×
INTELLIGENT WORK FORUMS
FOR ENGINEERING PROFESSIONALS

Log In

Come Join Us!

Are you an
Engineering professional?
Join Eng-Tips Forums!
  • Talk With Other Members
  • Be Notified Of Responses
    To Your Posts
  • Keyword Search
  • One-Click Access To Your
    Favorite Forums
  • Automated Signatures
    On Your Posts
  • Best Of All, It's Free!
  • Students Click Here

*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail.

Posting Guidelines

Promoting, selling, recruiting, coursework and thesis posting is forbidden.

Students Click Here

Jobs

Plastic Section Modulus for Cold Formed Steel Sections

Plastic Section Modulus for Cold Formed Steel Sections

Plastic Section Modulus for Cold Formed Steel Sections

(OP)
How can we calculate the plastic section modulus for cold formed steel sections? I am the light gage speciality engineer. The EOR has asked me to design connections based on plastic section modulus for blast resistance design. I would appreciate your response.

RE: Plastic Section Modulus for Cold Formed Steel Sections

Can a light gauge member even reach the plastic moment?  Won't local buckling preclude that?

DaveAtkins

RE: Plastic Section Modulus for Cold Formed Steel Sections

I would just follow the same procedure that you would for a rolled shape, it is just a lot thinner and not as neat and quick.  There are a little more calcs involved.  Could you do it for a rolled shape?

RE: Plastic Section Modulus for Cold Formed Steel Sections

I agree with dave,

I very much doubt that these would even reach a plastic moment as the local plate buckling would occcur first.

Have you looked at the option of designing them as a catenary tension member. This would induce higher loads on the structure though!

There have been a lot of papers  on this type of thing recently, I would suggest you google it.

RE: Plastic Section Modulus for Cold Formed Steel Sections

(OP)
Thanks for your all help.

I agree with you all. I would not recommend to design light gage members to reach plastic moment. However, my question is if I have to do calculation plastic section modulus for light gage section, is it possible to calculate? If so, is there any reference book or section of AISI I can look into? I already googled it, and could not find any.

RE: Plastic Section Modulus for Cold Formed Steel Sections

Yes it is possible to calculate.  You can use the same procedure as for hot-rolled shapes as suggested above.

Whether or not is means anything in reality is the question, also noted above.  If you look in the NASPEC, you'll see there is no provision for CFS members reaching Mp, because most of them can't.  So you couldn't really design to Mp even if you wanted to, again for most cases.  Perhaps the EOR is intending for you to use the inelastic reserve capacity?  I would put together some notes and give the person a call and try to clarify.

Are you using the UFC 4-010?  The last edition permitted you to use the full yield stress for steel calculations, but didn't require connections to meet Mp.  Basically you just remove all the safety factors or resistance factors.  I don't know if this has changed in the latest version of the UFC spec.

RE: Plastic Section Modulus for Cold Formed Steel Sections

Do you have a decent hot-rolled steel design book or even a mechanics of materials book?  Either of these should provide examples for calculating Mp for arbitrary shapes.  

I'm curious as to where they got the idea to design connections so that the members can reach Mp.  Any idea?  Like many folks have typed so far, these sections can't develop anywhere near Fy*Zx.

RE: Plastic Section Modulus for Cold Formed Steel Sections

You should not calculate plastic section modulii for cold formed members as they will never reach this load level, they will fail out by some other mechanism (as others have quite right pointed out) well before they ever reach plastic moment capacity.

My two cents:  You should be designing for combined bending AND SHEAR to elastic section properties for your connection.  Although I do not know the US code, the combined Australia & New Zealand AS/NZS 4600 CFS code requires a combined check to:

(M*/phiMs)^2 + (V*/phiVv)^2 <= 1.0  (but not always; You really need to check your specific code)

Bottom line:  I do not believe you are checking against a realistic condition.  Your connection (more specifically the member very near or at the connection point) is more likely to fail under combined action/loading well before the plastic moment.

