Tensile capacity/minimum engagement 8

[RMPE]

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?

 

[CoryPad]

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.

F[sub]max,nut[/sub] = &[ignore]tau[/ignore]; &[ignore]middot[/ignore]; A[sub]shear,nut[/sub] &[ignore]middot[/ignore]; C1 &[ignore]middot[/ignore]; C3

where

F[sub]max,nut[/sub] is the maximum force the nut can withstand

&[ignore]tau[/ignore]; is the nut material shear strength

A[sub]shear,nut[/sub] is the nut shear area
A[sub]shear,nut[/sub] = (&[ignore]pi[/ignore]; d m[sub]eff[/sub])/P &[ignore]middot[/ignore]; [P/2 + (d - D[sub]2[/sub])/&[ignore]radic[/ignore];3]

&[ignore]pi[/ignore]; = 3.141 592 654

d is the thread major diameter

P is the thread pitch

m[sub]eff[/sub] is the thread engagement length

D[sub]2[/sub] 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

 

[vonlueke]

RMPE: Full capacity of the bolt itself, if adequate thread engagement length is supplied, is bolt tensile stress sigma equal to S[sub]ty[/sub] on bolt tensile stress area A[sub]ts[/sub], where S[sub]ty[/sub] = bolt material tensile yield strength. (This assumes your above FS is FS against yield.)

Bolt tensile stress sigma = max(FS P[sub]t[/sub], U P[sub]i[/sub] + FS C P[sub]t[/sub])/A[sub]ts[/sub]; the parameters here are defined in thread725-34325. Once sigma is obtained, axial thread shear stress is tau = sigma*A[sub]ts[/sub]/(A[sub]shear,nut[/sub] 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 S[sub]sy[/sub].) Thread shear stress level R = tau/S[sub]sy[/sub], where S[sub]sy[/sub] = 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 P[sub]i[/sub] often plays a major role in thread shear stress on tapped holes in weak material (unless joint gapping occurs).

 

[vonlueke]

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.

 

[CoryPad]

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.

 

[vonlueke]

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.

 

[morbark]

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!

 

[TVP]

morbark,

No, the second part is not under the numerator. The units for A[sub]shear,nut[/sub] are mm[sup]2[/sup], so just working through the units will prove that the first part is supposed to be multiplied by the second part.

 

[CoryPad]

TVP is right: &[ignore]pi[/ignore]; d m[sub]eff[/sub] is numerator, P is denominator, and everything in square brackets is numerator.

 

[morbark]

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.

 

[CoryPad]

morbark,

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

 

[morbark]

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

 

[morbark]

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?

 

[Metalguy]

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.

 

[morbark]

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

 

[Metalguy]

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).

 

[Metalguy]

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.

 

[morbark]

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.

 

[peteswift]

corypad

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

 

[hrehman7]

Height of the nut.