okay all right we'll continue with tap
threads and in case you're wondering
what page you were you're on those of
you who have joined us for this session
this page should be page 926 and now
tapping as done with either by hand or
by machine and the bulk of the metal
those is taken out with the tap drill of
course which has a diameter equal to or
slightly greater than the root diameter
the thread and of course that we covered
the number of tempered threads and so on
and then the bottom tap one of the
things I wanted to mention there is that
I guess in some cases you have to even
take a they have the hundred and twenty
degree cone and I think on the bottom of
them and you have to grind it off I
think sometimes if you really want to
get all the way down to the bottom of
the hole now here's Acme threads and
those are kind of an oddball type but
nevertheless they've been around since
the 1800s and they're used for
transmitting power unlike on jacks and
reversing motions on machinery in fact
those of you who've ever leveled a house
or something with a house jack they are
Acme threads they're kind of a square
cut tape thread and scissors Jack's
sometimes have Acme threads on them they
have a general-purpose fit class of two
G 3G and 4G with two G being the
sloppiest and four G the tightest and
they have a series of diameters and
threads that are to be used whenever
possible and they call it centralizing
for the tolerances and have the three
three classes and the two see of course
is the the worst and the four C's the
best depending on what you want as far
as backlash or anything like that goes
and the same tolerance designations are
used for both
internal external threads now here they
are as you can see they're kind of a
square type thread very thick stubby and
transmit a lot of power and in this case
they really don't have much of a radius
in the bottom because they make them so
strong if they figure that they'll carry
a carry the load and of course there's
no there's no impact loads normally on
these because it's something that you're
turning so slowly that you don't
generate any impact loading then we go
to stub acne it's about the same thing
as the other one except that it has a
shorter height on the threads and the
seat this is the one I believe no it
isn't either I was thinking one of them
with a English and the Americans have a
different set up on it but they stub
acne is the regular is 0.5 pitch while
the stub is 0.3 and if you turn over you
can see the difference on the next table
you see it really just has shorter
threads on it in in this direction and
of course all the different thread
geometries and everything are on there
and the pitch diameter and all that you
can look up at your own leisure when you
feel that do you need something to help
your insomnia ah buttress threads they
have been around a long time too and
they're kind of special and they're used
where loading is in one direction
typical examples are airplane propeller
hubs columns were hydraulic presses and
breech assemblies of large guns they
have a flat angle on the the loading
side of only 7 degrees from the
perpendicular and in a pressure angle of
45 degrees and this is the one that the
British in the Americans differ on the
height of the threads
point four pitch and 6/10 pitch but with
us prefers the point four and the
British believe the use of the point six
now I'm sorry Americans use the point
six and the British use the point four
but anyway a guy pointed out an example
of these to me here while back that they
had a press in their plant that they had
to fix and he found that it had these
odd ball threads on it called buttress
threads and he knew that I was into
fasteners he said you ever hear a
butters threads down there I've heard of
them they're not very common and you see
there aren't kind of odd here here's
that seven degree angle on the pressure
face of them here now this is this is
two different pictures from a an suspect
I believe one shows threads with a
radius up here the other one shows
threads with no radius and they have
their use and the the thing about this
this guy found out with his press if you
want to fix them these are normally
machined cut on there's no no taps no
dice no nothing for them you have to fix
them yourself drain them in place now if
we go to cross-sectional areas for third
calculation you have different cross
sectional areas for tension and shear
stress calculations if a fastener is
loaded in shear with no threads in the
shear plane of the hole and the full
shank area can be used for the shear
stress calculations for tensile stress
you use a minimum area through the
threaded portion of fastener but it's
it's not a circle with a diameter of
equal to the minor diameter because
since you have a root on one side and
thread on the other side you get
slightly better benefit than that on the
diameter so so you get an effective
diameter this slightly larger and there
is a formula for calculating it there
are a number of formulas for
that goes but here is a common one in
which n is the threads per inch in the
English system and D is the shank
diameter so you have this is your
correction factor here for the fact
you're not using the full diameter of it
and then for metric fasteners you have
this for the correction factor where P
is is the thread pitch in millimeters
