Statically indeterminate problem? 8

[Drej]

I'm analysing a hollow cylindrical (shell) structure using FEA. The cylinder is supported along its length at several (15) equally spaced points and a 1g 'vertical' load applied to obtain the 'vertical' reaction forces at the constraint points. These reaction forces are used to obtain the mass distribution of the structure.

I'm well aware that this method is only approximate at best wrt determining the mass distribution. However, a member of my stress team keeps bleating on about how this problem cannot be solved by FEA because it is statically indeterminate.

Any thoughts?


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[ishvaaag]

FEM that I know is used to solve both statically determinate and indeterminate systems. Other thing is that the setup of the model (particularly, non realistic constraints) and the charting/reporting abilities of the program may difficult to ascertain some particularly targeted magnitudes.

 

[Qshake]

From a distant perspective, I presume you're looking for how much mass is distributed to each of the fifteen supports.

That said, if the cylinder is modeled as a beam element or some higher element wherein the program is using as input the second moment of inertia, the area, in at least 2 directions and the program is capable of using the stiffness method, I don't see how the statically indeterminacy has any impact.

One could use old multi support reaction diagrams and realized that the interior reactions will approach 1.0wL where w is the distributed load and L is the span length. The exterior reactions will approach 0.5wL.

This is simplified so I hope I've not missed the point.

Regards,
Qshake

Eng-Tips Forums:Real Solutions for Real Problems Really Quick.

 

[rb1957]

"bleating" is entirely (IMHO) the right term ... of course FEA solves indeterminant problems. but if i understand your problem right, it makes sense if there is a rseriously skewed (non-uniform) distribution on the "beam". if it's uniform then i'd've thought the 13 inner supports each react 1/14 of the load and the outer 2 1/28 ... if it's slightly non-uniform, let each support react the load applied within 1/2 a pitch either side of the support.

hopefuly you can silence the "bleating"

 

[Stillerz]

I thought FEA was for indeterminate systems.

 

[EdR]

Recommend to the member of your stress team that he read up on FEM...There are many books and articles available...

...Then pay absolutely no attention to anything else he may say about FEM........(and maybe about structures!!!)

Ed.R.

 

[Drej]

Cheers for the replies.

I'm rapidly losing my patience with this guy at work, particularly since he doesn't support his 'thinking' with an argument of any substance (unless of course 'nothing' counts).

That said, yes, I'm looking into different methods of obtaining each 'section' mass using this method, and the more I look, the more variables seem to pop up and bite me. Someone in the office told me the old nugget that "we've been using this method for years" but I looked at some sensitivities and found some fairly big discrepancies in the RFs.

@rb1957, you're quite right - if the mass/CoG of the structure is entirely uniform at each section, then the reaction forces (RFs) reliably give the section masses (but not at the ends like you say).

My problem involves a structure with sections of (i) different mass and (ii) CoGs which do not occur at the centre of each section. If you constrain only a few nodes at each section (instead of the whole ring of the shell at each section), the RFs become 'skewed' - this replicates a condition where you have a low-rated spring supporting a relatively much stiffer structure. In this extreme case, the RFs across the structure become uniform. You have to hold the entire section to obtain the 'correct' RF and hence the correct mass. But even doing this, the method falls over big time when you have a non-uniform structure.

Gah!


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[cntw1953]

I have some trouble to understand your intend, so I could be way off the base.

In general, FEM is used to collect support reactions and internal forces induced by varies forms of distributed weight (w,p), and/or force (F,M), on a "stable" system that is either structurally determinate, or indeterminate. The system stability is achieved through varies degree of restraints, the restrains then would affect and determine how the applied weight/forces are distributed to the supports.

For example:
A) Uniformly loaded one span beam, R1 = R2 = wL/2
B) Uniformly loaded three span beam, R1 & R4 (outer supports) = 0.4 WL, R2 & R3 (int. supports) = 1.1 WL
C) Uniformly loaded four span beam, R1 & R4 (outer supports) = 0.393 WL, R2 & R4 (supports adj to outer supports) = 1.143 WL, R3 (center support) = 0.928 WL

Does your mass distribution vary with degree of restraints?
I doubt it is the case. For your case, assume equal span L between two supports in any system (1, 2,...n span), the mass on outer support may always be 0.5 mL, and interior supports always be 1.0 mL (m = mass). If this is what you need, why use FEM?

 

[crisb]

Why not use the programe to work out the mass and CG of each section? It may even be easier than the approximate method.

 

[rb1957]

maybe a web RBE3s joining the masses (?) to the reaction points ??

 

[dhengr]

I’m siding with the bleater, while he may not know exactly how to express his position, that often happens when you have the blind leading the blind. The reactions are not all 1g, and if you are not working on a dynamic problem, get rid of the g and mass; the reactions are not all 1.0(wl) either. He is correct, because this is an indeterminate structure. And, we knew this long before you could get your hands on a FEA program. Several people have given you very good approximations for the various reactions on this indeterminate beam, assuming equal span lengths and uniform loading. That “These reaction forces are used to obtain the mass distribution of the structure.,” seems absolutely bass-acwards to me. In most structure’s, hear on earth, the weight () distribution of the structure and any superimposed loads dictates the reaction forces.

