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Tensile capacity/minimum engagement
8

Tensile capacity/minimum engagement

Tensile capacity/minimum engagement

(OP)
Need to find the tensile capacity of a bolt in a tapped hole condition.  

Lifting a tank that has 6-3/8" tapped holes about 3/8" deep.  Tank flange is Cu-Ni and weighs about 5,000 lbs.  Considering FS of 2 on lift and additional 20% for prying action on bolt heads.  Therefore I need a 2,000 capacity per bolt (looking at A307 or Grade 5 if available).  We have a lifting lug (1" thick plate) that will be bolted to the flange via the six bolts.

How much thread engagement do I need for full capacity of the bolt (assuming steel base material)?

Can I calculate the reduced capacity if less than optimal thread engagement?

How do I determine capacity of connection based on shear strength of actual base material?

RE: Tensile capacity/minimum engagement

6
A good rule of thumb for steel/steel fasteners is to use an engagement length equal to the screw major diameter.
 
For exact calculations, you can use the methods developed in VDI 2230 Systematic Calculation of Bolted Joints, available at:
 
http://www.beuth.de
 
I can distill the entire treatment to get you in the right direction.
 
Fmax,nut = τ · Ashear,nut · C1 · C3
 
where
 
Fmax,nut is the maximum force the nut can withstand
 
τ is the nut material shear strength
 
Ashear,nut is the nut shear area
Ashear,nut = (π d meff)/P · [P/2 + (d - D2)/√3]

π = 3.141 592 654
 
d is the thread major diameter
 
P is the thread pitch
 
meff is the thread engagement length
 
D2 is the nut pitch diameter
 
C1 is a nut dilation factor - you can use 0.91
 
C3 is a nut thread bending factor - you can use 0.897

RE: Tensile capacity/minimum engagement

RMPE:  Full capacity of the bolt itself, if adequate thread engagement length is supplied, is bolt tensile stress sigma equal to Sty on bolt tensile stress area Ats, where Sty = bolt material tensile yield strength.  (This assumes your above FS is FS against yield.)

Bolt tensile stress sigma = max(FS Pt, U Pi + FS C Pt)/Ats; the parameters here are defined in Thread725-34325.  Once sigma is obtained, axial thread shear stress is tau = sigma*Ats/(Ashear,nut C1 C2), where the denominator here comes from CoryPad's post.  (My tau is not to be confused with CoryPad's Greek tau, which I'll call Ssy.)  Thread shear stress level R = tau/Ssy, where Ssy = nut or tapped material shear yield strength.  If R > 100%, the analysis indicates tapped hole is overstressed w.r.t. thread shear (stripping) yield stress.

Note from the above that bolt installation preload Pi often plays a major role in thread shear stress on tapped holes in weak material (unless joint gapping occurs).

RE: Tensile capacity/minimum engagement

CoryPad:  Wouldn't nut dilation factor C1 = 1.0 here?  For tapped holes, we have no nut, hence (generally) no nut thin wall allowing internal thread dilation.  (An exception would be tapped holes in sleeves.)  Thanks for your excellent post.

RE: Tensile capacity/minimum engagement

vonluecke,

C1 could be 1.0 if the hole is surrounded by a relatively large amount of material.  If the hole is in a boss, then it depends on the hole size vs. boss outer diameter.  Considering the information in the original post, I would agree with you that C1 = 1.0 is accurate.  Good catch, and thanks for the compliment.

RE: Tensile capacity/minimum engagement

Correction:  "C2" in my first post should be "C3."

Usability note:  Greek characters in CoryPad's first post, above, are nonportable.  E.g., they show up in IE5 for PC and Macintosh, but do not show up correctly in Netscape 4.78 for PC and Macintosh and possibly other browsers and platforms.  For those who can't read his formula, "& radic;3" means sqrt(3); i.e., 3^0.5.

CoryPad, good point regarding bosses.  Thanks.

RE: Tensile capacity/minimum engagement

Corypad...could you please clarify the equation for A shear,nut.  I'm wondering if the second half w/ (P/2 + (d-D2) etc etc is under the numerator of n*d*m...or what.  Please help.  I'm trying to use this equation to determine if a 8" dia nut w/ 1 3/4" of thread engagement is stonger than eight 1" dia.
Thanks!

RE: Tensile capacity/minimum engagement

morbark,

No, the second part is not under the numerator.  The units for Ashear,nut are mm2, so just working through the units will prove that the first part is supposed to be multiplied by the second part.