Good luck,

YS

B.Eng (Carleton)
Working in New Zealand, thinking of my snow covered home...

RE: Plastic Section Modulus for Cold Formed Steel Sections

Let's back up a bit, guys.  dcredskins isn't sizing a cold-formed member as if it can reach Mp.  He's designing connections for blast design using the load that can cause Mp.  At least that's the way I understand it.

RE: Plastic Section Modulus for Cold Formed Steel Sections

Check with him that he meant ultimate capacity instead of plastic moment. The blast criteria I recently had to comply with has the following under the "Window Frames" section where the supporting cold formed elements and connections had to be designed for blast resistance:

"Design frame connections to surrounding walls to resist a combined ultimate loading consisting of a tension force of 35-kN/m (200-lbs/in) and a shear force of 13-kN/m (75 lbs/in). Design supporting elements and their connections based on their ultimate capacities."

RE: Plastic Section Modulus for Cold Formed Steel Sections

(OP)
My question is how to calculate plastic section modulus. I am not talking about if this is a good idea to design cold formed steel sections to reach Mp. I agree with most of you that the failure modes for cold formed steel sections are different than hot-rolled sections. Those of you who know, at least the design concept of Blast Resistance, I presume you understand what I am talking about. I have not designed any structure for blast resistance yet, although I can take lead on other structural design issues. I was talking to EOR on this case, and this is what pretty much explained to me, the rule of blast resistance design. He clearly said, connections design in this case should be based on plastic section modulus. I am preparing myself to discuss with him on this issue tomorrow anyway. Since I am designing connections only in this case, I am talking about components design, not the whole structure design. Those of who know the properties of cold formed steel sections, the calculation of section properties is not as simple as hot-rolled section. Please refer to AISI. And I bet the calculation of plastic section modulus, if possible, for cold formed steel sections is not as easy as hot-rolled sections as some of you guys are refering to.

RE: Plastic Section Modulus for Cold Formed Steel Sections

In plastic design, the entire section in bending is assumed to be stressed to yield, so the area in tension and the area in compression are equal.  Find the centroid of each of the area above and below, multiply the area of one half by the distance between the centroids.  That is the plastic section modulus.

RE: Plastic Section Modulus for Cold Formed Steel Sections

Or, it is the integral of sigma_yield*y*b dy

where b is the total metal width at height y above the neutral axis.

I imagine that the neutral axis may not be same neutral axis as it is for elastic bending (check for net axial force to determine that)

Cheers

Greg Locock

SIG:Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.

RE: Plastic Section Modulus for Cold Formed Steel Sections

You're looking for the axis of equal force (or equal area for a single material cross section).  Force above axis equals force below axis when using A*Fy.  Location of this axis is the PNA.  Find the area above or below PNA times the distance to the centroid of that area.  It's a little tedious but should not be very difficult at all.

A decent mechanics of materials book should give you what you need.

Link

RE: Plastic Section Modulus for Cold Formed Steel Sections

Mark's mechanical engineers handbook indicates that the Plastic Section Modulus is 1.14 times the regular section modulus, for "I" shapes. This is most likely an averaged "Rule of Thumb" value.

RE: Plastic Section Modulus for Cold Formed Steel Sections

Here is the procedure for a homogenous section of constant Fy and E.
First find the PNA - this is done by finding the axis about which there is an equal amount of area above and below.
Now, find the centroid for the top portion and the bottom portion seperately (from simple statics).  Call the distance from the PNA to the centroid of the top portion ybar1, and the distance from the PNA to the centroid of the bottom portion ybar2.  Call the Area of each portion A.
the plastic section modulus, Z, will be A*(ybar1 + ybar2) in in^3.
This is like the 5th or 6th time I've typed this out.  I think I'm going to copy this into a word document for next time.

RE: Plastic Section Modulus for Cold Formed Steel Sections

Do what StrlEIT typed, and you'll be good to go.  This is really pretty easy, especially for something like a cee or zee because the centroid is in the middle.

