Simple Structural question, about section properties

[bertyboy]

Can someone plese tell me whether an angle, i.e. a L shape has a plastic neutral axis. Because I have just used a program which gave ( second moment of areas ) Zpl,x & Zpl,y, as both equal to 0 ?

 

[JAE]

Yes, angles do have Z values - check out the AISC steel manual tables for angles.

This is in metric - but you can search for others:

http://www.roymech.co.uk/Useful_Tables/Sections/U_AngleA_dim_prop.html

 

[bertyboy]

JAE, thanks for your reply.
However, you didn't read the question properly.
The question is, do angles have a plastic neutral axis, in addition to an elastic neutral axis ?

 

[prex]

Yes, they do of course.
Look in the site below, under Beams -> Cross sections -> Angles : you'll get what you are looking for. However only plastic neutral axes locations along geometrical axes x,y are given.

prex

http://www.xcalcs.com

Online tools for structural design

 

[bertyboy]

Prex, thanks for your reply.
I can see that the person that has written that small program has included the plastic nuetral axes.
But this really still doesn't proove that they are permissable for use in angles.
I was really wondering if the codes of practice, in the USA, or Europe, allow angles to have a plastic Z value ?

Thanks again.

 

[JAE]

bertyboy - I guess I don't understand your question. To have a value of Z - this implies that the entire section has gone plastic and there IS an axis where the tensile plastic zone switches to a compressive plastic zone.

What prex showed in the link is that you would have a geometrical axis (x,y) and AISC also describes principal axis - both of which can be applicable based on the nature of the bending and bracing.

 

[UcfSE]

It sounds like you need to dig out some paper and a pencil and try it out for yourself. I wouldn't think that would be terribly difficult. Force equilibrium of the section right? Tension force = Compression force, solve for the location that gives these results.

Check out this link, it was the first site in a Google search...

http://www2.umist.ac.uk/construction/intranet/teaching/civil res/mod305/305l03.htm

Look toward the bottom.

 

[apsix]

I think bertyboy's question is whether Codes allow the use of the plastic section modulus of angles to determine the section moment capacity.

Referring to the Australian Code AS4100, the plastic section modulus can only be used if the section is compact (ie. element slenderness limits are not exceeded). There doesn't appear to be any limitation on shape.

I can't speak on other Codes.

 

[UcfSE]

No, he is asking if an angle has a PNA. Apparently his program isn't working, or something like that.

 

[bertyboy]

Apsix, thank you for your valuable post !!!
That is indeed what I am asking !

Any shape can have a plastic neutral axis, and therefore a plastic Z value ( second moment of area ), but the question is, is it valid to use it for the case of angles.

 

[trainguy]

bertyboy,

Most handbooks do not give a Z value for angles because it is not standard practice to design angles and other non-doubly symmetric shapes for plastic moments. It it very difficult to ensure stability though the whole range of plasticity of such a shape.

It's hard enough to get yielding at the extreme fibre (S) for non-symmetric shapes...

By the way, Z is the first moment of area, and I is the second moment of area.

Z = sum [area x (distance of the centroid of this area to PNA)]

The plastic neutral axis is sometimes also called the equal area axis - you have equal cross-sectional area above and below it.


tg

 

[reeves111]

the problem with L sections is that they are not doubly symmetric like trainguy has stated. due to this lack of symmetry the max stresses due to bending will not occur about the centroidal axis, but instead about its principal axis. Hence the neutral axis does not coincide with the orientation of the centroidal axes. Therefore I would recommend an ASD approach (using S) instead of Z when analyzing/designing these sections to get a feel for the stresses and how they are obtained differently than in "regular" shapes, W, S etc..

 

[VTPE]

According to AISC, angles are allowed to be designed for plastic moment capacity. Go to the AISC web site (

http://www.AISC.org),

click on "epubs" and then go to "Specifications and Codes". There is a PDF file for the design of angles using LRFD. It covers the design of angles with both equal and unequal legs, about both the primary and geometric axes.

Hope this helps.

 

[bertyboy]

Trainguy, Revees111, and Vipe,
thanks for your comments, they were all worthwhile !
I have definately learned something from this thread.

Rob.

 

[kwrohde]

does anyone have good way to calculate the plastic section modulus(Z) for corrugated steel decking. I created an excel document that I an pretty confident in but the number dont seem to make much sense.