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Calculating stresses in object with circular pattern

Calculating stresses in object with circular pattern

Calculating stresses in object with circular pattern

(OP)
This is the top view of the object:
The parts that are cut out are actually plain bearings with a pin in them. The drawing is just for specifying the pattern (120° apart).
These 3 pins are used to hold the object in place with respect to another object (so the pins are connecting the 2).

A moment (3D) and a force (3D) are acting in the center of the circle (due to something else that is attached to it).
Now I need to calculate the stresses in the earlier specified pins, but because this is a circular object where the pins are positioned in a circular pattern, I don't know how to do this.

Can anyone help me?

RE: Calculating stresses in object with circular pattern

(OP)
Something went wrong with the image. Here is the direct link: Link

RE: Calculating stresses in object with circular pattern

So you have 3x pins (of unknown diameter) inserted (how far, over what type of bearing surface ? ) into 3x counterbored (?) smooth holes (or threaded holes?) at 120 degrees apart symmetrically into a flat disk (?) of unknown thickness (or a sphere ?) with a single central axle (?) holding the disk (?) against gravity (?) or against some additional radial and axial forces (?) on the disk that is (or is not ?) restrained against movement (or rotation ?) by the "hole" and its recesses (?)

Are the 3x pins closely fitted, sliding fit, or threaded, or loose fit - That will also determine how the stresses (if any) are "leveraged" against the outside of the pin and then onto the inside of the smooth holes/threaded holes and then through the disk into the central axle.

Define your problem from the textbook. Good news is: once defined (FEA perhaps ?) then it is symmetric, so you don't have to do it three times.

RE: Calculating stresses in object with circular pattern

(OP)
Thank you for your answer.

I see that I haven't given enough details, but to me it was all about the principle of the calculation I have to apply. The numerical details are not important.
It is a flat disk, on which a moment and force are situated in the center of the top plane of the disk. In fact, this moment and this force result from an object that is attached to the top plane of the disk, but as an approximation this has been reduced to a moment and force in the center. This "box" on top can vibrate which causes the moment and force in the center of the disk (approximation). This is a simple picture of it: Link
The 3 pins are closely fitted.

RE: Calculating stresses in object with circular pattern

I'll give it a shot. So you want to find the loading on the pins?

Figure out the distance 'r' of the plane of the pin from the center. And the shear load due to the moment is F1 = M/(3r).

And the shear force due to you vertical load 'P' is F2 = P/3.

Maybe I misunderstood your question. Let me know.

RE: Calculating stresses in object with circular pattern

(OP)

Renderu, I don't think it is that simple. I think I have to calculate the reaction forces on the pins, and then calculate the stresses. But the problem is that I don't really know if this is hyperstatic or not..

RE: Calculating stresses in object with circular pattern

It will be up to you to decide if shear is a good representation of the stresses in those pins. They seem large with respect to the disc, and maybe FEA is warranted. For multiple bolt/pins like this, I may assume that only two are taking up the loading.

RE: Calculating stresses in object with circular pattern

(OP)
Why do you assume that only 2 pins take up the loading?
I do indeed think that shear stresses are most important.

RE: Calculating stresses in object with circular pattern

That's commonly done. Not all pins can act at the same time. For example, if one of your pin was off tolerance by a very small amount, the other pins would take more loading, or maybe even most of the loading.

RE: Calculating stresses in object with circular pattern

(OP)
Okay I get it. Would that mean that factor 3, in the equations for the shear stress you earlier specified, becomes a factor 1 (worst case)?

RE: Calculating stresses in object with circular pattern

It would be 2 for two pins. Again, I'm not sure this is the best approach. It's just a possible way to approach it. This does not replace the normal safety factor either.

Note that shear force F1 and F2 are not in the same direction, but I'd add them directly for simplicity.