and D is the shank diameter in
millimeters so and in the appendices
which you people don't have but we'll be
getting later we have a derivation of
this tension formula for calculating the
cross sectional areas now here's a
little handy-dandy formula for
calculating thread pullout and this is
one that I've never seen in a textbook I
got it from some of the people I worked
with at Martin Marietta it's for
sheering off threads in a hole where
normally when you tap into a hole the
material you're tapping into is weaker
than the fastener so you're concerned
about how long the thread engagement you
have to have keep from pulling the thing
out so this this formula helps you to
conservatively arrive at that you have
pi times a mean diameter and the mean
diameter is usually a pitch diameter and
you have an allowable for your material
in shear whatever it is if you're
working with yield you put in the shear
yield allowable and if it's ultimate you
put in the ultimate allowable then the
length of engagement now that length of
engagement is a length of full thread
engagement the denominator has the 3 in
it if you were going to be totally
theoretical about it you had a perfectly
mated threads then that bigger could go
down as low as 2 because actually if you
visualize it for a moment what you're
doing you're pulling out a little
cylindrical shell and if you
things exactly at the pitch diameter so
the the external internal thread were
the same then you would be splitting
that little shell between the two of
them so this factor could go all the way
down to two but since threads don't make
that way the three is put in SA fudge
factors I have mentioned mentioned here
and there are some other methods given
in h28 mill handbook h28 for calculating
pull out and once again you can some of
them are a lot more complicated than
what I've done here what I've done if
you have a chance to do it will work so
you can go ahead and go with it now
moving into the fatigue resistant bolt
section of course people usually don't
even think about that and it gets them
in trouble but if you have cyclic
loading on a joint then you need to
minimize the stress risers created
during the manufacturing cycle and some
of these are the threads thread run out
thread Phillip radius and work hardening
through forming of the bolts so you also
have to monitor the installation the
bolt closely to minimize the cycling
modes and of course one of the things
that you do is this is one of the cases
in which Murphy can tighten them up
tight because with a particular knit to
be as tight as possible because it cuts
down on the cyclic loading now one of
the things you can use of course is the
cold fasteners with cold rolled threads
because that gives you the residual
compressive stresses in the thread
surfaces and it gives them more
particular resistance because the TIG
only works in tension so as long as you
keep things in compression
you're right it's just like with glass
they don't worry about cracks and glass
if it's in compression because doesn't
do anything it's just in tension well
it's the same same way here if you
fatigue is compression compression is
fine but tensions where it gets you in
trouble so some of these fasteners as I
mentioned earlier you actually have to
cold roll the threads in order to get it
up the strength that you want it so
that's a good fatigue bolt also the J
threads are better than regular threads
in fatigue because they have the larger
radius then here's one of the other
problems that you can run into that
people every once in a while forget
about is the elongation limits on
materials one of the rules of thumb on
designing of fasteners is don't use a
material at a strength level that has an
elongation below 10% because when you
get down below 10% your stress risers
become much more important as a matter
of fact h-11 tool steel which is used
for high strength fasteners you can get
in trouble and some of the aerospace
companies are backing off on using it at
the real high strength because of that
because it goes down about a 7 or 8
percent elongation and when you get down
that low then you can get brittle
failures now J threads as I mentioned
they're our batter and using countersunk
coursers under the heads to minimize the
washer contact with the Phillip radius
and then if you really want to get
sticky and have a super-duper for taking
tight bolt you can undercut the shank
down to the same diameter as the minor
diameter the threads and this does away
with your stress concentration on your
thread run out because you know having a
run out there because you just have a
smooth shank and when the thread runs
out it runs out on top of the thing more
or less so so that a undercut diameter
fastener
is better in fatigue than one a regular
fastener where the shank diameter is
normally equal to the major diameter of
the threads now the hardness of nut less
than bolt hardness that one can be very
much a problem in some cases since the
bolt load is initially reacted on the
first one or two threads and then has to
deform something in order to spread it
out you want your nut to be softer than
the bolt so you can spread your load out
and a rule of thumb is that the maximum
hardness of the nut should not exceed
the minimum hardness of the bolt and
that's even stretching it normally you
would want it to be for instance a
