Cold-formed Steel Framing - Flat Sheet Steel Diaphragm Shear Capacity?

[P1ENG]

I could find no answer using the forum search, so sorry if I have overlooked a previous discussion. I am looking for some help determining the diaphragm strength of cold-formed steel framing with a steel sheet (NOT corrugated) shear member. AISI S213 allows a shear wall to be clad with 0.018" steel which provides a nominal strength of 485 plf or a 0.027" sheet which provides a nominal strength of 647 plf (assuming fastener spacings of 6"/12"). However, there are no tabulated diaphragm values for the same steel sheet thicknesses. Therefore, I thought I would calculate the shear resistance based on Principles of Mechanics per section B2 of AISI. This is where I am having problems. I am calculating the shear strength of the sheet steel per section C3.2.1 of the AISI design manual assuming transverse stiffeners. You can see in my attached example that a 20' long, 8' deep diaphragm sheathed with 14 GA steel yields a very low allowable shear capacity. The problem stems from the h/t value and the a/h limit of (260/(h/t))^2. Perhaps I am using the wrong values of "a" and "h" and the fastener spacing affects these values? Currently "h = diaphragm depth" and "a = joist spacing". Sheet edges will be blocked when orientation of the sheet would otherwise be unsupported. I am currently comparing the shear at the diaphragm ends, but what about the longitudinal shear between the sheet and the chords? I am currently ignoring that, but maybe the community thinks it should be addressed? If so, would my "a" and "h" values need to change because of the change in direction of the shear?

Something gives because:
A shearwall (cantilever beam) sheathed with 0.027" steel has an allowable wind shear load of 323.5 plf (2.0 safety factor) per the tabulated values of AISI S213 while a 2.8 times thicker sheet used in a diaphragm (simple span beam) has an allowable capacity 6.6 times weaker per my calculation.

Additional Info:
Once this is resolved, I will also incorporate this to be used in calculating headers sheathed with sheet steel on both sides. I already have a method of calculating the diaphragm deflection with the sheet steel by combining concepts of both the sheet steel shear wall deflection equation and the wood sheathed diaphragm deflection equations given by AISI S213-07. If you would like to see that, just let me know. I will not allow the aspect ratio to control when I use this method, rather I will allow the strength and deflection calculation to control.

Juston Fluckey, SE, PE, AWS CWI
Engineering Consultant

 

[P1ENG]

Sorry for bumping this, but I would really appreciate the community's opinion. This is not an academic exercise, but rather something I would like to apply in one of my analyses rather soon. Thanks again to whoever responds.

Juston Fluckey, SE, PE, AWS CWI
Engineering Consultant

 

[racookpe1978]

You're sort of mixing two different materials being used in three different ways against three different forces:
gravity causing simple tension into a horizontal diaphragm,
tension forces, but caused by shear resistance at the ends of a shear plate across a frame
compression forces caused by shear forces acting at the edges of a shear plate across a frame.

A thin diaphragm (like the bottom of a barrel or the bottom of a box) works "adequately" if its edges are firmly held all around a frame or the barrel walls. it will deform (bend) as weight is added, but you can calculate fairly accurately when the bottom of the barrel will yield, or when a the rivets or nails holdign a piece of sheet metal on will pull through.

A thin sheet of un-reinforced (smooth, not deformed or rolled with grooves) is terrible against compression all the time. A simple frame using thin metal to resist shear will see two corners under compression, and two opposite corners in tension. Trick is to make sure the total resistance against shear is adequate for those two corners, until the wind changes and the situation is reversed. That load shifting (bending one way then the other) over time tends to work and loosen all of the fasteners, gradually loosening holes and allowing more movement.

 

[Triangled]

http://www.sureboard.com

might give you some ideas....

 

[Hokie93]

The shear buckling coefficient (k_v) is too low if you are assuming the ceiling joists act as stiffeners. If they do function in that capacity, a/h = 0.25 and k_v = 89.44. This will help to increase the capacity but you are still limited by the high h/t ratio. I recommend adding some blocking at mid-height such that h = 48", rather than 96". That change will considerably increase your capacity.

 

[P1ENG]

@racookpe1978 I don't understand your comment. Diaphragms and shear walls consist of thin sheets (plywood, OSB, gypsum, sheet steel) applied to repetitive framing members and is very common practice. Again, AISI has produced tabular values of shear walls sheathed with very thin (in comparison) sheet steel. I'm just trying to do the same thing, but horizontal with both ends of the "beam" supported (i.e. rather than a cantilever shear wall). Since there are no tabular values, I have to calculate something and I would expect that "something" to give me similar results to the shear wall values.

@Triangled Thank you for the link, but I found no application of what I am trying to do. Most of the sureboard products are metal sheathed gypsum. Looks like they have a just metal product (to be released), but there was no information on it yet.

@Hokie93 We are on the exact same page. In the attachment in the OP, I showed a/h=0.25, however because of the transverse stiffener requirement that a/h must be less than [260/(h/t)]^2, the (k_v) value cannot be 89.44. However, I have used my (I feel very conservative) calculation already in a header analysis where I applied blocking at the mid-height of the header to control my (h) value. I think the (h) value has to be either the framing spacing (24" o.c. in this case), the fastener spacing, or some combination thereof. A tighter fastener spacing on the edge of shear walls and diaphragms usually yields higher shear capacities and the only screw contribution to my analysis is checking the shear between the sheet and the chords. So in order for tighter fasteners to allow a strength increase, the screw connection needs to control (currently not based on the low shear strength of the sheet) or my sheet strength needs to be much stronger so that it does not control and/or a function of the screw spacing which it currently is not.

Juston Fluckey, SE, PE, AWS CWI
Engineering Consultant

 

[P1ENG]

No more words of wisdom?

Juston Fluckey, SE, PE, AWS CWI
Engineering Consultant

 

[Teguci]

AISI B1.2 is not satisfied (h/t < 300 with bearing stiffeners (diaphragm chord/ceiling track) and intermediate stiffeners (ceiling joists)). The web height of your member, h is 20 ft and your beam cantilever is 8 ft. a is 24 in. I think it'd be better to analyze this as an element with diagonal tension straps and reinforced compression elements.

 

[P1ENG]

I'm still seeking an analytical approach for determining the sheeted diaphragm strength. This is something I will be thinking about some more, but I thought maybe someone had done this before and could drop some knowledge on me. The sheeted diaphragm will not have a strength of zero just because my h/t limit is beyond that allowed by the code. One direction I could take this is the sheet could be assumed to contain the "X" strapping. However, I think the fully sheeted diaphragm will be stronger than cross strapping.

Juston Fluckey, SE, PE, AWS CWI
Engineering Consultant

 

[jayrod12]

I agree with an assessment that a lower bound capacity would be that of a flat strapping brace of the same gauge. It would obviously be higher than the capacity of the cross strapping, but I wouldn't know how to quantify how much without testing.

 

[P1ENG]

This leads to the question of how wide of strap do I assume. I still haven't had the time to think about moving forward on this future problem of mine.

Juston Fluckey, SE, PE, AWS CWI
Engineering Consultant