RE: Calculating stresses in object with circular pattern

Leonimus:
Hyperstatic... that’s such a nice new important sounding engineering term. I would assume that you have to divide that by the Mach number at std. atmosphere, before you torqueify the mass density of the flat disk. Would you please explain the origin and meaning of that word?

Hyperethetically, I think you problem is a least several times indeterminate. First, you haven’t done a good engineering job of explaining your problem and your sketches leave so much to be desired in furthering this cause. All those loads, load directions, dimensions, etc. really confuse the explanation. Despite all our technological advancements we still can’t see what you are imagining if you can’t do a few good sketches to show what you’re thinking. Secondly, it is very difficult to tolerance, manufacture and fit three pins so they really share equally in any type of loading. So your problem is indeterminate to the extend that one or two of the pins, and/or holes around them will have to yield a bit to bring them all into play. And, you probably don’t know for sure that the loads are perfectly centered either, and then randomly vibrating too. These kinds of problems require as much engineering judgement as they do exact calculation. Loads/3 = pin load; then multiply by 1.5 for pin design load for the pin shear, bending and bearing stresses and for hole bearing stresses. Or, maybe not.

RE: Calculating stresses in object with circular pattern

(OP)
@renderu: Thank you for your help.

@dhengr: In my language we use a certain word for "statically indeterminate", and being too hurried I translated it in the wrong way, leading to hyperstatic. I'm sorry for the confusion.
Anyhow, I have attached a sketch of the situation in the following link:
Forces and moments are acting on the inner disk. The pins are used to keep the inner and outer disk connected. Now I need to calculate the stresses those pins will have to endure.
I hope this somewhat explains the situation.

Thanks for all the responses.

RE: Calculating stresses in object with circular pattern

Leonimus:
I was partly pulling your leg, but do you know what hyperstatic really means? I don’t, please enlighten me. I believe I have heard it used to mean statically indeterminate, mostly by M.Es. I think it is a bit pretentious.

That certainly is a better sketch. I guess that is about what I thought you had in mind, but show it so you don’t make us guess at what you mean. Show some dimensions and approx. loads too. I’m not talking about +/- .0001" or 1 pound, but you would be surprised at how reasonably accurate proportions, approx. sizes and loads, etc. influence how an experienced engineer might approach a problem. Are you talking about an 8" dia. ring or a 3' dia. ring? That makes a difference in how you might approach the problem. The proportions btwn. the ring dimensions and the pin dia. may be important, which will fail first, which do you want to fail first? How is the ring supported, or how and what does it transmit its loading to? Why 3 pins and not 4 or 8? Are the pins just driven shear pins or are they threaded at some point?

What is the tolerance btwn. the O.D. of the inner disk and the I.D. of the outer ring, so you can make a judgement about pin bending, or the pin only being in shear at that faying surface. Pin bearing on the hole will be an important consideration. Can you match drill or bore the holes through the ring and into the disk all in one set-up? This significantly improves the hole alignment and tolerance. Maybe you want to use a light shrink fit for the pins to tighten them in the holes. How do you remove the pins, or don’t you need to? The pins don’t need to be nearly as long as you show them, in proportion to their dia.

RE: Calculating stresses in object with circular pattern

Leonimus, coming back to your original question.
Your problem is not "hyperstatic" or statically indeterminate (dhengr: that is the term we use in neo-latin languages, not really pretentious...). As almost anyone knows, a chair with three legs is determinate, one with four is not.
The distribution is (lever arms for moments are not difficult to figure out):
Fx and Mx: left pin 0, right pins 1/2 each
Fy and My: left pin 1/2, right pins 1/4 each
Fz and Mz: all pins 1/3 each

prex
http://www.xcalcs.com : Online engineering calculations
http://www.megamag.it : Magnetic brakes and launchers for fun rides
http://www.levitans.com : Air bearing pads

RE: Calculating stresses in object with circular pattern

(OP)
dhengr: Hyperstatic does indeed mean statically indeterminate.

