Elastic modulus is the steel modulus based on the stress strain curve before yielding. The plastic modulus is after yielding. Plastic section modulus (Z) for various shapes are given in the steel book. I'm not sure how its' calculated. Plastic design is based on maximum strength of the steel and is covered in Chapter N of the 1989 ASD. I think the new 360 spec to uses it.
The elastic section modulus assumes the section remains elastic. The plastic section modulus assumes the entire section yields. For a rectangular section the ratio of plastic section modulus to elastic section modulus is 1.5. For WF shapes it is around 1.13-1.17.
The plastic section modulus is calculated by first finding the PNA (plastic neutral axis). This is the axis about which there is an equal amount of AREA above and below.
The next step is to find the centroid of the area above and below the PNA independently.
Now multiply the total area of the section times the distance between these two centroids. Now you have the plastic section modulus. This for a ductile material like steel. It is similar for something like a steel beam with a composite concrete slab, but not exactly the same.
i think terms are getting mixed up here, 'cause we use "modulus" in so many ways.
perhaps dcnnng could clarify if he's using the term referring to stress/strain curves or to "section modulus" (menaing stresses for a cross-section in bending).
Thanks Bagman for your prompt response. But I am interested to know as how to calculate manually the Plastic Modulus for a built-up steel box section instead of a standard section. Appreciate very much for any expert advising me. Thank you!
rb1957, I am referring to the steel Section plastic modulus.
Thank you StructuralEIT for your input, do you mean that the neutral axis for elastic modulus is based on linear triangular stress block with only the outer layer at full stress whereas the plastic modulus is based on full rectangular stress block ? Thank you!
Yes, that is correct. That is why the PNA will be different than the ENA if the section is not symmetrical about the horizontal axis. To satisfy statics, the compression force and tension force must be equal. Since both are being stressed to full fy, that means there must be an equal area of steel in compression and tension.
The total area of the section mentioned by StructuralEIT above I believe must be the area of the section above or below the PNA, not the cross section area of the entire member.
Ah, nice catch Bagman. It should have been the area above or below, and they will be equal. Not the area above and below. I should probably re-read these posts before I hit the submit button.
The rest of it is correct.
You should be asking your supervisor(or lecturer) these sorts of questions, this forum is not really a good place to learn these types of fundamental concepts.
csd72, yes we can go back to ask our lecturer but we have left school long time ago. Sorry that I don't agree with you that this is not the right place to ask this sort of question. Well I get my problem answered and many thanks to all of you.
Appologies but we do get students on this forum every now and then and I know nothing about you.
If you have to ask about something so fundamental then it shows me that you do not understand it. You will get quick answers in this forum, but it will not necessarily help in your understanding.
As engineers we should not only know, but also understand. It is often the lack of the latter that leads to engineering failures.
I am so what agree with csd72. I think not just the newly graduates, but quite a few of seasoned engineers do not know or remember how to do this type of calculation. But as a professional, we shall at least open some text books to understand what we are looking for, especially when engineering assumptions were involved.
Just to throw this in there the PNA is only dependent on the area if the cross section is homogenious - with hybrid girders, cover plates of different yield strength, etc, the PNA should be based on force balancing (area*fy) as opposed to just area balancing.
What I would like to know is, how come in the US and maybe elsewhere S is elastic section modulus and Z is plastic, and in Australia and maybe elsewhere it is the other way around? Is it just because we are down under?
