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# Huth Formula for Fastener Flexibility6

## Huth Formula for Fastener Flexibility

(OP)
I asked this in another forum as well.  But I thought a discussion on different methods of determining fastener flexibility may begin here.  I have been using Tate and Rosenfeld and recently read the paper by Huth and felt that since his formula was determining lower compliance that the increased stiffness would produce more conservative results. However, unlike the T&R, it appears that the Huth is dependent on which element you make T1 or T2 (for single shear joints).
My question from the other forum:
In the Huth formula for fastener flexibility (Huth on Influence of Fastener Flexibility).  If you have a single shear joint with two different sheet thicknesses (t1 and t2), which sheet thickness do you utilize for t1 and t2(i.e. the thin sheet for t1 and the thicker sheet for t2 or vice versa).  Due to the 1/2nt2E3 factor in the right hand side bracket, this multiply by two in the denominator can make a  difference depending on which thickness you utilize.  Also, since this equation is also good for double shear with n=2 in lieu of 1, I am wondering if this 2 is a typo.  My example:  I have a 0.056" thk skin doubler on a 0.050" thk skin, I am obtaining my fatigue stress from the original skin which I am making t1, the doubler, which is thicker, is then t2.

Now I understand that in the grand scheme of things this difference of 0.050 and 0.056 is going to have an insignificant affect on the calculation.   Additionally, for most joint designs, the two parts should be close in thickness which would also provide an insignificant change.  However, it would be nice to now which way the formula was inteneded.

### RE: Huth Formula for Fastener Flexibility

The thinner sheet should be defined as the "strap", and the thickner sheet defined as the "plate".  Thre are also some alternate forms ofth eHuth equation in the literature that have the factor of 2 in the plate term: 1/2nt1E3.

### RE: Huth Formula for Fastener Flexibility

SW, can you cite a source?  The ASTM STP 927 paper seems ambiguous to me.  Looking at our company spreadsheet, your same conclusion is used in our calcs, but I'm still not sure where the basis for this conclusion is.

I also searched Knovel for other instances of Huth on flexibility in the literature, but came up empty.

### RE: Huth Formula for Fastener Flexibility

Conclusion is based on proprietary test data.  One paper with modified Huth equations is (though it may be hard to find):

Postupka, S.; Kühweg, A.; Arendts, F.J.; “Determination of the Bolt Flexibility of CFRP-Joints” ECCM-8, 1998, pp. 61-68

### RE: Huth Formula for Fastener Flexibility

Their is a German paper that review Tate & . It may be helpful. I'll see if I can find the reference.

### RE: Huth Formula for Fastener Flexibility

You’ll see the Huth equation as  C = 4.2* ((tp+ts)/(2D))^2/3 + (1/(tpEp) + 1/(tsEs) + 1/(tpEb) + 1/(2tpEb)).      Because of the 2 in the last term, the designation of plate vs. strap affects the answer which makes no sense.

The original Huth equation (in German) lists the flexibility as:

C = ((t1+t2)/(2D))^a + b/n(1/(t1E1) + 1/(nt2E2) + 1/(2t1E3) + 1/(2nt2E3))

For single shear, n = 1

The first equation listed above is missing a 2 in the (tpEb) term.  I’m not sure why it’s different than the original Huth equation.  This equation is used a lot – is it a mistake?

### RE: Huth Formula for Fastener Flexibility

Actually, the ASTM reference doesn't use the ts, tp, etc. notation; rather it uses t1, t2, etc. with no reference to straps or plates.  I think if a reference to straps and plates were given, it could be inferred that the plate is the thicker of the two.

FYI: The Tate paper is available here:
http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19930081668_1993081668.pdf

### RE: Huth Formula for Fastener Flexibility

Hi 737eng:
Some time ago i found in internet a good work named "Defining a standard formula and test method for fastener flexibility in lap joints" by Geoff Morris ( TU Delft ).

It may be useful for you.

Cheers !
Mohr

P.S: If you can not find it let me know and i will send you
a copy of this paper.

