Calculating Allen Screw Diameter with Parallel Load

[ara_anandv]

Hi,

Please help me in solving this problem.
I need to calculate the dia of the Allen screw.

I have an assembly (2 parts).
Hydraulic fluid is passing thru the drilled hole.
I need to calculate the dia of the Allen screw (for fastening 2 plates).
The load is acting parallel to the fluids flow.

If the load is acting vertically I know the calculation to get the dia of the Allen screw.
In this case the load is parallel.


If the load is vertical the total load is divided be the number of bolts, which gives the load acting on each bolt, from that cross sectional area is calculated and from the Area dia of the bolt is calculated.

But in this case I load acting is parallel. the load acting is 3286N
Please guide me in solving this problem

Thanks

 

[FredGarvin]

I think you are calling an allen head something other than what I am used to. Are you possibly referring to a socket head cap screw?

In regards to your question, what stress is there other than normal or tensile stresses?

 

[ara_anandv]

yes.its a socket head cap screw.

In regards to your question, what stress is there other than normal or tensile stresses?
Please expalin this?

 

[Q_Goest]

I believe Fred is asking if you have any loads on the screws other than the loads created by fluid pressure.

Assuming the only loads are due to fluid pressure, you'll need to identify the seal used to contain the pressure. There is no seal I can see in this picture. An O-ring would work nicely.

Let's assume you add an O-ring. The fluid pressure is then acting on the two halves at this O-ring. Calculate the separating force by multiplying the maximum pressure times the area (usually, I use the OD of the O-ring gland to calculate area just to be conservative). This is the load which must be resisted by the bolts. For the sake of simplicity, let's assume the pressure is the same in both the ports and this pressure is equal to the maximum pressure.

Knowing the load, and that the part is symetrical, the load can be equally distributed among the four screws. The screws have a tensile area which is equal to the area of a circle at the thread root. So if a 1/4" bolt has a 0.195" thread root diameter, you use that diameter to determine tensile stress area for the bolt.

Now you need to determine some allowable stress on this bolt. ASME code gives it, or you could just put a safety factor on the tensile strength of the material and use that. For example, a 100,000 psi ultimate tensile strength fastener with a 4 to 1 safety factore would give you an allowable stress of 25,000 psi.

Now calculate the size of the bolt needed by dividing the hydraulic force by the number of bolts and the force on each bolt by the tensile area. The stress calculated should not exceed the allowable stress for your bolt.

There's a bit more that really needs to go into this unfortunately. If you're using a gasket, the clamping load required is generally a few times higher than the load estimated by using an O-ring. Also, you need to calculate a torque, and you don't want the torque to create a load exactly equal to the separating load. For an O-ring, I'd suggest doubling or at least adding 50% to the load created by the pressure and then applying the above rules. For gaskets, you need to understand what load is required to make an effective seal, then apply a torque which will ensure that this load is met regardless of variations in thread friction - which can be substantial.

This is an abreviated outline of what needs to be done, so feel free to ask more questions and perhaps others can chime in as well.

 

[FredGarvin]

I believe Fred is asking if you have any loads on the screws other than the loads created by fluid pressure.

That's what I was wondering. I should have been more clear with my question.

This is the second time we've seen this part. I believe we recommended that you get some kind of face seal around those ports. They will never seal in the configuration you have it in unless you put in some kind of transfer tubes. You'll probably want two more bolts along the vertical centerline. If that drawing is 1:1, I think you'll have sealing issues due to the plate flexing if the pressure is high enough. As a first pass rule of thumb, I like to make the distance between bolts in a joint between

Nice post Q. That pretty much nailed it. I guess the only thing the poster needs to understand is the concept of preloading a joint and the induced stresses due to the initial tightening.

 

[ara_anandv]

I believe Fred is asking if you have any loads on the screws other than the loads created by fluid pressure.

Assuming the only loads are due to fluid pressure, you'll need to identify the seal used to contain the pressure. There is no seal I can see in this picture. An O-ring would work nicely.

