where service
loads are transmitted purely by static friction - moment connections,
end restraints for slender columns, connections with slotted/oversized
holes to facilitate assembly. Bearing/shear of the bolts is obviously
checked, but day-to-day the loads in those structures are transmitted
via static friction between the members. By design. AISC references
these as slip-critical connections. HSFG (High Strength Friction Grip)
is another term. Due to construction methods and tolerances, those
connections may only have one bolt out of the whole group that is
technically "bearing", maybe none. My point is that friction as a
mechanism for transferring loads to a wood prop is not really all that
unique or unusual as an engineering concept.

To address an earlier part of the thread, however, I wouldn't count on
friction for a wood-spar attach fitting. The fittings are often made
from thin material. Out-of-plane bending prevents the fitting from
developing much friction away from the bolt holes. And you have
humidity changes constantly modifying your wood dimensions. Tried-and-
true phenolic bushings, match drilled and reamed to the fittings, cost
about a dollar per hole. In the plane I'm building, that is less than
$50, so it was an easy choice to make.

Another statement that doesn't sit well was the reasoning that a pre-
tensioned bolt has better fatigue characteristics because metal
fatigues less when the stress cycle is all in tension as compared to
stress reversal. This is a clear misunderstanding of the factors in
play. Study the S-N diagrams of these materials and you will see that
increasing the mean stress decreases the fatigue life for a given
stress cycle amplitude. The reason some pre-tensioned bolted
connections (esp. shear) have better fatigue characteristics is
because the cyclic portion of the load is transfered via friction. The
bolt actually experiences a drastically reduced or eliminated cyclic
stress, thereby extending it's fatigue life even though the mean
stress of the bolt is much higher. Tension connections see improvement
through a different mechanism, but the result is the same - reduced
cyclic stress in the bolt and increased fatigue life.

Matt, P.E.

"Gunny" wrote

To address an earlier part of the thread, however, I wouldn't count on
friction for a wood-spar attach fitting. The fittings are often made
from thin material. Out-of-plane bending prevents the fitting from
developing much friction away from the bolt holes. And you have
humidity changes constantly modifying your wood dimensions. Tried-and-
true phenolic bushings, match drilled and reamed to the fittings, cost
about a dollar per hole. In the plane I'm building, that is less than
$50, so it was an easy choice to make.


Oh, I've becomne a believer in that part of the tale. It does make perfect
sense that the plates are not ridgid enough to develop any significant
friction.

There are too many conflicts with what I have read from people who's word I
trust, that props are driven mainly from shear loading.

I remember a few months back, that one of the guys on the group
(occasionally) that works at Scaled Composite in an important capacity,
threw the prop on his (vary-easy ?) There were warning signs, as I recall,
that were missed before it flew off.

A top Boeing engineer is not likely to have enough experience with wood
props to make his word more valid than the local guy at the airport that has
been flying wood props all of his life.

I really don't have a dog in this fight. I'll attempt to let it lay, and
let those out there with a dog in the fight make up there own minds. I
could be all wet, but if I am, I have badly misunderstood some reading I
have done.
--
Jim in NC

On Aug 24, 1:38 pm, Gunny wrote:
On Aug 22, 2:55 am, "Morgans" wrote:



I'll bet that you structural engineer friends are not experienced with wood
props, and their failure modes. It seems to be their own unique circumstance.
It has been found that the props fail, not the bolts.
--
Jim in NC

Jim,

I share your skepticism. As a structural engineer, I am also curious
about the statement that friction is only considered when it works
against you. It's not clear to me whether these were aircraft
structural engineers or otherwise, so I'll have to give Bud the
benefit of the doubt. However, Chris Heintz, designer of the Zenith
aircraft, that has stated that the reason fatigue isn't much of a
problem for the rivets in the aircraft skin is because the friction
between the joined surfaces typically carries the cyclic loads from
engine vibration (See "Riveted Joints", Chris Heintz, P.E.). I won't
speak to use in aircraft, but in general construction friction is
often considered a working part of the structure.

In fact, there are many instances in steel structures where service
loads are transmitted purely by static friction - moment connections,
end restraints for slender columns, connections with slotted/oversized
holes to facilitate assembly. Bearing/shear of the bolts is obviously
checked, but day-to-day the loads in those structures are transmitted
via static friction between the members. By design. AISC references
these as slip-critical connections. HSFG (High Strength Friction Grip)
is another term. Due to construction methods and tolerances, those
connections may only have one bolt out of the whole group that is
technically "bearing", maybe none. My point is that friction as a
mechanism for transferring loads to a wood prop is not really all that
unique or unusual as an engineering concept.

