Bolted Joint Bending Analysis
2

Question

Bolted Joint Bending Analysis

grantmech (Mechanical)

(OP)

21 Aug 24 20:57

Hello!

I am designing a fall restraint system for one of my vibe tables and I would like to incorporate the existing geometry into my design. Specifically I am looking at using the the M56 threaded lifting points (2 per side) as thru holes for 2'' 4-1/2 UNC bolts which thread into custom mounts into which a 2'' x 2'' support post seats, retained in the mount by a quick release pin. The posts have thru holes which allows for a connecting rod to slide in/out via a quick-release pin on one end. I have attached a diagram below with more detail.

The only requirement for the system is that it "must withstand an ultimate load of 3000 lbs. applied horizontally in any direction". I have already analyzed the reactions of the custom mounts, support posts, and connecting rod. The vibe table lifting points are located on 5'' thick steel plate and all the other components are 4140 steel so the joint would be stiff.

My question is regarding the 2'' bolts - I am not sure how analyze these joints, specifically the substantial out of plane bending (~ 93,000 in-lbs.) that will be transferred to the bolts. I searched through Shigley's but couldn't find any information about a bolted joint loaded in this particular configuration. I understand that subjecting bolts to bending should be avoided but I am wondering if there is an accepted method that can be used to analyze a case like this? Specifically I would like to know:

1. How much much preload is required?
2. Is 2'' of thread engagement in the mount (purple part in diagram) sufficient?

Any guidance would be appreciated, thanks!

https://files.engineering.com/getfile.aspx?folder=109025c8-1a27-445d-9a24-d

mfgenggear (Aerospace) · Answer 1 · 2024-08-22 04:48:53

I suggest run a destructive test on an actual assembly.
I believe the test results will be far less than expected.
Just know from experience that rod will fail. Because of moment on the end.
It will take less to bend that rod, or to yield.

mfgenggear (Aerospace) · Answer 2 · 2024-08-22 04:51:43

Is there a reason not using std eye bolt for lifting.

kingnero (Mechanical) · Answer 3 · 2024-08-22 07:34:54

Basically, if your clamping preload is big enough there won't be a bending moment on the bolts. You'll only have a bending moment if the purple mount comes loose from the surface of the table. I'd start with an energy method, as the posts will also reduce the bending moment at the base due to deformation.

Stress_Eng (Aerospace) · Answer 4 · 2024-08-22 20:18:40

There are ways of calculating the amount of bending the bolt will see under an applied moment even when preload is applied. Visualise a plane at the interface between the purple mount and the table surface. Under preload, the plane will move axially and when under moment it will rotate. There will be a level of moment where gapping on one side will start.

An easier method is to assume no preload. The bolt will see both tension and compression stress, while the surface between the purple mount and the table surface will see only compression. You can assume a plane defined by a location of the neutral axis and a rotation. These two unknowns can be found by the boundary conditions that the sum of the internal load is zero and the internal moment equals the applied. Once found, the resultant stress over the bolt area can give you an axial load and a moment.

These methods are based on 1st principles. Hope they give some ideas in how to approach the problem. An example of the non-preloaded case is available, if it is considered relevant.

Stress_Eng (Aerospace) · Answer 5 · 2024-08-25 17:42:54

I found this problem interesting, so I produced an analysis template. The applied loading can consist of axial (set to zero for stated situation) and bending moment. It also allows a preload to be applied. It hasn't been checked or validated, but it may give you some ideas on how the problem could be approached by hand analysis.

https://files.engineering.com/getfile.aspx?folder=ad7cc55e-6efe-46b2-bdc0-4

mfgenggear (Aerospace) · Answer 6 · 2024-08-25 18:23:51

Stress
The issue is not the bolt in the assembly, it's the orange rod with lateral load of 3k psi. Calculate if the rod will be stiff enough to with stand the force.

mfgenggear (Aerospace) · Answer 7 · 2024-08-25 18:26:27

Stress
The 2 inch bolt will not fail.
I built fixtures with 4 equally spaced
1/2-13 soc head screws. Never had a failure.

Stress_Eng (Aerospace) · Answer 8 · 2024-08-25 20:38:08

Just a question about loading. It is said that a 3000lbf load is applied to the yellow horizontal beam. Is this load only capable of being applied at the centre of the beam, or is it capable of being applied at different positions along the beam?

mfgenggear (Aerospace) · Answer 9 · 2024-08-25 22:04:28

RE: Bolted Joint Bending Analysis

mfgenggear (Aerospace) 25 Aug 24 22:04

Op
Please draw a free body diagram

dik (Structural) · Answer 10 · 2024-08-28 03:42:47

Stress... I'll see if I can port that to SMath... thanks.

-----*****-----
So strange to see the singularity approaching while the entire planet is rapidly turning into a hellscape. -John Coates

-Dik

Stress_Eng (Aerospace) · Answer 11 · 2024-08-29 10:02:26

Dik … hope you find the template useful. The file was created in Mathcad. I would think SMath can do the same calc’s.

dik (Structural) · Answer 12 · 2024-08-29 15:47:11

Thanks...

-----*****-----
So strange to see the singularity approaching while the entire planet is rapidly turning into a hellscape. -John Coates

-Dik

mfgenggear (Aerospace) · Answer 13 · 2024-08-30 17:30:06

Stress
I believe if had strait horizontal load no issues.

Stress_Eng (Aerospace) · Answer 14 · 2024-08-30 17:47:46

mfgengger
The original post does state a horizontal load, and in any direction (assuming 360deg rotation about the vertical). If the load is applied in the middle of the horizontal beam, you could be right, as each vertical beam will take 50% of the applied. It all depends on if the applied load, when normal to the beam, is capable of being positioned at different locations along the beam, then the load split will change. As you suggested, a FBD would be useful.

Stress_Eng (Aerospace) · Answer 15 · 2024-09-06 17:39:39

Just out of curiosity, if anyone has taken a copy of the posted analysis template and generated their own version (Excel, SMath, Mathcad, etc), I would be interested to know if you were successful and if you've modified the method in some way.

mfgenggear (Aerospace) · Answer 16 · 2024-09-06 17:47:42

Stress
My friend you are well appreciated and respected. I would run it but I am retired. And not involved with real world task.

Stress_Eng (Aerospace) · Answer 17 · 2024-09-06 19:36:28

RE: Bolted Joint Bending Analysis

Stress_Eng (Aerospace) 6 Sep 24 19:36

Mfgenggear, thanks for your post.

dik (Structural) · Answer 18 · 2024-09-06 21:04:49

Quote (Just out of curiosity, if anyone has taken a copy of the posted analysis template and generated their own version (Excel, SMath, Mathcad, etc), I would be interested to know if you were successful and if you've modified the method in some way.)

I haven't gotten around to doing it yet; I'm still recovering from a serious problem.

-----*****-----
So strange to see the singularity approaching while the entire planet is rapidly turning into a hellscape. -John Coates

-Dik

Stress_Eng (Aerospace) · Answer 19 · 2024-09-07 06:20:02

RE: Bolted Joint Bending Analysis

Stress_Eng (Aerospace) 7 Sep 24 06:20

Dik, hope you have a quick recovery.

dik (Structural) · Answer 20 · 2024-09-07 14:49:48

Thanks... slow but steady.

-----*****-----
So strange to see the singularity approaching while the entire planet is rapidly turning into a hellscape. -John Coates

-Dik

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