Let's assume you add an O-ring. The fluid pressure is then acting on the two halves at this O-ring. Calculate the separating force by multiplying the maximum pressure times the area (usually, I use the OD of the O-ring gland to calculate area just to be conservative). This is the load which must be resisted by the bolts. For the sake of simplicity, let's assume the pressure is the same in both the ports and this pressure is equal to the maximum pressure.

Knowing the load, and that the part is symetrical, the load can be equally distributed among the four screws. The screws have a tensile area which is equal to the area of a circle at the thread root. So if a 1/4" bolt has a 0.195" thread root diameter, you use that diameter to determine tensile stress area for the bolt.

Now you need to determine some allowable stress on this bolt. ASME code gives it, or you could just put a safety factor on the tensile strength of the material and use that. For example, a 100,000 psi ultimate tensile strength fastener with a 4 to 1 safety factore would give you an allowable stress of 25,000 psi.

Now calculate the size of the bolt needed by dividing the hydraulic force by the number of bolts and the force on each bolt by the tensile area. The stress calculated should not exceed the allowable stress for your bolt.

There's a bit more that really needs to go into this unfortunately. If you're using a gasket, the clamping load required is generally a few times higher than the load estimated by using an O-ring. Also, you need to calculate a torque, and you don't want the torque to create a load exactly equal to the separating load. For an O-ring, I'd suggest doubling or at least adding 50% to the load created by the pressure and then applying the above rules. For gaskets, you need to understand what load is required to make an effective seal, then apply a torque which will ensure that this load is met regardless of variations in thread friction - which can be substantial.

This is an abreviated outline of what needs to be done, so feel free to ask more questions and perhaps others can chime in as well.

Thank you.

Please explain the tensile stress area for the bolt.

If the load is acting vertical to the bolt we usually calculate the tensile area using the thread root diameter.
In this case the load acting is along the axis of the bolt. in this case stripping of threads take place.
My question is in this case whether we need to take the shear area.

Formula explained in the below link
http://www.engineersedge.com/thread_strength/thread_bolt_stress.htm

Please advice

 

[FredGarvin]

In a properly designed joint, the threads should not strip. The preferred mode of failure is to have the bolt shank fail. This is where the thread stress area comes into play. Thread shear tends to happen over extended periods of time due to relative motion in the joint. Shank or body failure tends to happen immediately and is very apparent.

You need to ensure that the internal threads are as strong, if not stronger than the bolt material.

 

[Q_Goest]

I'd agree with what Fred has to say here, but will add a few more things.
<edit: Hey Fred, the Engineering Guru award looks good on you! Thanks for helping out all the students on here as well as some of us 'older students' >

Attached is an excerpt from a book called "An Introduction to the Design and Behavior of Bolted Joints" by John Bickford (3'rd edition). Note that he breaks up the thread shear into:
- Nut material stronger than bolt material
- Nut material weaker than bolt material
- Nut and bolt of equal-strength materials

Also attached (4'th page) is a page from a course I took which looks at preload for a bolt. This particular equation uses coefficient of friction instead of the typical "nut factor" which is predominant. I prefer this equation over the nut factor only because the nut factor is emperically determined and covers a host of variables. Applying the coefficient of friction gives you a slightly longer equation but I feel it's a bit more flexible since you can plug in friction coefficients which are better understood IMO.