About the loads and dimensions:
The maximum force will be about 15kN in all 3 directions. These forces however can change in size and direction quickly because of the vibrations of the object on top of the disk. The moment will be about 5kNm in 2 directions (say x and y), while it will be neglegible in the 3rd direction (z). These directions however can also change.
The diameter of the outer ring will be about 15". Thickness t is about 2 to 3".

The load is attached to the inner disk (on top of it) and the pins are connecting the inner disk and outer ring ("ground"). This connection may not fail in any way. The pins have to be removed at a particular time, however it is not yet clear how. The pins are just shear driven.

It is safe to assume the pins will only be in shear.
It is indeed possible to bore the holes through ring and disk in one set-up.


prex: That's clear, thank you.

RE: Calculating stresses in object with circular pattern

would it be reasonable to assume that the pins react shear only ? for example, Fx is reacted by two pins (the pin aligned to the the x- direction would be ineffective). i think you should be able to solve each of the 6 loads separately and superimpose.

is this a practical problem (so we can be reasonable) or a theoretical problem (ie school) ?

Quando Omni Flunkus Moritati

RE: Calculating stresses in object with circular pattern

(OP)
rb1957: This is a practical problem.
It is indeed reasonable to assume that the pins react to shear only.

RE: Calculating stresses in object with circular pattern

so doesn't that provide a simple solution ?

two pins react Fx, with an in-plane shear of Fx on both,
three pins react Fz, with an out-of-plane shear of Fz/3 on each,
...

you're looking for the pin loads at the R4 circle ?

Quando Omni Flunkus Moritati

RE: Calculating stresses in object with circular pattern

(OP)
rb1957, do you mean the circle with radius r1 on the above sketch? I am looking for the stresses on the pin at the intersection between the inner disk and the outer ring.

Thanks for all the help.

RE: Calculating stresses in object with circular pattern

yes

Quando Omni Flunkus Moritati

RE: Calculating stresses in object with circular pattern

(OP)
Alright, I have found the forces on the pins.
Now I need to find the bending and shearing due to these forces in the gap between the inner disk and the outer ring. Let's just assume the gap is large enough to consider bending as well.

On the side of the outer ring, the pin has a fixed support. However, I don't know how to treat the connection at the inner disk.
The disk will rotate/translate due to the forces. Because the pin must have 0° angular deformation right outside of the hole in the disk and the disk has rotated/translated, I don't know how to treat this.

Can anyone help me?


(If it is not clear what I mean, then I will post a sketch later today)

RE: Calculating stresses in object with circular pattern

I don't think it's clear enough to get a proper response.

RE: Calculating stresses in object with circular pattern

(OP)
For now I can't make a sketch yet, but I'll try to explain for now.

Consider one pin, but only the section between the inner disk and the ring (they are not completely connected) (which will be very small, if not negligible).
The pin has a fixed support in the outer ring and also in the disk. The disk, however, can rotate or so due to the forces and moments that act on it. Now if I'm correct, I need to find the reaction forces in these supports to find the bending and shearing stresses. How do I do this? Or am I wrong? And what would be the right approach then?

If it's still not clear, then I will post a sketch in about three hours.

RE: Calculating stresses in object with circular pattern

If I understand correctly.... You already figured out the total shear in your pin. I think you want the bending due to the small gap. The way I would probably do it is assume one end fixed and the other pinned as a worse case. You now have all the info you need to find the bending moment. It will be your shear force times your gap dimension (assuming it is fixed exactly at the ring face).

RE: Calculating stresses in object with circular pattern

(OP)
Isn't it necessary to treat this as statically indeterminate, and then calculate the forces and deformation with FEA or another method? Or am I making this way too complicated?

RE: Calculating stresses in object with circular pattern

Just because it is statically indeterminate doesn't mean you need FEA.

RE: Calculating stresses in object with circular pattern

"Hyper", from the Greek for "beyond". Hence a "hyperstatic" structure is one that is beyond being able to be solved by statics alone. The word was a standard part of the engineering vocabulary when I was a student (in Australia in the late 1960s).

