My dilema in proving a theory (bending a steel tube)

[not_an_engineer]

Hey everyone !
I am trying to learn how to mathematically prove that a steel tube (with wall thickness of ~ 1mm and external diameter of ~ 15 mm) will have ...

At any point along its length, the shaft must :
1) bend in such a way that the deflection is the same regardless of how the shaft is rotated about its longitudinal axis; and
2) twist the same amount in both directions

To make this even more difficult, I propose to bend channels into the shaft with 120 degree spacing, a depth of 2 mm and a width of 2mm (channels to be placed at 60 degrees, 180 degrees, and 300 degrees.) with a length, along the longitudinal axis, of 250 mm.

My issue is that I want to be able to mathematically prove that the combined resultant forces on the shaft will effectively remain constant, regardless of shaft rotation, due to the spacing of the channels. There is no requirement that I have found that states that all points along the tube must react in the same manner to other points along its shaft, in respect to flexing, bending or twisting

My hypothesis is that since the channels are spaced at 120 degree increments, the combined resultant forces when measured in any direction will be the same relative to the channel locations, but regardless of tube rotation, and can meet the requirements set forth above. I believe that if I can establish this theory mathematically, it will prove true in physical testing as well.

Any help that can be offered is greatly appreciated.

 

[Spinnor]

Can you tell us what is the use of this shaft and why you need to add channels?

 

[JBA]

What specifically are the resultant forces (torque vs. lateral vs combined) and where and how will they be applied to the shaft?

 

[not_an_engineer]

Can you tell us what is the use of this shaft and why you need to add channels?

This may sound a bit overprotective, but I am not comfortable discussing the designed use for the shaft or the need to add the channels at this point. They are not dangerous in any way, but I still don't feel comfortable discussing that at this point. I hope this does not offend you or anyone else reading this thread. Thanks

 

[Spinnor]

This may sound a bit overprotective, but I am not comfortable discussing the designed use for the shaft or the need to add the channels at this point. They are not dangerous in any way, but I still don't feel comfortable discussing that at this point. I hope this does not offend you or anyone else reading this thread. Thanks

No problem, just curious.

 

[not_an_engineer]

What specifically are the resultant forces (torque vs. lateral vs combined) and where and how will they be applied to the shaft?

I can honestly say that I am not quite sure. As close as I can determine, I would need to be able to show through mathematical and physical testing that the characteristics of the shaft, i.e. flexing, bending and twisting, would be the same in any direction at any point along the length of the shaft, regardless of shaft orientation along the longitudinal axis. There is no evidence that I would have to prove the same characteristics between the channeled section and any unchanneled section.
I hope this didn't cause everyone to get even more confused.
Thank you for your inquiry

 

[not_an_engineer]

No problem, just curious.

I hope I didn't offend.

 

[Spinnor]

I hope I didn't offend.

Nope.

 

[JBA]

No offence taken.
Let me approach the issue from these perspectives.
1. As long as the applied forces remain in the same orientation to the centerline of the shaft there should be no reason to expect a change within what could described as a "uniform system" orientation shift. Additionally, the orientation change must also not introduce any dynamic forces if it occurs during the operational conditions of the shaft, i.e no gyroscopic or inertia effects form reorienting the rotating shaft.
2. However, if there is a gravity force component related to the shaft or any of the applied forces that will be variable due to a vertical angle orientation change in the shaft centerline or an applied force then that could present an problem even in the "uniform system".

Edited to add "inertia"