## Pre-FEA Hand Calculation Methodology

## Pre-FEA Hand Calculation Methodology

(OP)

Hi.

I want to figure out a methodology for reliable hand calculations prior to any FEA analysis. I'm having a hard time try to limit what falls under 'hand calculations' as there always exist a complex, semi-empirical equation in a reference book or research article. I'm training, so there's a long way to go before getting actual jobs.

Below is a fictitious thin walled mixing vessel, fabricated from 12 gauge, SA240. The vessel must sustain 45" WC vacuum, or roughly 1.6 psi.

Here's the model:

My method would be as follows:

1. Check the shell for stress

2. Check torispherical vessel/dome head stresses from Roark's

3. Use Omer Blodgett and figure out the weld stresses at all nozzle-shell joints using thrust forces

4. Check the stresses/max deflection transition section from Timoshenko/Roark's

5. Check the bending stresses and deflection of a combination of stiffeners and flat sheets on the transition section

6. On sections of least stress, figure out the location of two lifting lugs

I'd appreciate any constructive suggestions, advise, insults, jeers, ridicule, sneers and taunts. Better safe than sorry.

Thank you.

I want to figure out a methodology for reliable hand calculations prior to any FEA analysis. I'm having a hard time try to limit what falls under 'hand calculations' as there always exist a complex, semi-empirical equation in a reference book or research article. I'm training, so there's a long way to go before getting actual jobs.

Below is a fictitious thin walled mixing vessel, fabricated from 12 gauge, SA240. The vessel must sustain 45" WC vacuum, or roughly 1.6 psi.

Here's the model:

My method would be as follows:

1. Check the shell for stress

2. Check torispherical vessel/dome head stresses from Roark's

3. Use Omer Blodgett and figure out the weld stresses at all nozzle-shell joints using thrust forces

4. Check the stresses/max deflection transition section from Timoshenko/Roark's

5. Check the bending stresses and deflection of a combination of stiffeners and flat sheets on the transition section

6. On sections of least stress, figure out the location of two lifting lugs

I'd appreciate any constructive suggestions, advise, insults, jeers, ridicule, sneers and taunts. Better safe than sorry.

Thank you.

## RE: Pre-FEA Hand Calculation Methodology

Since the vessel is under external pressure, what are the essential, simplified buckling stability checks for the model?

Thank you again.

## RE: Pre-FEA Hand Calculation Methodology

How do I know whether the formula used from codes/handbooks etc. are suitable for my analysis?

Thank you again.

## RE: Pre-FEA Hand Calculation Methodology

TLDR: https://www.amazon.com/Analysis-Design-Flight-Vehi... plus roark

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

## RE: Pre-FEA Hand Calculation Methodology

## RE: Pre-FEA Hand Calculation Methodology

You do calculations done by any method because there is something important that you do not know, but that you are able to work out somehow. Someone may have to review this afterwards?

I do calculations by hand either because the FEA cannot extract the information I want, because I don't have convenient access to FEA, or because I want a sanity check on FEA results. I run FEA because the problem is difficult to solve by hand, and because I want a sanity check on hand calculations.

When you finish your calculations, what will you do with them? Do you study them, make design decisions, and relegate the calculations to a design folder? Has someone challenged the safety of your design and demanded calculations they can review? Are you justifying a design decision to management?

Perhaps there is a hand-calculation methodology that reliably produces safe results!

--

JHG

## RE: Pre-FEA Hand Calculation Methodology

To elaborate further and get some clarity, I'm considering just the transition from the vessel.

How would I idealize or break down a hand calculation (since its not a standard shape) for this part for external pressure and axial loading? Is there a thought process that deems certain calculations as absolutely necessary prior to FEA?

## RE: Pre-FEA Hand Calculation Methodology

I am not a pressure vessels guy. If this were my problem, I would probably tell management to take it to someone who analyses pressure vessels.

How do you think your vessel will fail? Those large wall areas will buckle under the pressure at some point. Axial force on that bottom flange will fail in buckling too.

--

JHG

## RE: Pre-FEA Hand Calculation Methodology

## RE: Pre-FEA Hand Calculation Methodology

If so, no need for Bruhn just yet (it doesn't look like semi-monocoque which is most of the content in bruhn). Try one of your solid mechanics texts from university. The hand internal loads methods in bruhn can be just as complex and fraught as FEM.