hundred and sixty ksi bolt you use a 125
145 nut on it in order to distribute the
load now this court case that I
mentioned to you earlier the chair
failure that was the thing that caused
that chair to fail was that they this
furniture manufacturers don't have too
many fatigue engineers on the job they
go out up the hardware store buy
whatever's cheapest and they bought the
bolts from one place and the nuts from
another place and this deformed thread
nut in deforming it they had actually
worked hardened it to where it was
harder than the bolt so what it did when
they put it on it just stripped the
threads the boldest that was going on
and then in a matter of about six months
this guy is brand new chair fell apart
and set him for a ride
so he sued the furniture company and
that's where I got in on it but
here's a desirable joint loading diagram
now you want a stiffness fastener joint
stiffness ratio of five or higher and
we'll go through some of the things on
calculating joint stiffness fastener
stiffness and so on to minimize the
cyclic loading on the fastener and
coming back again I keep repeating this
one but it's worth repeating avoid
capped holes if you can don't use them
unless you have to I was on a design
review here one time in which this young
engineer came up with a design and he
had heard that when you used aluminum
you were supposed to use inserts so
instead of bolting through he put
through holes in butt tap them for
inserts because after all you're
supposed to use inserts in aluminum but
if you have a chance to use through
bolting that is the most efficient most
trouble-free way of doing it regardless
of what what you're bolting in all right
now the tap holes are cut rather than
rolled and the radius of a tap Pole is
not measured normally if you want it
measured it's a lot of trouble so you
could get all sorts of undetected stress
risers because think had it from a
practical standpoint you've got a
quarter inch hole inspector is gonna go
up and look down in it and say yep
there's all there it looks alright to me
and that's about the amount of
inspection you'll get on it now use a
lot of small diameter bolts if you can
in order to give you a more elastic
system because the that gives you a
better ratio of bolts joint stiffness to
fastener stiffness and of course that
kicks a labour cost up so you have to
wait to see which what you're going to
do in order to make the joint survive
now the other thing you you have to do
is consider the thermal loading and the
joint remember I mentioned
earlier about using Belleville washers
to give you a longer spring constant if
you will and a bolted joint to take the
thermal cycling and particularly if the
bolt and the joint materials are
different then you have to watch it
closely we had a problem on the center
vehical when they were using good old 80
to 86 bolts on aluminum flanges the only
thing is they tighten them up Terk them
down at room temperature then when they
tanked up with liquid hydrogen and
liquid oxygen the temperature went down
to something like minus 300 the aluminum
shrink and it started leaking because
the bolts got loose so they like to
never hit a happy balance on that of
getting bolts the fact they had to get
higher strength bolts and they could
crank the torque up so that the thing
would be alright at room temperature and
still not leak at the cryogenic
temperature so this is a this is a
problem you have to be careful about
then here's the other thing that that
you should do this is one of the few
places that I agree with some of the
automotive companies on is turcica
fasteners close to yield point if it's a
fatigue joint and if you do enough
testing to determine where it is then
you can torque up to 90 to 95% of yield
and the higher preload decreases the
cyclic loading and I have some figures
here to indicate this if you want to
leaf back and forth between 10 7 and 10
8 the or I'll tell you what if you will
go to the next page with the the graph
there and and then bets it can keep hers
where it is there we go now we work back
and forth on here here is the initial
loading here is yield so we're so here's
the initial loading before putting
external load on the thing
now when you put the load on the cyclic
loading on the fastener is just the part
between here and here so if as you'll
see when I show the the next one of
these where I deliberately put the two
points closer together you get lost what
les cycling then this is the clamping
load remaining when you go all the way
up to yield now this represents the
stiffness of the bolt and this
represents the stiffness of the joint so
if you get a better ratio between the
two and lean those lines over a little
bit you get less cyclic loading on the
bolt when you apply an external load now
if you go over here we're torque above
yield because here's a yield point
there's above yield then on this one we
really applied two loads that took it
way above yield and failed it it
separated so now if you look at the ten
point nine there I put the the initial
preload and yield are fairly close
together so you see the cyclic loading
is just the between here so therefore
you get less cyclic loading with the
higher torque on the fasteners now this
figure was over torqued
if you notice it's kind of Wiggly here
that's the over Turk trying to scan it
into the scanner and it wouldn't scan in
right
