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Join Date: Jun 2007
Posts: 72

# Calculating the root area of a bolt

07/11/2007 8:25 AM

the bolt is of type 3-3/4" - 8 UN - ASTM A354 BD

where can i also find its allowable design stress at design temperature information ?

thanks

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Anonymous Poster
#1

### Re: Calculating the root area of a bolt

07/11/2007 12:22 PM

In ASME B&P Vessel Code Section II Part D. What is the Design Temperature ?

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#2

### Re: Calculating the root area of a bolt

07/11/2007 12:38 PM

t design = 90

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#3

### Re: Calculating the root area of a bolt

07/11/2007 1:43 PM

90 F, 90 C, 90 K ? The 'root area', Forgive me but are we talking thread engagement? where is root area referenced (what code) for what application?

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#4

### Re: Calculating the root area of a bolt

07/12/2007 12:33 AM

my bad i didnt elaborate in explaining but its a T= 90 C. Forgive me but i dont understand what do you mean by thread engagement.. ( i am still new to the field of design....still doing research )

as for the application its for the hydratightening of two 32" flanges with 20 bolts of this type. obviously the flanges are WN and swivel respectively.

I have the gasket details ( i ve spent 5 hours yesterday trying to interpret how we got them and from where as they are briefly mentioned on the design calculation sheet of the supplier). i also have the flanges details and drawing.

here are a couple of codes mentioned on the design sheet:

for the design data, Code: ASME B&PV Code Section VIII - Div.2

for allowable stresses (ASME B&PV Code Section II - Part D)

for the gasket details (ASME B&PV Code Section VIII - Table 3-320.1)

as for the bolts its not mentioned which section or table but i am guessing again that the ASME B&PV Codes are used.

on the same design sheer its mentioned that the min root area per bolt = 6521.9 mm2

total root area Ab = 130438 mm2

i do know that the total area is number of bolts x min root area per bolt = 20 x 6521.9

but i did want to know how we can get the minimum root area for this bolt and how to calculate it.

let me know if you need anymore info, cause i ll be more glad to research it for you. thats all i am doing these days...research research and more research....i have a good background in construction but i am still new to the design part.

talk to you later.

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#5

### Re: Calculating the root area of a bolt

07/12/2007 4:29 AM

Dear

It is obvious now days that you have a lot of questions concerned with ASME code design, it is ok, but for you as a beginner designer, you have to read and learn the ASME code, where you can't learn every thing through CR4. There are a lot of details to be easily learned directly from the code itself.

Do u have a copy of ASME code? If yes, there are a lot of questions you will not ask for. If no, it will be very very difficult to be learned or familiarized with that code.

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#17

### Re: Calculating the root area of a bolt

02/24/2012 12:59 PM

Dear Mr. Abdel,

VERY TRUE and WELL SAID-LIKE "ROME IS NOT BUILT IN ONE DAY"

DHAYANANDHAN.S

Anonymous Poster
#6

### Re: Calculating the root area of a bolt

07/12/2007 10:19 AM

Get a copy of Machinery's Handbook.

Root area for a bolt is basic mechanical knowledge. Its calculated with root diameter of the thread. It depends on diameter, pitch and thread class. Look up spec for bolts and it'll all be there.

Pineapple

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#8

### Re: Calculating the root area of a bolt

07/12/2007 10:45 AM

At TEMA code, there is a Table D-5 at Section 9 which includes a full bolting data, from which you can locate the recommended min. bolt root area directly related to bolt size.

For example: for stud bolt size 3/4"

- No. of threads : 10 per inch

- Root area : 0.302 inch2 per bolt

- Wrench dia. : 2 1/16"

- in addition to a lot of data about its nut, spacing, ... etc.

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#7

### Re: Calculating the root area of a bolt

07/12/2007 10:45 AM

I've got to get on the bandwagon here. The best designers in the world don't necessarily know much more than any other designer with similar experience. It is a matter of knowing WHERE to get info and HOW it applies to the task at hand.

Happy apprenticeship my fellow.

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#18

### Re: Calculating the root area of a bolt

06/28/2012 3:47 AM

I appreciate ur attitude

A person with a lot of enthusiasm should not be stopped by old advices.

I myself have currently the situation of Primavera and my searches led me to here

Experience is an invaluable treasury but should find its way properly to be used by others

TY

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#9

### Re: Calculating the root area of a bolt

07/12/2007 3:27 PM

Temperatures below 100C should not affect the strength of any steel bolt. You would have to reach a high enough temperature to affect the micro-structure of the metal before that would change.

My copy of ASME B1.1-1989 (Unified Inch Screw Threads) gives the following for 3-3/4 x 8 UN, Class 2A and 3A threads, External (Bolt, not Nut) Minor (same as Root on External) maximum (Ref.) Diameter:

2A - 3.5985 inch

3A - 3.6012 inch

These are Ref. because the standard is given for Major and Pitch Diameter, from which Minor diameter could be calculated. The tolerance for the Pitch Diameter is .0090 and .0067 respectively and .0150 for both classes on the Major Diameter. The minimum minor diameter is not given, primarily because that would have little effect on fit, but we know it IS our concern for strength. Since it is such a small variance as compared to the actual diameters involved, we could get away with using the max. Minor Diameter. You should use a safety factor anyway, so we should call this close enough.

So if the Minor Diameter. d, is approx. 3.5985 inch (Class 2A is worst case), or 91.4019mm, the "root area" is A = π x (d2)/4 = 6561.5 mm2.

