Plastic Section Modulus for Cold Formed Steel Sections 1

[dcredskins]

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.

 

[DaveAtkins]

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

DaveAtkins

 

[Lion06]

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?

 

[csd72]

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.

 

[dcredskins]

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.

 

[UcfSE]

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 M_p, because most of them can't. So you couldn't really design to M_p 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 M_p. 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.

 

[271828]

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.

 

[youngstructural]

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...

 

[271828]

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.

 

[haynewp]

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."

 

[dcredskins]

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.

 

[hokie66]

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.

 

[GregLocock]

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

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[UcfSE]

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*F_y. 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

 

[EddyC]

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.

 

[Lion06]

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.

 

[271828]

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.

 

[tedamiao]

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.......

 

[nutte]

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.

 

[271828]

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)