okay moving on now to fastener torque
which is 11:1 now determination of
torque values is one of the most
difficult and controversial aspects of
fastener design and if you tuck to
Murphy he says if tight is good a little
tighter is better but it doesn't always
work out that way Murphy's a guy that
runs the wrenches but the variables
involved the joint material strength the
coefficient of friction between mating
surfaces the effect of friction between
the bolt head and nut or its mating
surface and the effect of coatings and
lubricants on the friction coefficients
themselves because the amount of
lubricant you put on changes it all
together now the percentage of bolt
tensile strength that you want for
preload that is something that is
difficult one of our guys just to show
you how how things can vary one of our
guys had some a stainless steel bolt nut
assembly that had been locks cleaned now
locks cleaned is like ultrasonically
cleaning your jewelry or something like
that it is clean clean and he was
required to have it that clean so he
went to assemble it he had used up his
allowable torque before you got it
seated because dry dry clean stainless
on dry clean stainless has a real high
coefficient of friction so this just
shows you what you can do going to an
extreme now the other thing is what is
the distribution of total torque to
tension shear and friction you know when
you twerk up a fastener that you have a
certain torque value applied but you
don't know how much of it went into
tension how much of it went into shear
and and how much of it has lost the
friction but it all has to be accounted
or then the other thing is the relative
spring rates the bolts and nuts and the
joints themselves and then accounting
for the running torque of the locking
devices all those different methods of
locking themselves have at what is
called a running torque that has to be
accounted for now head friction if the
fastener is tightened from the head the
bearing surface for the bottom of the
head becomes a big part of the friction
load that's why that having a smooth
washer hardened washer under the head is
a good idea even if you don't
necessarily have to have it it's good
because it gives you a hardened surface
that will have a lower coefficient of
friction than the joint material itself
plus the washer will deter or prevent
embedment of the head where the joint
material is softer than the boat which
is usually the case
now if head friction locking is desired
then you can maximize that head friction
use remember earlier I covered the
serrated head with that you could use
without a washer or don't use any
lubricant on the thing and then then of
course you will use up more of your
torque on friction and have less in it
and axial load which you have to account
for nut friction pretty much the same
thing you can you can go either way you
can maximize it or minimize it by using
lubricants and stuff like that and the
nut usually contains a locking device
it's easier to install a locking device
on a nut normally than it is on the
bolts so most of the nuts carry the
locking device so the running torque the
locking device and I'll go through
definitions on it but the running torque
is the amount that it takes just to seek
the thing down to the surface and it's
usually a small fraction of the total
now the k-factor people say T equals
2/10 F D and that 2/10 is used
religiously well at 2/10 is this budge
factor which has this formula right here
and for those of you who have a copy my
fastener manual I'd I had the right
calculations in the manual but I had the
wrong terminology I had a Greek sigh for
this this angle here it should have been
lambda according to the formula and I
the calculations were done right the
terminology was wrong in it but anyway
this is this is the formula that you use
for calculating that K factor now the D
sub M is the mean thread diameter which
you use pitch diameter for lambda is the
thread lead angle and mu here is the
friction coefficient between threads and
alpha is the thread angle in this case
since you have a 60 degree angle it's
half of that which is 30 and u sub c is
the friction coefficient between the
bolt head or nut and the clamping
surface so if you throw all those
together and you're able to determine
them well enough that you feel that you
have some confidence in them then you
run a calculation and get an actual
value for that k factor now I did some
calculations using these coefficients of
friction and in this case I used
identical ones although you could have
different ones that doesn't for the
between threads and between the bolt or
or nut and look at the variation that
you can get with the variation in
friction coefficient you see the the K
factor the point two that we use is
actually a little bit high because it
would be somewhere in here would be
a more realistic value however one of
the objections to using zinc plating is
that the friction coefficient with zinc
can vary enough that that value can go
anywhere from point forward up to almost
1 so now when you do this then most of
the torque that you're applying is going
into overcoming friction and your axial
load on the fastener isn't very much
here are some torque definitions and
these are courtesy of sae AS 1310 and
marshall standard 486 and some of them
have been cleaned up slightly to make