RE: Plastic Section Modulus for Cold Formed Steel Sections

For most cases we have done in our office for past several years, we are using Plastice modulus Z=1.25*S.  We have done step by step calculations and found most of C and Z shape (16GA, 14GA, or 12GA) Z > 1.25*S, therefore we selected to use 1.25*S as plastic modulus.

If anything wrong or under designed, please input.......

RE: Plastic Section Modulus for Cold Formed Steel Sections

tedamiao, if you're using the plastic modulus as the basis to determine the required connection capacity, your procedure would not be conservative.  You would want to find the maximum ratio, and then use something a bit higher than that.

Back to the original post, I am surprised how often this comes up, and how often StructuralEIT has to type the procedure out.  This is a basic concept included in any decent mechanics of materials book.

RE: Plastic Section Modulus for Cold Formed Steel Sections

nutte, that's because of all the 89 ASD folks (LOLOL -- sorry couldn't resist!!  Just giving you a hard time, but that's obviously the reason)

RE: Plastic Section Modulus for Cold Formed Steel Sections

271828-
You are probably right.  I actually learned ASD in school, just 3 years ago.  I never learned how to calc Z, but I figured I should know how so I just figured it out.

RE: Plastic Section Modulus for Cold Formed Steel Sections

Good job.  I'm amazed that anybody taught 89 ASD in 2005!

RE: Plastic Section Modulus for Cold Formed Steel Sections

Tell me about it.  I didn't realize until I started working that everyone else learned LRFD (even though everyone in our office and most of the offices in the surrounding area used the Green Book).  That only lasted until the 13th edition manual came out and then we switched to LRFD.

RE: Plastic Section Modulus for Cold Formed Steel Sections

271828, nicely done!  I, however, am a renaissance man.  9th ASD, 2nd LRFD, 3rd LRFD, 13th ASD, 13th LRFD...  Doing connections, we have to use whichever code the EOR calls for, so we have to become proficient in all of them.

I also enjoy going through the older specs (8th edition and earlier) to see how the equations have changed over the years.  How sad is that, that I "enjoy" such things!

RE: Plastic Section Modulus for Cold Formed Steel Sections

If he had taught LRFD instead, the transition to the 13th Ed. would be trivial.

LOL, I hope your former professor isn't on your Christmas card list, due to his short-sightedness.  About 1-1.5 years before the 13th Ed. Spec. was available, the steel prof. at our school was teaching from a draft copy so that his students wouldn't have to make the trivial transition from 3rd Ed. LRFD to 12th Ed. LRFD/ASD.

You seem to have come out fine, but it seems to be from work ethic and the wilingness to study.

RE: Plastic Section Modulus for Cold Formed Steel Sections

Oops, you know I meant 13th Ed., not 12th Ed. LOL.  I guess that was the "phantom spec."

RE: Plastic Section Modulus for Cold Formed Steel Sections

Nutte, thanks for the input. The thing is for connection design, screws are always control rather than section itself.  Also we will not try to make moment connection. Almost every connection was considered as pin connection.

RE: Plastic Section Modulus for Cold Formed Steel Sections

You are correct, but I think the goal here is to size the connection for the plastic capacity of the section, even though it can never get to plastic, to ensure a ductile failure.  This is the same process used for seismic connections, where you size the connection for more than the gross member can take to ensure a ductile failure in the member rather than a brittle failure in the connection.

Red Flag This Post

Please let us know here why this post is inappropriate. Reasons such as off-topic, duplicates, flames, illegal, vulgar, or students posting their homework.

Red Flag Submitted

Thank you for helping keep Eng-Tips Forums free from inappropriate posts.
The Eng-Tips staff will check this out and take appropriate action.

Reply To This Thread

Posting in the Eng-Tips forums is a member-only feature.

Click Here to join Eng-Tips and talk with other members!


Resources