With FE validation, break the problem down into several Fe models of increasing complexity, so that you can understand by hand calc or otherwise the incremental change between each model. The simplest model you should be able to validate against a hand calc.

## RE: Pre-FEA Hand Calculation Methodology

A hand calculation from Bruhn is another method of approximation for problems that are complex. With FEA, we are trying to validate one approximation with another within 5 to 10% error? Therein lies my confusion. What happens when simple models from Burhn's/Roark's may not be the best way forward? How do you break a complex problem down to something that could be close to an exact solution?

## RE: Pre-FEA Hand Calculation Methodology

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

## RE: Pre-FEA Hand Calculation Methodology

https://enterfea.com/web-under-local-loads-hand-ca...

https://enterfea.com/web-under-local-loads-linear-...

https://enterfea.com/web-under-local-loads-nonline...

- Rob Campbell, PE

[link Practical Precision]practicalprecision.com[/link]: Precision and optomechanical design resources and services.

## RE: Pre-FEA Hand Calculation Methodology

It's a closed volume, subject to a pressure differential across the wall, which you expect to fail due to said pressure differential.

That, my friend, is a pressure vessel whether it's sole purpose of existence is to contain pressure or not.

I make this point not to disagree with you for the fun of it- but to point out that if the failure you expect is due to pressure (and not due to something else like localized mechanical stress from a lift point or whatever) then the methods usually used to analyze pressure vessels will be instructive to you.

Short of going back to first principles and doing a great deal of high level math to develop your own model, using simplified mathematical models (whether you get them from Roark's or not) is your only real option.

Prior to the advent of computers, this is exactly what was done, and still is done when the situation warrants it. You have to accept the fact that an approximation is all you are going to get; you're never going to hand calc a model that will yield exact, precise results without a loooooong time (months, perhaps years, either way impractical) modeling, testing, adjusting the model with test results, and modeling again.

With that said, break your assembly into components. If a side of your component looks vaguely like a supported triangular plate, well, Roark's has an answer for that. Calculate, sanity check, extract information needed to simply model whatever that triangular plate touches (edge forces or moments, etc) and move on until you have a complete set of information, or until you are close enough to complete to meet your needs.

## RE: Pre-FEA Hand Calculation Methodology

## RE: Pre-FEA Hand Calculation Methodology

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

## RE: Pre-FEA Hand Calculation Methodology

## RE: Pre-FEA Hand Calculation Methodology

## RE: Pre-FEA Hand Calculation Methodology

Guys doing FEA of stuff like this every day would validate their software against a simpler model (which could be quickly sanity checked by hand) and then run a few iterations of models, increasing in complication; each stage would be given a hard look to make sure results were tracking a reasonable trend, until they finally reached whatever level of detail was required.

Guys who do this all the time also know the limitations of the models they build and test, and are good at clearly communicating those limitations to make sure the uninitiated don't misinterpret published results.

Nothing about this process is simple, or particularly fast.

## RE: Pre-FEA Hand Calculation Methodology

A professor from my graduate courses reminded me that maybe we could hypothetically create a mathematical relationship to describe the stress in some abstract geometry by traditional PDE relationships, but as you might know if you took a course in PDE's, you get to a point where we simply have no tools to evaluate certain identities. Only a few simple cases are able to actually be evaluated. The way to deal with this is to create numerical approximations. These methods might be found in the finite difference method or finite element methods (or some other abstract ones that live in the math/physics world). The FEA programs we use are only a graphical user interface of the numerical approximation methods that allow you (the user) to have input. If you get a chance to look at ANSYS's theory books, you will find that they are many thousands of pages long and written by PHD's in the field.

Your only recourse at this point is to either rely on professional code like ASME (which is based in both theory and observation), or to create a physical test to validate your results.

If neither of those are available to you then you might want to walk yourself through your model to check every single assumption you made to see if it makes sense for your application (especially contact definition and material property) and then you will need to trust that you got a 'reasonable approximation' based on what you supplied to your program.

I'm not old enough to remember design work before software but I think you might recognize that 'abstract geometries' were probably not load bearing (at least in a significant way) for this reason prior to say the 1940's or so.

## RE: Pre-FEA Hand Calculation Methodology

Oh they were, they just had massive factors of safety. That's called architecture.

Greg Locock