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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[Drej]

Can I just finally add that my issue is not whether this problem can be solved by FE - I have already proven this to myself by looking at this problem carefully and in great detail, and the results tie very nicely for the case described above. As my original post said, I am interested in rational, useful comments as to solving indeterminate problems using an FE approach.


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[cntw1953]

So, is it fair to say "mass distribution is based on the tributary length(s) to the sides of a support"? If as simple as this, why use FE?

 

[rapt]

Drej,

Answering your main question - yes FEM is perfectly suited to solving indetermninant structural problems. If it was determinant, why would you waste your time, you can normally do it quicker on a piece of paper as some above have suggested and get exactly the same answer.

In fact, the simple case you have suggested above (though indeterminant) would be solved by most engineers who understand simple statics on a piece of paper in 2 or 3 minutes using simple beam theory (or even quicker by looking up a simple formula in the steel designers manual or many other texts) and the answer would NOT be 5, 10, 10, 10,..., 5! It would only be the answer you have suggested if the cylinder was not continuous at each support i.e. a series of determinant cylinders.
But this solution assumes a flexural member which structural engineers deal with all of the time. Your 1m diameter cylinder with 1m spans is not a flexural member so normal plate or 2D beam elements could not be used to model it accurately in FEM. It would have to be modelled as a cylindrical shell. It would be interesting to compare the results to everyones flexural member results to see the difference.

dhengr,

I have been expressing the same views for a few years. It is worrying.

 

[ishvaaag]

Then I need to add a discordant note... yes, the forum may misguide; but also can the codes, and do. Ah, but they are based on peer review ... hey, a democratic technical desicion can be a wrong one, can't be? Then I don't see as bad to support advice on experience; most of us are structural designers that perfectly discern one structure that barely stands afoot from one that has the proper reliability and safety, so our "experience" has the qualification of both some level of understanding and actual behaviour. In short, it is long time ago that I realized that our technical tenets may be useful, that's our art, but ... true? Only in some theorical way.

Respect perpetuation of error, heavens, I know as much of some esoterical matters as on technical as to know that in such "mad" books there are diamonds of intelligence included, far more true than our technical matters. I will quote a boisterous god in Oahspe:

"I am Haoma, who distroys the Libraries to prevent the perpetuation of human errors"

That all is mathematics?... a platonic ideal world, or a real one, but not for us ... the gnostic Job:

"Where is understanding? Between the living, it is not"

 

[trainguy]

Drej,

If you want a rational, useful comment about FE, mine would be it's all about RELATIVE STIFFNESS.

Making a node a support point makes it infinitely stiff, and the structure around it is clearly not, so I tend to use springs to get closer to what I would expect in a hand calc. Then I repeat with different stiffnesses to really peg what is and what is not important.

In a statically determinate system, using springs versus a rigid support makes no difference, because statics alone are sufficient to solve for reactions.

By the way, it's indeterminate, not indeterminant.

tg

 

[cntw1953]

For anyone has interest in math expression, have a look on article linked below.

http://hyperphysics.phy-astr.gsu.edu/Hbase/cm.html#cmc

 

[Stillerz]

Best answer here is trainguy's; not the pathetic, tired rants of the others about hand calc's and real engineers.

I would have to agree that relative stiffness is the key here.

Hey, guess what, there actually are bending forces on trusses!!!
You know what else? The load distribution in some trusses wont be what your statics book tells you they will be.

It is really nice that the problems dont have member sizes on them because that can make them a little more tricky.

Try doing a hand analysis of a braced tower and then changing some of the brace sizes...your hand calc will show the same load in the brace, which is, of course, not reality....not even close to reality.

 

[Stillerz]

...or, you can construct a massive matrix and be a real engineer and do it by hand for 6 weeks,

 

[ishvaaag]

Only to note that for a system of quite variegated solicitations and initially unknown response, as in aseismic design, I think an adjudication of the masses based more in mere tributary area might be more appropiate to estimate the demand than based on the reactions, at least over the whole period of the solicitation; this because the elements will be showing different values of stiffness than for an static analysis, and even negative stiffness, so assuming that some attribution of masses in the model quite in accord with the initial reactions on the static structure should be more in error than the contrary, because that method places the masses where -relatively- we think would conceptually stay, and the other, where -relatively- are.

 

[rapt]

Stillerz,

I hope you are allowing for construction sequence in your truss analysis, rather than treating the whole trus as one completed structure, or your answers will be wrong too, possinbly by more!!

No-one is suggesting that complex structures should be analysed by hand thesedays, if a computer program can do it faster and better! But they are suggesting that the designer understand enough about statics to check the results that the computer is giving him and have enough experience to know what results to expect, or when the results look doubtful.

The example given above is not a complex structure. Its solution is relatively simple and can be done quicker and as accurately by hand.

To give an example of a complex structure that is often done by computer and whose results are significantly unconservative, consider a multistorey building with a transfer member at the bottom. Many people analyse this on an FEM program to determine the reactions the transfer member has to be designed for. But they do not allow for construction sequence, just a single complete structure. The results are way out! Yes, a hand calculation based on tributary areas is possible as inaccurate, but on the conservative side. I know which I prefer.

Just learn to believe your engineering judgement before the computer when assessing the results, if you have developed any yet!

 

[Stillerz]

I am by no means advocating the blind use of the FEM with computers. By the same token, one should not discount it's proper use.

BTW...in working the power industry for a few years (top supported boilers weighing 30,000+ kips), I am quite familiar with running analysis for construction.

 

[hemis]

Are these the results that are required. The pipe diameter plays no role other than for deflection. The results are for a unit load of 1kN per metre length of pipe with rigid supports allowing rotation.

 

[kellnerp]

Drej,

Are you trying to back out the mass distribution in this hollow cylindrical structure by measuring the reaction forces on the supports? In other words is there some type of loading that can change inside the structure like filling with a liquid or granular substance? The mass distribution for the dead load can be gotten using a 3D CAD system will little trouble.

TOP
CSWP, BSSE

http://www.engtran.com

http://www.niswug.org

"Node news is good news."

 

[ThomasH]

Hi

I'm not sure if this really adds anything to the discussion.

As far as I know FEA can solve a beam in two spans. And since that is statically indeterminate that should answer the original question.

Regards

Thomas

 

[structurallyyours]

If you are using finite element software to find the mass distribution then please ensure that supports which you have given are fixed one......... if it is pinned one then there are chances of moment distribution and changes in reaction.