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# Plastic Section Modulus

## Plastic Section Modulus

(OP)
Hi,

Using limit state design methods, I have come across the need to use Plastic Section Modulus.

This is usually given as the expression S=I x Ymax, where I= Ix or Iy depending on axis you are looking at etc. Ymax is distance from Neutral Axis to outer edge of section.

Does this expression hold true for all symmetrical sections about the axis in question??

### RE: Plastic Section Modulus

(OP)
oops, the expression above should be S=I/Ymax....

### RE: Plastic Section Modulus

Hi djw2k3

Here in the uk we call it the section modulus=Z=I/Y and yes it applies to all symmetrical sections as far as I know.

hope this helps
desertfox

### RE: Plastic Section Modulus

My limited understanding about elastic and plastic section modulus and that there is a significant difference between the two.
The difference is that elastic every part of the section remains below the 0.02% yield region and plastic means some of the material goes beyond this point but the section still holds the load. What i am trying to say is that in plastic design the shape is important and this is allowed for by a shape factor which is different for different geometries. In eleastic design only the I of the section is required. So if you are designing something that will go beyond elastic stress at any point, then its plastic design and shape is important.

### RE: Plastic Section Modulus

I was carefully staying out of the way on this one, since I haven't used it in 20 years, but the plastic analysis of a frame is done using the moment of plasticity, crudely given by integral (dA*y*yield stress)

There will be no simple relationship between this and the elastic properties of the section.

On the other hand the plastic limit on the beam is when

yield stress=(M/I)*y

which seems to involve the original poster's question. It is entirely general so long as the usual conditions of beam theory are met.

Cheers

Greg Locock

### RE: Plastic Section Modulus

(OP)
Thanks everyone for thier feed back,

Have got it sorted, the original question related to a design standard NZS 3404 (structural steel, and probably all standards using limit state design) when designing pin connections.

The Plastic modulus in this case turns out to be 1.5 x "elastic modulus" for a solid circular section for this particular standard.

### RE: Plastic Section Modulus

djwk3,
be careful with all these figures: the plastic modulus for a circular section is about 1.7 times the elastic modulus; the ratio is exactly 1.5 for arectangular section.
See the site below under Beams->Sections for values and formulae of plastic moduli for various section shapes.

prex

http://www.xcalcs.com
Online tools for structural design

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