As compared to your minimum root area call-out of 6521.9 mm2 I would say this is pretty close, and hope that the factor of safety (2X, 3X, etc) was already figured into those numbers. If it wasn't, the minor variation in diameter is going to make no difference when the bolt lets go because of other uncontrollable factors! Even if we apply the large major diameter tolerance (.015in) to the minor diameter, and calculate 6507 mm2 for the minimum root area, we are still pretty darn close.

I think you can safely say this size bolt meets your specs (might double check on the safety factor though).

As a "sanity check", if you know the load these bolts must take and the alloy that will be used, you can check the yield strength and sheer strength of the bolts (usually in Kilo-pounds per square inch, or KSI) and see if they correlate. Hopefully the load (per bolt) will be some fraction (1/2, 1/3. etc) of the theoretical strength.

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#10

### Re: Calculating the root area of a bolt

07/13/2007 3:07 AM

The computation diameter is not the smaller diameter of the thread. It depends on the nominal diameter and on the pitch. For metric threads it is dc= d-0.9382*P.

The stress limits are given for this dimension and the area related to it.

It is preferable not to got to stresses over 0.8 Re for the grade you want to use.

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#11

### Re: Calculating the root area of a bolt

07/13/2007 10:44 AM

"The computation diameter is not the smaller diameter of the thread. It depends on the nominal diameter and on the pitch. For metric threads it is dc= d-0.9382*P."

I am not sure what you mean by this, but the weakest point of a well-made (no defects) screw or bolt WILL be the minor (or root) diameter, not the major diameter, which is generally the same as or very close to the nominal diameter. Not only does this have the smallest cross-section to give strength and resist deformation (necking) under tensile stress, but it also has a concave corner which is a likely spot for crack formation and propagation.

In internal threads (nut or tapped hole) you are unlike to find failure if the same or stronger material as the screw or bolt is used. This is because the smaller screw is more likely to fail first. However, if the hole material is much weaker or brittle (potential for cracking is very high), failure will likely be at the major (or internal root) diameter, since that has the concavity where a crack is likely to start.

In a very ductile material failure of an internal thread could begin by deformation of the first point where the external thread makes contact, usually somewhere between the minor diameter and the pitch diameter, most likely closer to the pitch diameter. However, milliseconds later, as all the load gets transferred to and becomes concentrated on the remaining portion of the internal thread, there would be a catastrophic failure as well, usually resulting in "stripped threads" in the hole, with surrounding material remaining intact. In a worst case, cracks propagating from the thread will remove a portion of the material surrounding the hole as well.

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#12

### Re: Calculating the root area of a bolt

07/25/2007 9:33 AM

I thought an example will make things clear. If you look at the failure you will notice that the minor diameter is not the origin of the crack. The crack starts at 20 to 30° from the plane with the minor diameter. Your error is to consider the problem as plane when it is a 3 dimensional one. If you look in all books dealing with stress concentration you will notice that the maximal values are not at the minimal section. I hope this way i shall help you to look at such problems in a way more adapted to reality.

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#13

### Re: Calculating the root area of a bolt

07/25/2007 10:24 AM

"I thought an example will make things clear. If you look at the failure you will notice that the minor diameter is not the origin of the crack. The crack starts at 20 to 30° from the plane with the minor diameter. Your error is to consider the problem as plane when it is a 3 dimensional one. If you look in all books dealing with stress concentration you will notice that the maximal values are not at the minimal section. I hope this way i shall help you to look at such problems in a way more adapted to reality."

I cannot quite agree with you. Yes, the problem is three dimensional, not two-dimensional. The screw thread is very complex, due its helical nature and unusual profile. Using the minor diameter is a way of simplifying the problem for a "worst case" scenario, not a statistically accurate "most case" scenario. I do not believe that there is an acceptable, even though statistically very small, failure rate. I hope this way I shall help YOU to look at such problems in a way more adapted to reality.

Failure mode can be a combination of sheer and axial stress and so could quite easily happen on the slope of the thread profile rather than at its root, however, depending on the sharpness of the tooling cutting or forming the thread, you could also have a stress concentrator directly at the root, at the transformation point between root and slope. This actually appears to be the case in the photo you present as evidence when I enlarged it. Even if the crack started "at 20 to 30° from the plane with the minor diameter" as you say, it still appears to be very near the minor diameter, rather than the major diameter, or even the pitch diameter.

It also depends on whether you consider failure to be fracture, or permanent deformation, which occurs first, as evidenced by the necking down of the screw thread below the fracture (on the side away from the nut). This type of failure could cause an unacceptable leak without any fracture whatsoever.

I did not commit an error, but an approximation. If you wish to call that an error, be my guest, but I think that you are picking nits here, which just might make you, at best, a nit-picker, and at worst, a nit-wit! <grin> Or is it the other way around?

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#14

### Re: Calculating the root area of a bolt

08/21/2007 5:29 AM

It is very interesting to look at your comment. In fact the dc vaue was determined by many research and analysis made by many persons it is not my idea but of course all other people are wrong and you are the only one to be right. I agree with you: you are the best and nobody else can reach your level. Be glad and selfsatisfied.

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#15

### Re: Calculating the root area of a bolt

03/13/2008 6:29 AM

Were you absent when they taught this in machine design (college) under machine elements/fasteners?

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#16

### Re: Calculating the root area of a bolt

12/09/2009 12:02 AM

the bolt is of type 3-3/4" - 8 UN - ASTM A354 BD

where can i also find its allowable design stress at design temperature information ?

thanks

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