To address an earlier part of the thread, however, I wouldn't count on
friction for a wood-spar attach fitting. The fittings are often made
from thin material. Out-of-plane bending prevents the fitting from
developing much friction away from the bolt holes. And you have
humidity changes constantly modifying your wood dimensions. Tried-and-
true phenolic bushings, match drilled and reamed to the fittings, cost
about a dollar per hole. In the plane I'm building, that is less than
$50, so it was an easy choice to make.

Another statement that doesn't sit well was the reasoning that a pre-
tensioned bolt has better fatigue characteristics because metal
fatigues less when the stress cycle is all in tension as compared to
stress reversal. This is a clear misunderstanding of the factors in
play. Study the S-N diagrams of these materials and you will see that
increasing the mean stress decreases the fatigue life for a given
stress cycle amplitude. The reason some pre-tensioned bolted
connections (esp. shear) have better fatigue characteristics is
because the cyclic portion of the load is transfered via friction. The
bolt actually experiences a drastically reduced or eliminated cyclic
stress, thereby extending it's fatigue life even though the mean
stress of the bolt is much higher. Tension connections see improvement
through a different mechanism, but the result is the same - reduced
cyclic stress in the bolt and increased fatigue life.

Matt, P.E.

Thanks for your comments, and before I put my comments on this
thread to bed, I want to say that the OP asked a question or two that
have been answered very well, and that is what this group is for. Even
I have learned things about working with wood. Anyone reading this
thread looking for info will find the correct way to construct a wing
joint.
As to whether or not the engineers I talked to were aircraft
engineers, most definately they are.
As to some of your comments, I need to clarify some things. If
you are a civil engineer that deals with steel structures, and you
have design and analysis standards that use friction to qualify
structure, then that is your way to do it. I don't recall seeing a
major building , bridge, etc, that wasn't either riveted or welded
together, but I don't know for sure. So I will take your word for it.
I stated in my first post that friction existed and carried load, but
simply that for aerospace structures it is never counted on to carry
load. You only consider friction when it works against you. That I
know is true. In your statements about why using friction in the wood
spar joint is not a good idea, I think you have begun to uncover some
of the reasons why it is true. Since most airframes are thin shell
material, most of these reasons apply just as well to metal as wood.
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. Why
you think I need it pointed out that higher stress levels result in
shorter fatigue life is puzzling. Of course the higher the load you
place on a structure, the fewer cycles it will survive before failure.
What is hard to understand about that? What you apparently don't
understand is what constitutes a load cycle, how much is the load, and
what preload does to that. Preloading the bolt reduces the cyclic load
that it sees, since the load in a preloaded bolt only increases about
10% until the applied load exceeds the preload. When the prop bolts
are allowed to lose their preload, the full applied load becomes the
amount of cyclic load that causes fatigue. This is best demonstrated
by giving an example. Take two identical bolts, having a breaking
strength of 5,000 lbs each, and preload one to 2000 lbs, and none to
the other. 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. Same bolts, same loads. The meaning of this is that if you
keep the prop bolts properly preloaded or torqued as it is, then BOTH
the bolts and the prop hub see a much smaller cyclic fatigue load than
if you allow them to become loose, thereby greatly increasing the
cyclic load that they see, and increasing likelyhood of failure.
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 best book to explain all this is "Mechanical Engineering
Design" by Joseph Edward Shigley, Professor at the University of
Michigan, chapter 8, "Design of Screws, Fasteners, and Connections".
It is THE most widely used text on the subject in the top engineering
schools of the country, and has been for many years.

Regards,
Bud
M.S. Aerospace Engineering

On Aug 24, 1:38 pm, Gunny wrote:
On Aug 22, 2:55 am, "Morgans" wrote:



I'll bet that you structural engineer friends are not experienced with wood
props, and their failure modes. It seems to be their own unique circumstance.
It has been found that the props fail, not the bolts.
--
Jim in NC

Jim,

I share your skepticism. As a structural engineer, I am also curious
about the statement that friction is only considered when it works
against you. It's not clear to me whether these were aircraft
structural engineers or otherwise, so I'll have to give Bud the
benefit of the doubt. However, Chris Heintz, designer of the Zenith
aircraft, that has stated that the reason fatigue isn't much of a
problem for the rivets in the aircraft skin is because the friction
between the joined surfaces typically carries the cyclic loads from
engine vibration (See "Riveted Joints", Chris Heintz, P.E.). I won't
speak to use in aircraft, but in general construction friction is
often considered a working part of the structure.