### RE: Huth Formula for Fastener Flexibility

(OP)
I understand that ts is the thickness of a strap which is the thinner member and tp is the thickness of the plate, but the equation is always written with t1 and t2.  So which is t1 and t2 referring to, strap or plate.

I believe:
t1 = tp (the thicker member)
t2 = ts (the thinner member)
This gives the lower compliance and thus a more conservative pin load than the opposite.

to make things more confusing, we wrote our program using the variable ti for inner and to for outer!!

Mohr,
thanks, I found the paper, didn't have time to review it thoroughly yet.  I am generally a little cautious about using someone's thesis without first going through and verifying everything first.

### RE: Huth Formula for Fastener Flexibility

Hi 737eng:
You are right to check the thesis but in this particular case it was checked by means of test.
Cheers

### RE: Huth Formula for Fastener Flexibility

3
Regarding the Huth calculation for spring constants for mechanically fastened joints, there is an error in Huth's equations printed in ASTM STP 927 (1985) which is what everyone seems to be using.

The second to last quotient reads:  1/(n*t1*E3)  The n should be replaced by a 2 and read: 1/(2*t1*E3).

Using the equation from the ASTM paper, you get a different spring contest based on your selection of which thickness is used for t1 or t2.

I have the original paper in German and I assume the author or the ASTM paper made a typo since he doesn't address his deviation from the German paper.

Huth, Heimo, “Zum Einflub der Nietnachgiebigkeit mehrreihiger Nietverbindungen auf die Lastübertragungs- und Lebensdauervorhersage,” LBF Report No. FB-172, dissertation, Technische Universität München, Munich, Germany, 1984.

Correct equation is...
C=((t1 + t2)/2d)^a    x   (b/n)  [ 1 /(t1  E1)  + 1 /(n t2 E2)   +  1 /(2 t1 E3) + 1 /(2 n t2 E3)  ]

### RE: Huth Formula for Fastener Flexibility

This is troublesome, to say the least.

Do you have a copy of the German paper, or can you point us to one?

I note your version of the equation would still give different values (at least for double shear, n=2) depending where you put t1 and t2 due to the n in the second and fourth terms of the second group.  Can you verify?

### RE: Huth Formula for Fastener Flexibility

Yes, you are correct, for double shear the error makes no difference.  For single shear however, that quotient is off by a factor of 2.  I scanned the Huth paper and it is 22GB.

### RE: Huth Formula for Fastener Flexibility

Correction 22MB  -  what was I thinking.

### RE: Huth Formula for Fastener Flexibility

I think you misunderstood my query regarding t1 and t2; I mean to ask if the corrected version will still give different values of C depending on the placement of t1 and t2.  This should be clear to me in reviewing the paper.

### RE: Huth Formula for Fastener Flexibility

First - YT - with the correct (original) equation, you get the same spring constant regardless which plate is t1 or t2.

### RE: Huth Formula for Fastener Flexibility

Alright, I'm thoroughly convinced that the ASTM reference is in error.  Kudos and thanks to analyst64 for sharing the original publication and spreadsheet.

My thinking is this - a joint has only one true stiffness; therefore for a single shear joint where you put t1 or t2 into an equation should make no difference in calculating K.  Flipping the joint over, so to speak, shouldn't make a difference, it just doesn't make sense.

I challenge, with respect, those who've reported test results saying t1 should be the thinner plate to explain how they created the two different test configurations for a single shear joint (mohr?, 737?).

Now, for double shear joints this gets a bit more complicated.  Since the equation only has t1 and t2 I'd assume that the inner sheet is one thickness and the two outer sheets are assumed to have another - equal - thickness.  But the question is which is t1 and which is t2?  Looking at (what I'm accepting as the) correct form of the equation, the n term (2 for double shear) is only associated with the t2 term in the second group.  Since I'm assuming bearing is the predominant factor being calculated by those terms, it seems logical to assume the factor being doubled would be the term associated with the outer sheets (since there are two of them).  Therefore I believe t2 refers to the outer sheets, and it only makes sense to distinguish between t1 and t2 in the double shear case.