them a little more readable because
they've gotten kind of out of hand
so just for torque itself it's of course
it's a force times a distance and you
have a moment arm which is the length of
your torque wrench and then of course
that you put on it and if you have a
torque wrench it'll it'll vary or we'll
register the amount of torque that
you're putting on or if you have the one
of the old do-it-yourselfers it has a
needle on it and you measure it by
deflecting the rod and that one is a
plus or minus 40 percent depending on
whether you can hold it in place long
enough to read it while you're doing the
turkey the applied torque is the torque
transmitted to the fastener of the
installation tool and then you the
running or prevailing torque is the
amount to overcome the locking device
itself so just to seek the fastener
and here are some other definitions the
double torque or retorque
to seek materials being joined where you
had interferences or sheet gaps or form
in place gaskets and stuff like that and
also where you turn around one time in a
circle of bolts and then you need to go
back and check them the the no load
torque is the torque required to
overcome kinetic friction between mating
threads without a locking device and
that is usually unless you have threads
that are damaged or something that is
usually next to nothing then the
installation torque design torque
applied the tightening direction and
includes kinetic static friction self
locking features and required to apply a
desired axial load to the fastener
assembly so its measured in the
tightening direction only and of course
the the thing that is usually in
determinants are not indeterminate but
hard to determine is how much actually a
load do you really get for a given
torque and here's limiting torque and so
on which you can read through these
multiple torque required to see parts
where you have heavy interferences and
assembly and one of these has to do with
where if you're torquing fasteners on a
flange or if you're torquing the lug
bolts on your car or something you know
you always talk 180 degrees apart and
after you get them snug down so that you
get the effect of the adjacent fastener
to the one that you're talking down to
make sure you're going to tighten down
because if you if you tighten tighten
them down and then tighten one down the
one next to it will have a slight amount
of loosening due to the give of the
flange itself so you have to go back and
recheck them back to guy by the name of
George Bible formerly of the University
of Akron came up with a
pewter eyes program on dealing with
large flanges and we're talking near
six-foot flanges or something like that
on the iterative process for doing the
Turks on them to get them all Turk down
within satisfactory limits and gave a
presentation one time at the voting
Technology Council now here's the
seating torque and that's just to bring
the bearing faces into a seated position
and then the the break loose torque
torque required to loosen the fastener
from its installed position there's
various other definitions that get too
confusing and Harold Casper and I went
through them and eliminated some of them
that created too much confusion now
here's the big question what part
tension and that's the most
unpredictable one and the clamp load in
general only represents something like
10 to 25% of the applied torque because
the rest of it is used to overcome
friction and various other things in the
joint so but the thing that you've got
to look at is just because you put a
certain amount of torque into a fastener
and it doesn't have a lot of axial load
on it doesn't mean that that torque went
away it's still in there and shir
somewhere it has to be accounted for so
that's why you got to be careful on over
torquing stuff and you got to combine
stresses and check them all against the
total strength of the fastener so and of
course this is the thing here that the
von Mises stresses can be calculated and
compared to yield and ultimate strength
of the material so or for those of you
who feel academically inclined you could
use a Mohr circle and take share in
tension and plot them out and get all
that sort of thing but stress ratios
work better so and their artwork values
and these are tongue-in-cheek not
one's for both inch and metric fasteners
in the appendices which you would get
layer clerk accuracies it's only as good
as the type of measuring device in the
operator and of all these methods the
worst one of all is the impact wrench
Joe Greenslade who is a writer
in the fastener world put out an article
here sometime back then I got a chuckle
out of he believe it was titled impact
wrench
the engineers worst enemy because the
impact wrenches that these garages use
are never calibrated probably and they
put them on real good and tight and then
you need a truck breaker bar to get your
lug nuts loose on your car when you go
to take it off so so that's the worst
one and if a perk wrench is used to
apply torque the applied torque should
be at least 70% a full scale of the
wrench in other words don't use a
hundred and seventy five foot pound
torque wrench with a number eight
fastener because there's no accuracy
there just like it is with any other
reading if you're doing instrumentation
you try to get say 70% of full scale in
the range of your actual measurements
that you're making because you don't