In fact, there are many instances in steel structures where service
loads are transmitted purely by static friction - moment connections,
end restraints for slender columns, connections with slotted/oversized
holes to facilitate assembly. Bearing/shear of the bolts is obviously
checked, but day-to-day the loads in those structures are transmitted
via static friction between the members. By design. AISC references
these as slip-critical connections. HSFG (High Strength Friction Grip)
is another term. Due to construction methods and tolerances, those
connections may only have one bolt out of the whole group that is
technically "bearing", maybe none. My point is that friction as a
mechanism for transferring loads to a wood prop is not really all that
unique or unusual as an engineering concept.

To address an earlier part of the thread, however, I wouldn't count on
friction for a wood-spar attach fitting. The fittings are often made
from thin material. Out-of-plane bending prevents the fitting from
developing much friction away from the bolt holes. And you have
humidity changes constantly modifying your wood dimensions. Tried-and-
true phenolic bushings, match drilled and reamed to the fittings, cost
about a dollar per hole. In the plane I'm building, that is less than
$50, so it was an easy choice to make.

Another statement that doesn't sit well was the reasoning that a pre-
tensioned bolt has better fatigue characteristics because metal
fatigues less when the stress cycle is all in tension as compared to
stress reversal. This is a clear misunderstanding of the factors in
play. Study the S-N diagrams of these materials and you will see that
increasing the mean stress decreases the fatigue life for a given
stress cycle amplitude. The reason some pre-tensioned bolted
connections (esp. shear) have better fatigue characteristics is
because the cyclic portion of the load is transfered via friction. The
bolt actually experiences a drastically reduced or eliminated cyclic
stress, thereby extending it's fatigue life even though the mean
stress of the bolt is much higher. Tension connections see improvement
through a different mechanism, but the result is the same - reduced
cyclic stress in the bolt and increased fatigue life.

Matt, P.E.

Thanks for your comments, and before I put my comments on this
thread to bed, I want to say that the OP asked a question or two that
have been answered very well, and that is what this group is for. Even
I have learned things about working with wood. Anyone reading this
thread looking for info will find the correct way to construct a wing
joint.
As to whether or not the engineers I talked to were aircraft
engineers, most definately they are.
As to some of your comments, I need to clarify some things. If
you are a civil engineer that deals with steel structures, and you
have design and analysis standards that use friction to qualify
structure, then that is your way to do it. I don't recall seeing a
major building , bridge, etc, that wasn't either riveted or welded
together, but I don't know for sure. So I will take your word for it.
I stated in my first post that friction existed and carried load, but
simply that for aerospace structures it is never counted on to carry
load. You only consider friction when it works against you. That I
know is true. In your statements about why using friction in the wood
spar joint is not a good idea, I think you have begun to uncover some
of the reasons why it is true. Since most airframes are thin shell
material, most of these reasons apply just as well to metal as wood.
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. Why
you think I need it pointed out that higher stress levels result in
shorter fatigue life is puzzling. Of course the higher the load you
place on a structure, the fewer cycles it will survive before failure.
What is hard to understand about that? What you apparently don't
understand is what constitutes a load cycle, how much is the load, and
what preload does to that. Preloading the bolt reduces the cyclic load
that it sees, since the load in a preloaded bolt only increases about
10% until the applied load exceeds the preload. When the prop bolts
are allowed to lose their preload, the full applied load becomes the
amount of cyclic load that causes fatigue. This is best demonstrated
by giving an example. Take two identical bolts, having a breaking
strength of 5,000 lbs each, and preload one to 2000 lbs, and none to
the other. 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. Same bolts, same loads. The meaning of this is that if you
keep the prop bolts properly preloaded or torqued as it is, then BOTH
the bolts and the prop hub see a much smaller cyclic fatigue load than
if you allow them to become loose, thereby greatly increasing the
cyclic load that they see, and increasing likelyhood of failure.
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 best book to explain all this is "Mechanical Engineering
Design" by Joseph Edward Shigley, Professor at the University of
Michigan, chapter 8, "Design of Screws, Fasteners, and Connections".
It is THE most widely used text on the subject in the top engineering
schools of the country, and has been for many years.

Regards,
Bud
M.S. Aerospace Engineering

wrote

The best book to explain all this is "Mechanical Engineering
Design" by Joseph Edward Shigley, Professor at the University of
Michigan, chapter 8, "Design of Screws, Fasteners, and Connections".
It is THE most widely used text on the subject in the top engineering
schools of the country, and has been for many years.

Hell, that explains it, when I see what your source material is from! BFG
--
Jim in NC

Ohio State University Alum, and former 5 year marching band member.

Go Bucks!