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# FEA stresses

## FEA stresses

(OP)
I am analyzing steel lifting trunnion with FEA (all 4-node plate elements). Since there are so many output stresses available I am not sure what output stress needs to be compared to what allowable? Thanks a lot.

### RE: FEA stresses

I would look at the plate surface stresses and the cross-sectional stresses first.  Not sure what software you are using, but should be able to isolate cross sectional stresses, surface stresses, torsion, etc.  The surface stresses will give you a good indication of impingement stress concentrations (for instance where a crane hook might be point loading the area of contact).  It will also show you where you might get tensile tearing around a hole.

### RE: FEA stresses

A very general method for getting a handle on the magnitude of the stresses would be to apply either Von Mises' or Tresca's hypothesis i.e. yield occurs when either:

max[|?1- ?2|, |?2- ?3|, |?3- ?1|] = Y   (Tesca)

(?1- ?2)2 + (?2- ?3)2  + (?3- ?1)2 =  2Y2   (Von Mises)

(afraid I can't get subscipts or superscripts)

where Y is the yield stress in simple tension and ?1,?2 and ?3 are the principle stresses which are the eigenvectors of the stress matrix and can be found by solving the cubic equation in ? for

?(?xx–?)        ?xy        ?xz    ?
det   ?    ?xy       (?yy–?)     ?yz    ?  = 0
?    ?xz       ?yz       (?zz–?) ?

A bit theoretical but should give you the answer you're after.

### RE: FEA stresses

Hmmm, appears that sigmas and taus don't come out very well on the web! Sorry!

### RE: FEA stresses

Don't mean to be crude, but, judging by your questions, it sounds like you are dabbling in finite elements.  This really is not a good idea.  Proper modelling and interpretation of results is not straightforward.

### RE: FEA stresses

Also unless you know what you are doing the use of 4 node plate elements will probably give you garbage for results...

Ed.r.

### RE: FEA stresses

Ed.R.:  Please elaborate on your statement.  I admit, I am not an expert on FEA, but I'm using it on a current project, with 4 node plate elements.  I thought the results were pretty straightforward, but now I have to wonder if the results are "garbage".

### RE: FEA stresses

rholder98,

Just because you are using 4 node plate elements does not mean you are able to model what you think is a plate.  You also have to know how many (and which) degrees of freedom are included in your mathmatical equations.  A four node plate may have only eight degrees of freedom, the x and y translations in-plane for example, which would never be able to model anything requiring plate bending.  If you were attempting to model a slab with these four node elements, it might look like a slab on the screen and you might get stresses in the output, but you wouldn't have a slab model and the output would be trash.

Even if you did, using the previous example again, use plate bending elements to model a slab, and you had the correct degrees of freedom, they may not have the proper boundary conditions representing the supports or whatever.  Most FE programs assume fully fixed supports unless told otherwise when you specify support nodes.  If you need a roller type support, you have to make sure and tell it which degrees of freedom are released.

But the real trick is interpreting the results.  Again, using plate elements, many softwares report the stresses at midplane unless otherwise asked for top or bottom surface.  Midplane may be OK for in-plane and max shear stresses, but are going to give you zero, literally, for the bending stress.

I recommend you talk to a colleague face-to-face to get your questions answered.  Good Luck.

### RE: FEA stresses

i'd also point out the issues with modelling a beam with a single element.  whilst some 4 noded quads can react a linear varying strain field, most are only good for constant strain, so modelling a web in bending requires several elements throught the depth of the beam to get a good picture of the strain distribution.

mind you, all this is probably in a thread somewheres

### RE: FEA stresses

I agree with jmiec and EdR.

Do not use a computer program unless you can justify your results by hand (2d modeling, 3d modeling, Finite Element Analysis, Matrix Analysis, anything and everything really)

Black box computer programs are the most dangerous thing in structurally engineering today.

### RE: FEA stresses

rholder98:

4 node plate elements can only represent a linear displacement field. This means that in order to get good results from any situation that is not linear you must mesh the problem in such a way that the actual displacement field can be approximated accurately by a linear field (and plate displacements are definitely not a linear field)....If large element sizes are used the resulting computations will not represent the actual situation, thus garbage for results....

The next question is how to know when this happens and what do you do to fix it?  I can't answer this question because the only way I know of to get these answers is through experience.

I have used linear elements for many different kinds of problem solutions for years and have achieved good results...I have also looked at many solutions which, as I said above, give garbage for results.....My assumption from your question was that you were not an experienced FEM analyst and thus probably were not aware of the meshing requirements necessary to achieve good results using linear elements....Thus I was just trying to inject a bit of caution in the intrepretation of the results (and perhaps suggest some additional checks to verify the results).

Ed.R.

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