since the tolerances are a percentage
you won't you do not want to be
measuring in the bottom 10% of your
scale when you're making readings on
anything now
here is a table with approximate values
for Terk measuring methods versus the
accuracy and cost now you see the feel
there in which the guy just says well
I've been doing this for years so this
is about what this should have on it
cheap way of doing it and a lot of it if
you've been I've been feeling those
joints for years like
that a lot of times it will suffice I
don't use a perk branch on my car unless
there's a specified value called for
like a tie rod end or something like
that where you have to go to a high
torque value then I get out the turqu
wrench otherwise I don't an impact
wrench and it's it's been probably even
worse than that but that's the value
that some of us had agreed to before the
torque wrench that actually gives you a
reading
about plus or minus 25 turn of the nut
now that's a method which I will cover
later which is fairly accurate as long
as you want to use it but you probably
wouldn't want to use it because you go
above yield on the passenger then these
load indicating washers they give pretty
good accuracy but of course the amount
of labor involved runs the cost up
remember I covered those the the one
that had the little bumps on it and the
other one that had the little internal
bushing that you compressed fastener
elongation now that could be used if you
are say bolting a flange and you have a
guy there with a scale an accurate scale
he can actually measure fastener
elongation velocity subtracts out the
dead part that didn't expand on it and
get some idea as to where he's at on it
but then you can go to string gauges now
strain gauges are real accurate but the
only thing is how do you do it how do
you put strain gauges on a bolt etre
installing down in the hole it's kind of
hard to do so so what what you normally
do with the strain gauge is is if you're
really interested in finding exactly
what you want you put them on one of the
bolts and test it under the same
conditions as nearly as you can to
duplicate the actual installation and
get a quick reading from that and then
use that torque reading on the bolt
you're gonna install then of course the
other thing was these direct
and indicating bolts which is kind of a
strain gauge type setup so I will cover
some of those in further texture now
perks draping that is used a lot by the
aerospace companies for after you have
decided the final torque value on a
fastener you actually just take a marker
of some kind they used to use a paint
now we use a blue sharpie pen to mark
across the head or the nut straight
across onto the surrounding surface now
this is a visual indication if the thing
switches position on you because it will
show up because the two marks don't line
up anymore and that is a very common
thing in the aerospace world that way
you can look in later and see whether
anything has changed on your
installation now joint relaxation that's
not what you're going to after today
it's defined it's the unloading of a
fastener after its final torque due to a
number of contributing factors and here
are some of the major factors embedment
of the washer the head or the nut in the
joint material yielding of a high spot
or blemish on the head nut or washer
joint surface after final tightening and
untwisting of a fastener from initial
torsion where the shank had an
interference bit in the hole so you
cranked it down but a lot of that went
in to putting some torsional twist into
the fastener and so after the thing
settles down it kind of makes its way
back creeps back to a equilibrium
position and in doing so that will
lessen the load on the fastener itself
and then creep of the joint material
itself
then here's the other thing I mentioned
on the like the lug nuts on your car a
failure of the Installer to wreak torque
a pattern of fasteners after initial
installation to come compensate for
effects of adjacent fasteners to each
other because when you compress the
surface next to the the fastener you
talked before then it changes the load
on that fastener you got to go back to
return also here's here's one here's why
I don't like to go up to the yield point
on fasteners inadvertently exceeding the
yield point of the fastener during the
initial turkeying process now there
you're in real trouble in fact that's
what they did on that first time around
on that Center volt problems talked
about with the cryogenic temperatures
they say well we just increase the
torque so they increased the torque and
they were yielding some of the fasteners
when they checked them again they were
down to something like 40% of the
initial load so they had to go to higher
strength fasteners then the other thing
is critical joints should be inspected
for relaxation a few hours after
installation you go through and check
them with the same torque and see if any
of them have loosened up any now here's
the turn of the nut process and this is
used in the construction business
because it's something that visually you
can do particularly with a big boat you
tighten the nut above yields so what you
do is you taken it to what you think is
about 75% of ultimate load then put a
mark on it
then turn the nut an additional 180
degrees this brings a bolt stress up
above yield but below ultimate providing