RE: Tensile capacity/minimum engagement

TVP is right:  π d meff is numerator, P is denominator, and everything in square brackets is numerator.

RE: Tensile capacity/minimum engagement

TVP...or square inches (for those of us still working in English units!).  Thanks guys, I'll do another attempt and see if I can make more sense this time.

RE: Tensile capacity/minimum engagement

morbark,

If you are using inch-based fasteners, remember that pitch is the inverse of threads per inch.

RE: Tensile capacity/minimum engagement

Yea...I know, but thanks for the reminder.  It's a common problem here.

RE: Tensile capacity/minimum engagement

Just for clarification...shear strength, T, is AKA Yield Strength???
I have data on UTS, Tensile Yield, Bulk Modulus, & Shear Modulus...I'm getting confused.
Which is the number I'm looking for?

RE: Tensile capacity/minimum engagement

You can use about 60% of the UTS for the shear strength.  BUT, you have to know what your UTS REALLY is, and not just an OD surface hardness measurement.

RE: Tensile capacity/minimum engagement

I'm using the UTS given by our material supplier.  Maybe I should be including a 'fudge factor' into this number.

RE: Tensile capacity/minimum engagement

Did the supplier furnish an actual CMTR, or just a surface hardness measurement?  While not impossible, the numbers you have reported don't match up well with the particular steels you have.  8620 is usually case-hardened, and while it CAN go to Rc45 or so full-thickness, it would probably have to be drastically quenched in your size (1 1/2" dia. IIRC).

RE: Tensile capacity/minimum engagement

Ok, just rechecked your numbers.  You have 1" dia. 8620 rods, so they probably HT something a little bigger.  But 8620 in 1" dia. quenched in oil only goes to ~Rc28-30 or so.  Ask your supplier how they quenched the rods-if they used water/polymer/brine you *could* have the Rc45-46 clear thru that you reported.  Since your proposed design WILL need to be stressed thru the full dia., you need to know what you ACTUALLY have.

RE: Tensile capacity/minimum engagement

I think you're probably right.  I doubt the rod is fully hardened through.  We need the outside to be hardened b/c of its abusive environment.
Also, the rod is actually 2 1/2" OD (furthering the arguement that it's not going to be 45RC all the way thru), and the bolt I'm proposing to use in the end of it is the 1" dia.

RE: Tensile capacity/minimum engagement

corypad

For VDI 2230 is meff the length of the thread along the helix or the height of the nut?

RE: Tensile capacity/minimum engagement

Height of the nut.

RE: Tensile capacity/minimum engagement

peteSwift,

hrehman7 is correct - meff is the axial length/height of the internal threads that are engaged with the external threads.



Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

RE: Tensile capacity/minimum engagement

CoryPad,
Per 'Handbook of Bolts & Bolted Joints, Bickford/Nassar, pg 175', Length of threads in a 90 deg countersink contributes 40% of shear strength. How does meff takes this into account? Is this c’sink depth added to clamp length lk or thread engagement meff? I could not find any treatment of c’sink (c’fer) on tapped holes in VDI 2230 latest edition. VDI also added 0.8P to meff. Any comments on this?
Many Thanks

RE: Tensile capacity/minimum engagement

hrehman,

meff does not account for countersinks.  The nut height m = meff + x, where x is the length of countersinks, etc.  VDI 2230 February 2003 edition does not show this, rather it references Alexander [48] on page 86.  This is the same source on page 175 of Bickford & Nassar.

Regarding the additional 0.8 P, they added it with research from 1995.  I have not seen the source, but my understanding is that the 0.8 P accounts for the non-uniform axial force distribution in helical threads.  I am trying to get some of the new references from the journal Konstruktion that are shown in VDI 2230, but the publisher won't return my email messages.  If I learn more, I will share it.



Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

RE: Tensile capacity/minimum engagement

CoryPad,

This 0,8xp gave me a lot of truble; I don't know if you remember but I brought this up a while ago and you were kind enough to point me in the right direction. However, at the time you left this detail out and my preliminary calculations didn't consider it. Later, when I got the February edition of VDI 2230 I included the 0,8xp into my calculations and that on itself made me change the bolts grade.

As I said before, there is not much information on the load distribution over the engagement threads, but I think they introduced it not because of this but because the first and the last threads, being incomplete, may not take much load.

I think it is important and I would be grateful if you would share the info you may get on this, I will do the same if I find any, should you be interested.

Thank you again,

Dulmant.

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