I only mention this because this is the second thread in a month in which the word has been used correctly then later queried.

RE: Calculating stresses in object with circular pattern

(OP)
Renderu, I see that I was a bit too fast concluding that.

In a previous post you said the bending moment will be the shear force times the gap dimension. Is it just that simple?

RE: Calculating stresses in object with circular pattern

As I understand your problem, it could be that simple. But I don't understand the tolerances therefore you need to evaluate as the designer. Maybe the real lenght for bending is longer than the gap. Mind the gap (I loved my trip to the UK).

RE: Calculating stresses in object with circular pattern

(OP)
By gap length I actually meant the real length for bending.

RE: Calculating stresses in object with circular pattern

By gap length I actually meant the real length for bending.


The real length for bending is not a known condition of bending. I'm not sure what you mean.

RE: Calculating stresses in object with circular pattern

1) how are you assemblying this ? ie you can't easily install the 3 pins as shown. which suggests the pins retract/extend away from the interface, which suggests a sliding fit ... possibly not a fixed support.

2) as you say, consider a pin ... as a free body. you've calc'd the shear load to be reacted on the interface, yes? ... now how does the pin react this load ? how does the disc apply this load to the pin ? ...
a) if there's a tight fit, then the pin will behave like a socket, with a distributed reaction. this also means there'd be a distributed load into the pin, building up the shear at the interface, yes?
b) if there's a loose fit, then the pin will be loaded by a point force (at the interface, where the pin bears against the disc) and there'll be two point loads to react this. i suspect that the pin will bend against the inner disc and the reaction here will sum to the applied load, so the interface reaction is larger than your calc'd interface load.

@denial ... i didn't encounter the term in my school (UNSW) in the 70s, i agree the word is correct (both parts, hyper- and -static, have greek roots) just that we have a perfectly adeqiate phrase (statically indeterminate) ... just my 2c

Quando Omni Flunkus Moritati

RE: Calculating stresses in object with circular pattern

Leonimus, disregard my last comment. I was tired and I don't know why I wrote that.

RE: Calculating stresses in object with circular pattern

re-reading, i wonder what is meant by "The parts that are cut out are actually plain bearings with a pin in them" ...

Quando Omni Flunkus Moritati

RE: Calculating stresses in object with circular pattern

(OP)
rb1957: The pins will be installed by sliding them into the holes (with a bearing).
I think it will be a tight fit (not sure about the meaning "tight" and "loose" tbh).

RE: Calculating stresses in object with circular pattern

"sliding them" probably means a sliding fit. unless you install frozen, then pins would be freeze fit.

the difference is how the pins react to transverse load ... freeze fit would act like a socket and react with a distributed load (and less bending), sliding fit would probablu cock in the hole bearing against the hole wall at two points (on opposite sies, yes?) ... more bending.

i imagine you'll line drill the hole in both parts (to make sure they align).

Quando Omni Flunkus Moritati

RE: Calculating stresses in object with circular pattern

(OP)
It is indeed a sliding fit. To calculate the bending, what do I have to pay attention to?

RE: Calculating stresses in object with circular pattern

the length, the distance between contact points ... envision a curved pin in a (slightly) bigger hole ... notice the inner disc will rotate (slightly) so that the outer body bears on one side of the pin and the inner disc bears on the other, so that the holes are (slightly) mis-aligned ... yes?

Quando Omni Flunkus Moritati

RE: Calculating stresses in object with circular pattern

(OP)
Yes that is what I understood.

Would it be acceptable to neglect this rotation and look at the movement of the inner disk as a pure translation? Otherwise I'm not sure how to calculate the bending.

RE: Calculating stresses in object with circular pattern

i'd calc the loads on the pins from your nominal geoemtry, and then look at the pins in detail, in isolation

Quando Omni Flunkus Moritati

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