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Plastic Neutral Axis calculation of a three segment composite section

Plastic Neutral Axis calculation of a three segment composite section

Plastic Neutral Axis calculation of a three segment composite section

(OP)
I want to calculate the plastic neutral axis of the section in the attachment (let's assume the materials are the same). I know that the areas above and below the PNA should be equal.

I want to write an excel sheet which could calculate the PNA with the dimensions entered by user. If it was sth like a T-beam, it would be easy, I think it would be enough to write the following :

"If PNA is within the flange, solve expression 1, If not, solve expression 2", and I would get the axis as a result of this If loop.

However for the case attached, I am not sure what I could do.. Should I write a more complicated if loop? Any ideas?

 

RE: Plastic Neutral Axis calculation of a three segment composite section

Assuming that these three pieces are actually connected and you just pulled them apart for the sake of showing us the three different parts, here's what I would do.

Pick one of the materials (I would go with the highest E) and "transform" the other pieces of the section to that material using n=Estiff/Epart.  Now that you have the section as a single material finding the PNA should be relatively straightforward.

RE: Plastic Neutral Axis calculation of a three segment composite section

(OP)
The three pieces are not connected though. This is a part of a beam where these pieces are connected at the supports.

When I have certain dimensions, there is no problem, I can find the PNA with several trials by hand.. But I want to write a simple code with which the location of PNA can be calculated with several inputs of dimensions.. I am not sure about the right algorithm...

RE: Plastic Neutral Axis calculation of a three segment composite section

Well, the same principal Applies if the section is composite.  How is the section acting compositely? Are these gaps between the parts short and intermittent?

RE: Plastic Neutral Axis calculation of a three segment composite section

hope the material is not concrete.

An expert is a man who has made all the mistakes which can be made in a very narrow field

RE: Plastic Neutral Axis calculation of a three segment composite section

Assuming the three parts are acting compositely (but this requires them to be connected not only at supports, otherwise you end up with three beams), then of course you'll need an if structure, just like for a T beam, but with three outcomes.
If area top flange > area web + area bottom flange
  ...PNA is in top flange
Else If  area bottom flange > area web + area top flange
  ...PNA is in bottom flange
Else
  ...PNA is between flanges
End If

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RE: Plastic Neutral Axis calculation of a three segment composite section

If only connected at the ends the pieces are simply individual pieces and not a composite member.

RE: Plastic Neutral Axis calculation of a three segment composite section

if the pieces aren't connected togther, they'll deflect as separate beams ... the two horizontal members will deflect readily (and not react much moment), and the web will react the vertical shear (and moment)

RE: Plastic Neutral Axis calculation of a three segment composite section

I think dcarr is correct.  I also don't know how you could prevent the compression flange from buckling if it isn't attached to the web.  

BA

RE: Plastic Neutral Axis calculation of a three segment composite section

@BA ... so ? ... i'd assume that only the web was effective in bending, so the "compression" flange would sustain it's initial buckling stress (in bending), like the upper flange, which would be pretty low (negligible) and the web would prevent the structure from collapsing ...
my 2c anyway  

RE: Plastic Neutral Axis calculation of a three segment composite section

@rb1957,

If the pieces are not attached to each other, the compression flange will buckle at a very low stress.  Then, the compression portion of the web will buckle at a very low stress.

The Plastic Neutral Axis calculation would have no meaning.  My 2c.

BA

RE: Plastic Neutral Axis calculation of a three segment composite section

(OP)
If the section is not composite, then the section would reach such a state shown in the 1st attachment below, right? I (scaled up the upper and lower parts' stress diagrams for the sake of demonstration)

However, in the composite case, the plastic state would be like the second attachment.

Then, doesn't this show us that the buckling of the lower part would take place earlier when the section acts composite, since a bigger portion of the element is under compression?

 

RE: Plastic Neutral Axis calculation of a three segment composite section

If the load is placed on the top member, how does it get into the other two?

BA

RE: Plastic Neutral Axis calculation of a three segment composite section

Is the member you are talking about the horizontal member of a 1 bay frame?

RE: Plastic Neutral Axis calculation of a three segment composite section

(OP)
Yes BA, the case would be this one.

RE: Plastic Neutral Axis calculation of a three segment composite section

(OP)
and yes dcarr, what I am talking about is the horizontal member..

RE: Plastic Neutral Axis calculation of a three segment composite section

(OP)
Actually BA, the shear wall can cover all parts of the horizontal member (I mean it can go up to the top part)

RE: Plastic Neutral Axis calculation of a three segment composite section

Well, perhaps I am being extra dumb today, but you have indicated that dcarr and I have both interpreted the problem correctly, yet he is talking about a horizontal member while I was talking about a vertical member.  

If my interpretation is correct, the three members act separately, each taking load according to stiffness. The contribution of the two walls normal to the applied load can be neglected as they have negligible stiffness compared to the shearwall parallel to the applied load.

If beam ABCD is extremely stiff, then wall AE will be stressed in tension, DH in compression while BCFG deflects under both bending and shear.  In any event, the concept of a Plastic Neutral Axis for the combined group has no validity.  Don't waste your time trying to write a program to calculate it.

BA

RE: Plastic Neutral Axis calculation of a three segment composite section

this is a might confusing ...

i read the 2nd pic to show a I-beam in normal bending (the top flange in tension, the bottom one in compression)

the 1st pic looks like the OP, the three elements are independent, with the stresses showing normal bending (but these couldn't develop as the horizontal flanges are too flexible)

the 3rd pic does show very much ... the arrow could be the load, maybe being applied laterally to the upper flange so the flange is in in-plane bending and the composite section has a torque applied to it

RE: Plastic Neutral Axis calculation of a three segment composite section

If I understand things correctly, the horizontal member of the frame is made up of the three individual pieces shown in the sketches.

If that is the case, the three pieces are not composite between the columns and shearwall.  You have (3) individual members, not (1) member.  Each will be loaded by their relative stiffness.

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