How to analyze thin-walled structures subjected to complex static loadings?

[andradesilva]

Hi,

I am working in a company as a R&D engineer. I will work on a new project that will involve analyzing thin-walled structures, such as girders and open cross section beams.

These beams with be subjected to compound (coupled) mechanical loadings. I would like to know what is the procedure for analyzing complex loading analysis in case of Thin-Walled structures. I am looking for the classical analytical procedure, not some recent innovation, as I need to study the classic references first.


Thanks in advance,
Best regards,
Andrade Silva

 

[JStephen]

Refer to Timoshenko's Theory of Plates and Shells and also to Roark's Formulas For Stress and Strain.
If there's enough time and money involved, you'd probably be looking at finite element analysis in a lot of cases.
If not, you're generally looking at some very approximate solutions from Roark. Your plate shape won't match his, or your boundary conditions will be different, etc.
If it's a one-off item, it will oftentimes be cheaper to reinforce or stiffen it than to show that the reinforcing or stiffening are not required.
It might be quicker and easier to build a sample and test it than to analyze it.
If the beams in question are circular/tubular, there are also resources available from the pressure-vessel field for analyzing nozzle loads, etc.

 

[Sparweb]

Bruhn, Analysis and Design of Flight Vehicle Structures.
It is definitely a "classic reference", being last printed in 1973.
For many combined load cases, you can simply read values from a chart.

Also, look up Flabel's textbook, Practical Stress Analysis, meant somewhat as an improvement on Bruhn's.

You may be unable to avoid stress concentrations at holes, penetrations, cut-outs. Then look for Peterson's Stress Concentration Factors.

STF

 

[GregLocock]

Back when we were validating FEA vs actual test results and hand calcs for cars (a process that created many red faces) Bruhn and Roark were the go-to refs.



Cheers

Greg Locock


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[MJCronin]

In my opinion, analysis of multiple thin-walled structures is the crossing point where you want to use FEA and NOT rely on classical "cook-book" solutions.

For structures that could undergo several modes of bucking failure, FEA is a the only reliable tool.

Simply because project management does not want to pay for the expertise or for the FEA program itself, does not mean that it is the proper choice.

Time proven programs such as ANSYS have provided correct answers for decades ....

MJCronin
Sr. Process Engineer

 

[WARose]

Not sure what the dimensions/shapes are for these "girders and open cross section beams".....but if they have the right ratios, you might be able to use AISC's steel manual. (See Table B4.1 (p.16.1-16) in the 13th edition for applicable shapes and limiting thickness ratios.) If they fall outside the scope of AISC, that is: we are talking about a shell type shapes.....ASME code is a good resource for allowable values. A cheaper one is 'Tubular Steel Structures: Theory and Design', by Troitsky. Put out by the Lincoln Arc Welding Foundation. (It's got bins, shells, etc.)

As far as analysis goes......any decent FEA package is good. More down to Earth: Troitsky's book is pretty good. Another real good one is the 'Pressure Vessel Design Handbook', by Bednar. I've used it a bunch of times to figure stresses from point loads on the sides of cylindrical, shell structures.

A word to the wise: be careful what you use as a allowable for a shell type structure. (I.e. make sure it is code or something that takes into account a good safety factor.) These types of structures can have their allowable load governed by initial imperfections which can drive the allowable down to a tiny fraction of the (theoretical) ultimate value. It's not like Euler or Lateral Torisonal Buckling where the safety factor (built into the code) is about 2.

I especially point this out because if you wind up using a FEA package.....I've seen a lot of people just run with a raw buckling value it spits out.....and that isn't right.

 

[CWB1]

Agreed with MJCronin. Outside of academia why would you want to use an antiquated, slow, and much less accurate method?

 

[EngineerTex]

FEA is unquestionably the most accurate system that can be used in stress analysis for most any application.

It is also the one that is 100% guaranteed to be used incorrectly by someone who is not supremely knowledgeable about what answers he should be getting.

Probably a good idea to have a solid understanding of the classical analytical approach, instead of having a secretary pulling double duty as a data entry clerk for the FEA system.

Engineering is not the science behind building. It is the science behind not building.

 

[Sparweb]

For all the FEA boosters who have replied touting the accuracy and speed of the method, may I respectfully ask if you have ever embarked on a validation of the results?
That process is decidedly not quick, has a learning curve just as steep as the arcane software does, and I have seen the red faces (per Greg's comment) myself.

One great thing about test data developed in the 1960's is that the materials they used for their tests had flaws, too. So for many reasons like this one, I respect the OP's request, and won't divert it in a direction they clearly don't want to go.

STF

 

[GregLocock]

Incidentally for several years the biggest part of my job was to perform experimental modal analysis on various things that people built FEMs of. We then had the fun task of correlating them. If you've learned FEA in uni and think that you can build a pretty mean model, see how well it replicates the real modal performance of the structure. I have been asked to check the clock rate of my analyser because a million dollar (back when a million dollars was a million dollars) FEA study was so far out in predicting the frequency of the FIRST mode (never mind all the others). I did so with glee.

Cheers

Greg Locock


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[CWB1]

I've done quite a lot of FEA validation building standard models and other tools for less-capable and non-engineering folks to use, designing safety critical components, and often analyzing parts with only a couple percent FoS. JME but I've seen just as many issues with validation as I have the model itself, and am usually the guy tasked to figure out where the disconnect is. Usually its a case of someone in either inspection or the lab deciding "good e-nuff" though they often will not want to admit it.

To each their own goals, but I am somewhat different in that I recommend less experienced engineers run the FEA first then very cautiously approach classical mechanics as verification. Personally I have always found that the visual nature of FEA allows folks to understand the trends and basic mechanics of their problem much better.