Forces on Rotating Member

[mechie17]

As part of a valve analysis I am looking at a swinging disc arm. I have not done an analysis like this for a while so I am using a previous calc (not done by me) as a guide. The portion I am looking at right now considers the bending moment acting on the arm as a function of distance from the pivot caused by the inertia of the arm (it's a pretty big valve). I have a number of reactions while looking at this. First, the original calculator (the person, not the program) defines the bending moment at X as "the moment caused by that portion of the arm to the right of x" (where the pivot is to the left of x). At first this makes sense because if you are considering inertia the more of the bulk of the arm involved the higher it should be. But then, this also means that at X=0 the moment is highest which seems counter-intuitive. This is complicated further (at least in my head) by the fact that the pivot is at the lower corner of the arm as opposed to being located along the central axis. So my questions is this:

How do I consider inertial moment as a function of distance from the pivot when the pivot is offset from the members central axis?

Please explain what this means physically as it is somehow eluding me.

 

[desertfox]

Hi mechie17

Might I suggest you post a picture, you know clearly in your mind what your describing but unfortunately we don't.

desertfox

 

[zekeman]

Please state the dynamic conditions and the engineering requirement.

For example, a torque is delivered to the arm in order to close it in t seconds and you need to know the value of that torque and perhaps the stresses induced in the member.

Absent the conditions and requirements, we can't comment on the solution as presented.

 

[mechie17]

I apologize. I think I was having a hard time verbalizing what exactly it was I wanted to know. I will try again. Attached is a simplified diagram of my system. I have a massive beam attached at it's lower left hand corner to a pivot. The beam is held horizontal at time=0 and released, allowing it's weight to swing it downward. I have the beams mass moment of inertia and both the speed and acceleration values at the moment in time I am considering. I know then that the torque produced by this falling beam is Torque = MOI * acceleration. So I want to understand how this calculated number relates to bending moments experienced internally at the beam cross sections along the length of the beam. In other words, how do I find the bending moment due to inertial acceleration at any section in the beam? As far as the pivot location is concerned I guess I am wondering how the internal bending moments change (if they do) since the pivot is not located along the centroid which is the typical location of the neutral axis.

 

[zekeman]

First off, in all my experience I never saw the need to analyze the stresses in a structural member rotating due to its own gravity. The stresses have to be very small. So this looks like an academic problem.

Now, the original calculation you mention is essentially correct in that you sum the induced moments to the right of the x point The offset center will effectively cause the inertial loading to be oblique to the beam centerline so the shear diagram would have a sine@ factor at each segment along the beam and the orthogonal cos@ factor would cause a compressive stress in the beam.

So, if you do this classically, develop a loading diagram normal to the beam which is the inertial forces on each segment multiplied by the sine term from which you get the flexural stress
MC/I.
To this add the compressive component.

You also have the centrifugal component which will add tension in the beam, which should also be small.

 

[desertfox]

Hi mechie17

If its a valve part your analsysing isn't there more to it than an arm falling under gravity?
I can see that stresses could be induced in the arm but only if it was closed under some resistance, I can't imagine a huge valve being allowed to slam shut under gravity can you please expand on the problem some more.

desertfox

 

[mechie17]

Alright, I apologize again. I was misunderstanding the physical nature of what I was calculating. I had previously determined the force put on the arm due to the valve disc's rotation (due to a differential pressure). So what I needed to do was find the bending caused by the torque on the arm. Thank you for trying to assist me despite my lack of clarity. My issue seems to have resolved itself through the act of learning more about the question I was trying to ask.

 

[evolvingape]

Nothing wrong with wanting to learn more. My thought throughout the complicated discussion was what you were wondering about relevant. Surely the material specifications of your system come into play ? Was the massive beam made of a material that would be affected by bending stresses at the loads you were subjecting it to ? All materials have a lower limit at which no discernible change is apparent. then they move through a stage, a bending moment, at a specific rate according to "variables" and they will have a maximum tolerance point at which they will snap. It would be helpfull in future to specify the materials involved.

I am glad you have resolved your problem through thought. Indeed, it is said Nikola Tesla never began work on a project until he had every aspect fully considered and balanced. Wise words if true.