The only other information you then need is tensile stress area and thread dimensions. I deal with US threaded fasteners, so this equation is not valid for metric threads unless properly converted:
1. Minor Diam (internal thread) = D-5/(8*N*TAN(30*PI()/180))

2. Minor Diam (external thread) = D-1.226/N

These were pulled from an Excel spread sheet (example attached), so note that TAN() is in radians. Also:
D = Nominal diameter of bolt
N = Thread pitch in threads per inch

To apply the torque-preload relationship (4th page of attachment) you'll need r_t and r_n.
3. r_t =D-0.676/N (effective contact radius of threads)
4. r_n =1.2 D (effective radius of contact between the nut and joint surface)

Also attached is an example of a spreadsheet I use to calculate bolt loading. It also looks at thread shear and many other things that aren't shown on the example. I'd suggest creating a spreadsheet like this to do calculations on. It makes life a whole lot easier. You don't want to be doing bolt load calculations with a calculator for the rest of your life, and doing things on a spreadsheet like this means you can simply save the calculation in a file on your computer for future reference. All my projects have these kinds of spreadsheets used to document various engineering analysis.

If you do a spreadsheet like this, perhaps you can post it for others and so we can look it over and verify it's done right. A check on such things by having others look over your work is a great way to avoid costly mistakes in the future.

 

[FredGarvin]

<edit: Hey Fred, the Engineering Guru award looks good on you! Thanks for helping out all the students on here as well as some of us 'older students' >

Thanks Q. I still think you should have this award and not me this year. I had 2006.

Attached is an excerpt from a book called "An Introduction to the Design and Behavior of Bolted Joints" by John Bickford (3'rd edition). Note that he breaks up the thread shear into:
- Nut material stronger than bolt material
- Nut material weaker than bolt material
- Nut and bolt of equal-strength materials

Bickford is a good book. There's a lot of information in there.

Also attached (4'th page) is a page from a course I took which looks at preload for a bolt. This particular equation uses coefficient of friction instead of the typical "nut factor" which is predominant. I prefer this equation over the nut factor only because the nut factor is emperically determined and covers a host of variables. Applying the coefficient of friction gives you a slightly longer equation but I feel it's a bit more flexible since you can plug in friction coefficients which are better understood IMO.

That is very true. It's still not a very tough equation to use. The tough part to get is that the scatter in friction coefficients is so great that you can count on an uncertainty in bolt pre-load of around 35% by using the torque control method. The end user needs to check the entire range that can be run into and make sure you cover the bare minimum. Also specify that the threads and nut heads (if used) should be lubricated.

The only other information you then need is tensile stress area and thread dimensions. I deal with US threaded fasteners, so this equation is not valid for metric threads unless properly converted:
1. Minor Diam (internal thread) = D-5/(8*N*TAN(30*PI()/180))

2. Minor Diam (external thread) = D-1.226/N

These were pulled from an Excel spread sheet (example attached), so note that TAN() is in radians. Also:
D = Nominal diameter of bolt
N = Thread pitch in threads per inch

To apply the torque-preload relationship (4th page of attachment) you'll need r_t and r_n.
3. r_t =D-0.676/N (effective contact radius of threads)
4. r_n =1.2 D (effective radius of contact between the nut and joint surface)

Also attached is an example of a spreadsheet I use to calculate bolt loading. It also looks at thread shear and many other things that aren't shown on the example. I'd suggest creating a spreadsheet like this to do calculations on. It makes life a whole lot easier. You don't want to be doing bolt load calculations with a calculator for the rest of your life, and doing things on a spreadsheet like this means you can simply save the calculation in a file on your computer for future reference. All my projects have these kinds of spreadsheets used to document various engineering analysis.

If you do a spreadsheet like this, perhaps you can post it for others and so we can look it over and verify it's done right. A check on such things by having others look over your work is a great way to avoid costly mistakes in the future.

I don't think you could have made it any easier to follow. Very nice references you provided.

 

[ara_anandv]

Thank you very much
Still a small doubt persists. Please mail me a solution.
It is very important.

I have attached 2 images with this
One condition explains when the load is acting vertical to the screw axis
The other when the load is acting along the screw axis.

Vertical load
If the load is vertical we calculate the shear area by using the thread root diameter

Horizontal load
If the load is acting horizontal, how to calculate the shear area?
Whether we need to take the shear area of the threads in contact (highlighted rectangular box in the image)

or
Calculating the shear area by using the thread root diameter (as explained in the previous posts)