Bolt Tensile Stress Area 1

[jtowne]

I want to specify the torque on a bolt with an axially drilled thru hole. I am subtracting the thru hole area from the tensile stress area(TSA) to get a modified TSA. Traditionally I use the equation T=kFd to determine the torque. What value of "d" do I use with the modified bolt? Is it the original major diameter or is it an equivalent diameter derived from the modified TSA?

 

[JNieman]

If you assume the D is working based upon area,
Figure out what your resultant area is when you take out material for the thru-hole.
Take that area and figure out what an /equivalent/ diameter would result in that same area.
Use that.

Wait a minute.

I don't think the thru hole has the effect you think it does. I don't know why you would want to modify the torque estimation value, actually.

 

[MintJulep]

In the equation T=kFd F is the tensile force.

The relationship between torque and tensile force will be unchanged by an axial hole in the fastener.

You need to relate force to area to get stress and decide an acceptable stress in your modified bolt, then calculate the torque that results in a force that gets you that stress.

 

[jtowne]

I have reduced the force based on the reduced TSA. Based on your responses "d" is the original major diameter.

Therefore: T = k x F(allowable reduced area force) x actual major diameter.

 

[desertfox]

Hi jtowne

Forget the bolt hole, the formula T=KFd is to estimate the force in the bolt for a given torque, it as nothing to do with the bolt hole. What is important is the materials being clamped by the bolt because if their strength is less than the bolt material it will yield and this will reduce the clamping force.
I suggest you have a look at this site and if you need further help just ask.

http://www.roymech.co.uk/Useful_Tables/Screws/Preloading.html#Initial_Bolt_Tension

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

 

[rb1957]

I think the preload from torque is unaffected by a hole down the axis of the bolt.

but the tension stress in the bolt would be higher (as the area is reduced)

another day in paradise, or is paradise one day closer ?

 

[jtowne]

It is critical that the cross sectional area of the modified bolt be considered. The maximum force that the bolt can withstand is dependent on its material properties and cross sectional area. Stress = Force divided by Area. The allowable force in the modified bolt is the allowable stress times the cross sectional area. That force is then entered into T=k*F*d to get the allowable torque for that modified area. And "d" in that equation is the major diameter of the unmodified bolt.

Example: M8 Aluminum bolt: TSA = 36.6 mm^2, Sy=270 MPa. Drilled thru hole = DIA 5.2mm, A=21.2mm^2

Modified TSA = [36.6-21.2] = 15.4 mm^2.

Allowable bolt force, F = 270 N/mm^2 x 15.4 mm^2, F = 4,050 N

Allowable Torque = k x F x d, T = 0.2 x 4,050 N x 8 mm, T = 6,480 N-mm

Thank you all for your input.

 

[desertfox]

Hi Townes

Please provide the source where the area of the drilled hole is subtracted from the bolt cross sectional area because in 46 years of engineering I have never heard of this.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

 

[rb1957]

like i said ? that the bolt load due to torque is unaffected by area.

Now I don't think anyone would preload a bolt to Fty.

The question is usually posed what Torque do I need to create a desired preload? because there's a cart and a horse with this ... you set the preload from the applied loads, then figure how to create that preload (by torquing the bolt).

another day in paradise, or is paradise one day closer ?

 

[MintJulep]

Please provide the source where the area of the drilled hole is subtracted from the bolt cross sectional area

From the original post.

axially drilled thru hole

 

[jtowne]

The hole is drilled axially, not radially. I find it hard to believe you have never seen a bolt with an axially drilled thru hole. Regardless; Assume you just have just seen one. How would you advise your client? Would you state that the hole can be as large as physically possible with no impact on strength?

I understand the adjustments I need to apply such as proof stress, yield strength, combined loading, joint stiffness, etc. Do I really need to list every modifying parameter to prove that I understand this problem? Those are not germane to this discussion. All I wanted to know was what value of "d" to use in the T=kFd equation. The answer which was logically stated by MintJulep, "The relationship between torque and tensile force will be unchanged by an axial hole in the fastener." And also RB1957, "I think the preload from torque is unaffected by a hole down the axis of the bolt."

Bottom line: Allowable load on a bolt is directly linked to Tensile Stress Area. If it weren't then we'd be assembling bridges with #2 hardware.

Refute my calculations, expose the error in my logic. Assume this is only an academic problem and not one with practical application.