Seems like FEA programs and computers have made for some really dangerous engineering going on in the world these days. Someone who doesn’t understand how his FEA program works, its limitations and restrictions on its use, or how to model the problem he is trying to address, can plug a bunch of number in, and out pops some numbers, called answers or solutions, which no one seems to know quite how to interpret, and that’s called engineering these days. A FEA program does not an engioneer make. In fact, it scares the hell out of me, I could be standing under one of those structure some day when it fails.

Then we have this new phenomenon where we get together, in community or committee or as a team; communicate like hell and come up with a real democratic, politically correct, solution to the engineering problem. And, even if nobody on the team really knows how to get to the correct solution to the problem, it must still be better by committee, if we communicate long enough and hard enough, we can come up with a pretty good, although mostly wrong, solution to the problem. No matter how many people on the team think 2 + 2 might equal 5; and we even took a vote and 5 won; that won’t often be the correct answer, even though it is quite democratic.

You really need a local mentor for these types of questions, and he/she should know more about the subject than you do, so they can offer constructive, and correct, guidance. Together, you are both looking at the same drawings, specs. and initial data, and that person can get you started in the right directions, ask you leading questions, and tell you when you are getting off track. When you guys ask your questions on these forums, you rarely give enough info. for a meaningful response, we can’t see the drawings, the problem isn’t well defined, so you often get a bunch of fairly good best-guess answers, which would probably be helpful if you knew what parts to pick out of them for your particular use. But, given the fact that you don’t understand your own problem very well, it is unlikely that you will pick out the important, applicable, nuggets from the many answers. This forum is probably not the best place to be instructing people in the first few courses in strength of materials, theory of elasticity, structural design and analysis, or basic design in any of the building materials. They should go to college for that, get an engineering degree or a technicians degree, so they can truly start to comprehend the significant parts of the engineering problem they are looking at. And, this forum is not the right place to develop a basic understanding of the use of a FEA program either, nor will that program compensate for lack of basic engineering understanding of the problem.

I believe that the respondents genuinely want to be helpful, but as often as not they can’t, they don’t see the whole picture and can only give half answers, which might then be misused. It seems to me that at times, we are perpetuating, tolerating, condoning or encouraging, people who have no business doing engineering, to pretend they are engineers. Worse yet, they may be designing something which could really be dangerous, and hurt someone. “We’ve been using this method for years” might be a good answer here, particularly if none of them, whatever THEY are, have failed in the past. Because, there isn’t much evidence that this forum exchange is really leading to a better more accurate solution to whatever the problem is.

 

[40818]

I think maybe a picture would help here, as i'm struggling to see the reluctance to use a pencil and bit of paper to come up with a pretty good load distribution....

Even accounting for varying sections along the length etc, this would seem a simple problem.

Have you any other info to help make yourself clearer if the problem is in fact different from the simple one i'm seeing in my head?

 

[johnhors]

dhengr,

That's probably the best post I have ever seen!

http://www.Roshaz.com

 

[paddingtongreen]

Telling the truth isn't bleating. I can't tell if this is a dynamic or a static problem. dhengr and one or two others have explained so I won't.

I'll just say that consensus support of a wrong answer doesn't make it correct.

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[Drej]

After reading that, I feel like I've just been in a washing machine all night on the spin cycle.

Sermons and irrelevant blurting aside, this is a perfectly reasonable approach at approximating the mass distribution for this type of structure, given we have an understanding of its limitations.

"In most structure's, hear [sic] on earth, the weight () [sic] distribution of the structure and any superimposed loads dictates the reaction forces."

Exactly. Hence, why it is entirely reasonable to do the reverse. From the reaction forces we can approximate - in some cases get the exact - mass distribution for a given structure, given an understanding of the structure and the assumptions of the mathematical model we use. It's what engineers do - here's an equation: we use it to find an unknown, given some knowns and then use the equation again to find another unknown given some knowns. It's mathematics. Pure and simple.

Amen.



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[rowingengineer]

dhengr,
good to see you have got up to speed with this forum posting. I think you have hit on a few very good points, I agree with everything but the last line. If there was a post of the year i think you would go close to getting it.

Arguing with an engineer is like wrestling with a pig in mud. After a while you realize that they like it

 

[Qshake]

dhengr - You've noted some points well but mostly seem to pontificate (vent?) on the system as a whole.

Best of luck to you and I hope no one poops in your Luck Charms tomorrow.

Regards,
Qshake

Eng-Tips Forums:Real Solutions for Real Problems Really Quick.

 

[Drej]

Consider a model of a uniform mass soda can with its ends removed, such that we assume a long, hollow, thin-walled cylinder. Consider this to be 10m long and 1m in diameter, and supported all around its ends and at 1m equal-spaced points in the same way, such that we have a ring of supports along its length at equal-spaced locations.

Apply a 1g body acceleration to the structure perpendicular to its 10m length (let's call this a vertical 1g load). Let's assume that each 1m long section of the can has a mass of 10kg. From simple statics, the sum of the vertical reaction forces at each support location will give the following in terms of the mass acting at that point:

MassRF (ends) = 10/2
MassRF (mid-points) = 10

Hence, the mass distribution is:

5,10,10,10.....,5

From this simple case we can find the section masses easily. This is similar to the problem I am working on.


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[cntw1953]

Are those results agree with FEM?

 

[Drej]

Yes - the analyses were undertaken using FE.


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