the material is ductile so that yield an
ultimate are far enough apart now that
is not used in the aerospace world
because you don't risk stuff like that
aerospace torque values usually are 50
to 75 percent of yield depending on the
application as to whether you have much
tension on the joint or none and so on
so that because you still have to check
for both
shiron axial load now tightening the
fastener beyond its yield is risky
because it's so difficult to determine
where yield is this is why that if you
go look at the definition of yield for a
material in a something like mil
handbook 5 you'll find that it's based
on two-tenths of a percent permanent set
because you don't know the track yield
unless you have the thing on a machine
until after you've exceeded it because
you're still going up on your elasticity
curve and until you pick out from the
straight line you don't know you're
above yield so as I mentioned earlier
the the usual reason for going up close
to the yield is to minimize the fatigue
effects on fasteners but unless you have
done an awful lot of testing it's not a
good idea to go up to the yield point on
a faster now on joint stiffness we have
alluded to it many times up to now and
and we covered the joint loading
diagrams and now we look just look at
the joint itself as we tighten the
fasteners John Bickford actually has
used a spring type analogy on this which
makes it easier to understand because
you take a piece here that has three
different cross sections it's three
different Springs with the three
different spring constants and so you
can think of a joint or a fastener that
way and here is another one with the
joint stiffness
next page I thought I thought we'd had a
stop a glitch during things okay alright
well so the alright that this one's 101
but just leave that not for anyway
here is here's another thing that kind
of shows you here the concept again of a
large spring representing the joint and
a fasteners a little little tiny spring
that's trying to compress the big one
and of course do keep the fasteners out
of trouble you want their stiffness
ratio to to the joint to be a pretty
large differential and there's there's
just showing clamping force all right
now you can leave yours up over there
and we'll go to the next one here and
which we look at a boat remember in
school you had calculating the expansion
our tensile elongation on a rod and the
Delta L or change in length was just PL
over AE where P is the axial load ELLs
of the elastic length and a is the rock
cross-section and ease the modulus of
elasticity and so if you apply this to a
a bolt you can calculate these Delta
ELLs for different cross sections and
their lengths and John Bickford uses an
extreme here on the next page in which
he took a bolt that had been machined
all over the place and he calculated a
delta L based on all these different L
over a ratios since since P and E are
constant so that that is how you can
arrive at a joint stiffness value for
the bolt now I mean the stiffness from
the bolt but now when you go to the
joint there's where the authors disagree
and there's all sorts of things so here
are three different types of models if
you will that are used to calculate
joint stiffness
the spear although it was listed I
couldn't find any equations for it the
cylinder is used a lot and the cone is
used a lot and there are various ways of
calculating the stiffness now what I'm
talking about is if you look at these
the hole here represents the hole where
the bolt would go through okay
now john Bickford uses the cylindrical
model with a modification for eccentric
loading at or near the edge of the joint
and that is if you are wanting to use a
circle and the bolt is close enough to
the edge that you can't get the diameter
circle you want you can put in a fudge
factor for the fact that you're closer
to the edge then you should be and this
brings up another standard which is used
a lot in the industrial world but
difficult to obtain so I found out is
the German standard Vern Dutch your
engineer or other otherwise known as VDI
since nobody could pronounce it that is
a standard for doing calculations on
fasteners that are loading the joint
stiffness and all that type of thing and
I have a copy of it but I had to get it
through the back door because the
library couldn't find a copy in English
sigelei who wrote a lot of books on
engineering uses the cone frustum model
with a cone angle 45 degrees measured
from the bolt center line and then nasa
langley had had another set up using a
straight cylinder with three different
equations depending on the minimum edge
distance of the shortest side of the
joint then another guy of the name of
alexander blake uses a cone angle with
angle determined by a line drawn from
the outer edge of the flat of the head
to the centerline of the clamp
joint so this is the clamp joint here to
here and there's a centerline but for
the cone comes to and then using all of
this stuff all of these measurements to
calculate a joint stiffness and he comes
up with a nice nice little equation here
and this is for a particular angle of 45
degrees I believe here no I'm sorry this
is the shig Lee method on the cone we
have the other one I guess in the
appendix but you can have you have an
equation there that you can use to
calculate the joint stiffness so that