I just drilled a 5.2mm hole thru the center of a 6061 Aluminum M8x1.25 bolt with Sy=270MPa. What is the maximum torque that I can apply before yielding? Assume k=the universally accepted value of 0.2.

 

[desertfox]

Right now I understand the hole is through the bolt, I was thinking the bolt was going through a normal bolt hole in a component.
I have a book on something about holes in bolts I'll have a look.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

 

[MintJulep]

For completeness, I think you should check the torsional shear stress too.

Some of your tightening torque will result in torsion of the bolt during tightening. How much depends on a bunch of things.

 

[jtowne]

I'm not even going to mention that I'm machining anti-rotation flats into the threads, further reducing the TSA!

 

[desertfox]

jtowne

For completeness I thought you were subtracting the area of a standard bolt clearance hole in a component and not a hole through the bolt so I never said I hadn't seen a bolt with a hole through, I stated that in my last post if you care to read it.

Right here is a page I found regarding holes drilled in bolts however what it suggests is that the cross sectional area (minor) should not be reduced further particularly if its subject to fatigue.

https://books.google.co.uk/books?id...q=stress in a bolt with an axial hole&f=false

I guess what we don't know the stress concentration factor if the hole is straight through the bolt including the threaded diameter, the link above shows the drilled hole stopping short of the threaded area.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

 

[3DDave]

That formula is a simplification. Every place that deals with fasteners in detail suggests significant testing if the results are critical.

http://www.smartbolts.com/insights/the-nut-factor-problem/

 

[rb1957]

the only thing I question is why would you have to tell the client the maximum torque before you yyield the bolt ?

say you've substituted a hollowed out bolt for a solid one. ok, then you have to check that the applied loads (including whatever installation torque you've specified) are good for the reduced area. Preload is not (IMHO) a load that exists in isolation, so why torque the bolt to yield ?

the smart people round here will reasonably object ... bolt preload (from torque) is a function of the bolt stretch (and therefore strain and therefore stress and therefore area) ... yeah, well that's a limitation of T = kPd

another day in paradise, or is paradise one day closer ?

 

[racookpe1978]

You are mixing two problems, then almost seem to be fighting us as each different person addresses different concerns about your original problem.

1. I apologize: Several answers did address radial holes (above and below the stress zone between the bolt head and the washer-nut contact face). An axial hole is going to behave differently.

2. Preload is an external condition that must be satisfied: More specifically, preload is the force imposed ON the clamped components BY the bolt head-washer-nut squishing the clamped components. So, your design requirement is to (a) determine the preload needed for your application, THEN determine what bolt and material and diameter can satisfay your requirement. A 1/2-13 bolt can provide sufficient preload. Sometimes. A 3-4 bolt-nut combination will fail to give you enough preload. Sometimes.

Now, you are correct, the preload is provided BY the compression of the nut-washer and bolt head. But, different bolts of the same dia and material will yield (and fail to give you your needed "continued load" (not preload) because some threads were rolled and some cut. Look again also at the hole dia of the washer, washer material and deformation, material hole size and material deformation. Preload assumptions (er, calculations) DEMAND you make a lot of assumptions about the connection details. Torque is only a minor one of many. Lubrication, torqueing sequence and torque steps, the methods of applying torque and many more matter even more.

A "hollow" threaded rod WILL fail (stretch) much more than a rolled threaded and machined bolt. So, go test your assembled bolt, after making a yield calc based on the STRETCH (yield) you get for a hollow rod pulled axially of OD = 90% of the minor diameter of the bolt (because of stress risers at the tip of each thread) and ID = your inner hole.

Once you know (assume) your hollow bolt will not continue to stretch (relax under the required preloaded conditions), then you can go back to the original diameter bolt and determine the "perfect" toque required to establish that preload for a normal solid bolt under normal conditions (clean threads, lubricated properly, properly sequenced in steps, etc.)

OK, now you have a theoretical toque that will be required under ideal conditions to a normal bolt. Go back to your hollow rod model of OD = 90% threaded rod minor diamter, ID = hole diameter, and "torque" that rod. That will tell you if a perfect hollow rod can withstand the torque needed to establish the preload needed for your application. Under perfect conditions.

 

[jtowne]

Thank you 3DDave. I use the simplified equation as a first pass for design and then test as you have astutely pointed out. If my test results aren't even remotely close to that predicted then I know something is wrong. There are just too many unknowns.

 

[3DDave]

In looking more, the T = kFd is an approximation for the pure torque load applied to the nut. It makes no predictions about what happens to the fastener.