Minimum screw thread engagement to support weight?

[piforyou]

TL;DR Summary

I’m trying to mathematically show what the minimum number of threads needed to support a certain weight is.

Hello All,
I know there are rules of thumb and thread engagement calculators online but I am trying to find mathematically what the minimum number of threads acceptable would be.

I currently have an eyebolt that will be torqued to a specific value. This eyebolt setup will then need to lift a specific weight.

How can I show that the number of threads of engagement that I have in my setup is acceptable?

I know the material and properties of the bolt, plate the bolt is threading into, the torque that the eye bolt will be tightened to, and the weight of the system. I also know how many threads of engagement I currently have.

I’ve struggled to find online a good example of what I am trying to solve for.

 

[Baluncore]

Welcome to PF.

You will need to find the minimum OD of the thread on the bolt, and the maximum ID of the thread in the nut. The difference of those two will give you twice the contact width, (because those measurements are diameters, not radii). Multiply that by the circumference of the contact and by the number of turns. You will then need to identify the materials used and the shear strength of that material.

If this computation is being used to design for a real situation where something might fall, you must use the appropriate code, as we cannot help you.

 

[piforyou]

Thanks @Baluncore. Does the torque and preload from this affect the calculation at all?

 

[Baluncore]

Does the torque and preload from this affect the calculation at all?

Everything depends on the details, which you have not provided. If you torque the eyebolt against a flange or nut, then as you load the eye, you will stretch the eye-end of the bolt, until it is under the same tension as the threaded section. At that point, both sections will stretch together, so the eyebolt flange or nut will begin to lift away. It will no longer be locked. Do not over-torque the thread.

 

[Baluncore]

https://roymech.org/Useful_Tables/Screws/Thread_Calcs.html

 

[Lnewqban]

... I’ve struggled to find online a good example of what I am trying to solve for.

Please, see:
https://www.omniamfg.com/mechanical...ate-fastener-minimum-thread-engagement-length

When estimating a safety factor, consider vibrations and cycling loads, which will tend to lose the connection over time.
Also important is the quality and machining tolerance of the threads: loose fit tend to overload a few threads only.

The bending load on the plate and any associated welding may be the weakest point, rather than the threads of the eye bolt.
During many years, I have seen several steel plates bend and break its welds to a stronger base when under serious loads.

 

[cherish]

Welcome to PF.

You will need to find the minimum OD of the thread on the bolt, and the maximum ID of the thread in the nut. The difference of those two will give you twice the contact width, (because those measurements are diameters, not radii). Multiply that by the circumference of the contact and by the number of turns. You will then need to identify the materials used and the shear strength of that material.

If this computation is being used to design for a real situation where something might fall, you must use the appropriate code, as we cannot help you.

Hi @Baluncore,

Does the area you mentioned is used for calculating the surface contact pressure of the mating area between threads?
One of the approach I have seen is checking the thread using beam theory. Then we check equivalent stresss of the thread which includes shear & bending. I will compare against the approach in the link you and @Lnewqban sent to see how much is the different...

 

[Baluncore]

Does the area you mentioned is used for calculating the surface contact pressure of the mating area between threads?

It is the area of the flanks of the thread that are in contact.

Bolt tension applies a diagonal pressure from the tooth flank, into the body of the bolt or nut. The direction of the pressure is at 30° to the axis for UN or Metric threads that have a 60° profile. Since the force is applied near the tip of the thread, failure of the tooth will be by shear.

A bolt should fail in tension before the thread is stripped. The failure in tension will probably be near the shank, at the first turn of thread that is cut to full depth.

 

[Lnewqban]

 

[cherish]

Thanks @Lnewqban,

I found a picture and a case study on the "beam theory":

https://www.researchgate.net/publication/285462605_Loading_and_Contact_Stress_Analysis_on_the_Thread_Teeth_in_Tubing_and_Casing_Premium_Threaded_Connection/link/618bfe4107be5f31b76386eb/download

But not find reference source from a book yet...

 

[Tom.G]

Try looking in MACHINERY'S HANDBOOK, Industrial Press Inc., New York.
The section on BOLTS, SCREWS, NUTS, AND WASHERS has 2 pages of explanation and formulae that likely answers you question.

The 23rd Revised Edition (circa 1988) has it on pgs. 1278-1279.

Cheers,
Tom

 

[cherish]

Just checked for an example of thread M20x2.5 & thread engagement depth 20mm, axial force 100 kN, approach in post #6 has equivalent stress 158 MPa while beam theory is 189 MPa, about 20% higher.