you can compare it to your fastener
stiffness to decide whether you're in
trouble or not now as far as the joint
stiffness calculations go here's one of
the bad parts about it the affect of
adjacent fasteners on joint compression
is not accounted for in any of these so
these are all empirical and the there
they're only an indicator then
unsymmetrical loading under a fastener
due to edge distance or cutouts is not
accounted for in other words you're
using a perfect cone or a perfect
cylinder and then if the bolt and joint
materials are different the stiffness
calculations must account for the
different moduli of elasticity for the
materials now so so you're in in a
little bit of trouble there on getting
these however things could be worse here
are some of the things you can do first
try just a simple cylinder with a radius
equal to the shortest edge distance the
fasteners this is called the barrett
theory of least work don't do any more
than you have to to show something good
if this stiffness is satisfactory
compared to the fastener don't go any
further go with it
if the simple cylinder is not
satisfactory add a washer with a
diameter larger than the fastener head
to kind of spread out the radius on your
cylinder then check it for that and
check the compressive stress under the
head contact area to make sure that the
compressive yield will not occur under
the maximum clamping load and then if
all else fails go do the calculations if
it is critical enough now in most cases
you are not critical enough that you
would have to go to a lot of lengths on
the difference between the fastener
stiffness and joint stiffness only a
rare case is now one of the things that
you want to be aware of is don't use a
big fat fastener on a thin joint because
chances are then the fastener is going
to be stiffer than the joint and you're
gonna have trouble you've been in
trouble on it but you can you can check
them and see what you've got and if if
your ratio is not too bad even for
taking that short cut method say 5 or
something between fastener and joint go
with it and it should be alright now
indirect reading of fastener tension
this question is asked how can I
determine the exact tension I have on a
fastener for a given torque
well the direct reading is possible but
it's not economically feasible for most
assemblies the technology is there that
you can't afford it so the usual
compromise is to test fasteners under
the closest actual installation
conditions that you can come up with and
determine a torque value then use that
torque value for your production
assemblies and so we'll cover a couple
of the upper three here of the direct
tension measurements now this one an
ultrasonic that's a good one
transducers mounted to the head of the
boat but as the bullet elongates the
travel time for the sound you know the
way ultrasonics work you bounce it off
of the back surface and back so if you
increase the length of the thing it
takes longer for thee for the ultrasonic
wave to get there and back so that is a
you can get a direct correlation between
the elongation of the boat which knowing
the cross-sectional area will give you
the stress well that's a very good thing
but the major drawback to it is you've
got to have the smooth surface to attach
it to because if you remember even if
you go in and have your heart checked or
something like that that they use an
ultrasonic fluid that they put on on
your body so that because you've got to
have a medium for it to go through so
you have to have a nice smooth surface
and then you have to have some sort of a
gel on there to put your transducer on
get it to hold so now what do you do if
you got a socket head Bowl you don't
have any place to attach the thing so
then once the bolt is calibrated for a
zero load you have to disconnect the
transducer in order to Terk the bolt
down to the load you want so that you
can measure it again so this one is is a
good method but it's not really
practical to do in most applications
neck next one is direct scaling now that
we had mentioned that earlier in which
where both ends of the installed bolt
are accessible such as pipe flange you
can actually measure the bolt and
subtract out the dead areas that are on
the the outside of the nut the heads and
so on and use the elongation there of
the boat to arrive at a load then of
course these direct tension indicating
washers that we covered in the washer
section those are used successfully in
the construction business because you
take a feeler gauge and inspect keep
talking until you get a gap of a certain
sighs and you have loads that you want
then we have this test machine by Ralph
shoberg of RS Technologies Farmington
Hills Michigan aides are one of my
fellow compadres on the lecture circuit
on fasteners and he has a machine that
will actually you can throw a bolt in it
and it will tell you for a given bolt
the exact amount that you have
pretension the exact amount for head
friction the exact amount for nut
friction but the only thing is it'll
tell you for that bolt it won't tell you
about your total installation so what
you have to do is take a bolt that
you're going to use and decide what you
want to load it to put it in the machine
and determine what perk it takes to give
you that stress and then use that for
your installation torque we will take a
break now and resume in a few minutes