This provides a tidy explanation for the nomenclature in 737's program which refers to inner and outer; and unfortunately provides a compelling argument that using the ASTM formula is incorrect.

### RE: Huth Formula for Fastener Flexibility

let he (or she, maybe even it?) who has never made a mistake cast the 1st stone ! ...

that'd be the sign for the rest of us mortals to stone the snot out of ASTM ...

### RE: Huth Formula for Fastener Flexibility

Well said, just let me pick up this particularly heavy one.

### RE: Huth Formula for Fastener Flexibility

(OP)
Thanks for all the info. I agree that for a single shear joint that it should not matter which thickness you use for t1 or t2 because it only makes sense that there is a single compliance for the fastener, which is why I questioned this equation to begin with.  However, at this time I did not know if there was a typo in the equation or since these equations are based on testing if somehow the equation pulled from the curve required the t1 and t2 to be dependent on the thk, etc.....

Due to this discrepancy, I have just continued to utilize R&T, however, I am going to try an obtain a copy of the original Huth report in order to possibly utilize the Huth formula in the future (properly).

### RE: Huth Formula for Fastener Flexibility

T&R (which I assume is NACA TN1051) is pretty limited in its application (maybe it's enough for what you need); or is there another report with more material combinations ?

### RE: Huth Formula for Fastener Flexibility

(OP)
Tate and Rosenfeld NACA TN1051 is what I was referring to.  I don't have any other references for T&R. I have seen it referenced in other papers, but nothing that expanded upon it.  It typically meets our needs. If required we do utilize other methods which most are aware of or we will just model the joint using beam elements.

### RE: Huth Formula for Fastener Flexibility

The Huth formula it’s not the only way to get fasteners stiffness, there are also some different approaches to the problems with different results also.

-Swift (Douglas)
-Tate & Rosenfeld
-Huth, Schwarmann (Airbus)
-Vought
-Grumman
-Delft University

Which one gives the right answer? That’s the question

Take a look to the attached document to see the details of every formula (I hoppe it works)

Veneno

### RE: Huth Formula for Fastener Flexibility

nveneno:

They all give the right answer, at least for the data they were based upon. Thats the key really. So the method you should use is the one that is agreed with the powers that be.

### RE: Huth Formula for Fastener Flexibility

yeah, there's no "correct" formula, taking the "legalistic" interpretation that one is "right" and all the others are (by default) "wrong".

there are an enormous number of varibles that affect different fastener geometries differently, and each author has assumed the shape of the interaction and which factors are going to be most significant.  if you look at the different solutions they work in contradictory ways and give wildly different results; at best each matches a set of data and one or another is preferred by whoever is looking over your work (as 40818 says, "the powers that be").

i think the important point is that whichever formula you use the results doesn't change in a really significant way.  if you have the time use a couple of formulas, see how the results vary ... if it is something that is really critical and you're getting questionable results, i'd then suggest a test.

### RE: Huth Formula for Fastener Flexibility

Hi, thanks 40818 & Rb1957

A few years ago, in my internship, I made some test in Nastran simulating fasteners joining two sheets, with RBE (rigid elements), CBUSH (6 dof springs), CBAR (beam elements), and CFAST (connector elements with 6dof springs), I also use different model to get the fasteners stiffness (only for CBUSH & CFAST).

In general terms, the stresses in the shell are quite similar in every model, but the stress in the surrounding areas of the fastener and the loads carried by the fasteners itself varies widely. I didn’t make any experimental test to validate the model

So that’s why I ask again, which one gives the right result?

veneno

### RE: Huth Formula for Fastener Flexibility

all and none ... each has been matched to a specific set of data (so each gives the correct answer for a limited set of geometry) but none successfully account for all the variables in the design (so there is at least some designs for each formula where the fastener model doesn't work).

i have modelled joints with CELAST springs; i chose the douglas model 'cause it was conveniently cloe to hand, and was happy in my work ...  i'm not going to say that the douglas model is superior to the others, but it is an industry standard so it has some "street cred."; any of the other standard models would have worked out equally well.

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