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Plastic Neutral Axis calculation of a three segment composite section 1

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ingdott

ingdott

Structural
Nov 3, 2009
17
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?

 
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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.
 
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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...
 
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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?
 
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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
 
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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

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

 
 http://files.engineering.com/getfile.aspx?folder=b06856a5-8774-42fc-a143-8afff7b4b8a3&file=SECT2.JPG
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If the load is placed on the top member, how does it get into the other two?

BA
 
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Is the member you are talking about the horizontal member of a 1 bay frame?
 
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and yes dcarr, what I am talking about is the horizontal member..
 
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Actually BA, the shear wall can cover all parts of the horizontal member (I mean it can go up to the top part)
 
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