Calculating Deflection for Gypsum Shear Wall

[P1ENG]

I have a single-story modular building that has a sidewall that is full of holes, and therefore I assumed the diaphragm to be rigid and have a (3) wall lateral force resisting unit. The diaphragm is light-gauge steel with a plywood decking. The walls are light-gauge with gypsum sheathing.

To validate the assumption of a rigid diaphragm, I am calculating the diaphragm and shear wall deflections. This is fine for the roof using deflection equations found in AISI Lateral Design, but I have found no equation for calculating deflection for a gypsum sheathed wall.

I would appreciate any suggestions.

Juston Fluckey, E.I.
Engineering Consultant

 

[msquared48]

If your "diaphragm" is a light gage metal - 28 or 29 gage, I would not consider it a rigid diaphragm. In fact I would mostlikely not consider it a diaphragm. I would use an underlayment of 1/2" CDX ply or structural grade OSB as the diaphragm.

As for the deflection of a gyp SW, I will have to look further in my "stuff"...

Mike McCann
MMC Engineering
Motto: KISS
Motivation: Don't ask

 

[P1ENG]

The roof is 12 GA with a 3/4" plywood diaphragm. The 2004 AISI Standard for Cold-Formed Steel Framing - Lateral Design is the basis for my diaphragm strength and deflection equation.

I will be assuming the diaphragm is rigid if the diaphragm deflection divided by the shear wall deflection is less than 2.

I haven't had an issue like this yet, but once it is resolved I will be adding it to my "stuff". Thanks for your help.

Juston Fluckey, E.I.
Engineering Consultant

 

[msquared48]

You might check out this site:

http://www.curee.org/projects/woodframe/element5/modules/shearwall/deflection.htm

I strongly encourage you though, to consider using plywood in lieu of GSB, as, if you are in a high seismic or wind zone, these deflections calculated will only be applicable to the first event, not subesequent events.

You have to remember that with GSB, the nail holes work and become less effective in shear with each event. Hence the reduction in values for seismic loads.

I will keep looking...

Mike McCann
MMC Engineering
Motto: KISS
Motivation: Don't ask

 

[P1ENG]

Mike, thanks for the website, but I am already aware of that deflection equation and how a shear wall works. The bending section of that equation doesn't pose a problem. The shear and nail portions of the equation differs in the AISI documentation. The building has the highest importance factors because it stores hazardous materials, but it is 90 mph wind and seismic design category "A" (without considering importance factor). Also, the walls are fire-rated assemblies so plywood/OSB is not an option.

Equations per AISI Standard - Standard for Cold-Formed Steel Framing- Lateral Design:

[Δ]_v = ([ω]₁*[ω]₂*v*h)/([ρ]*G*t)
[Δ]_n = [ω]₁^5/4*[ω]₂*[ω]₃*[ω]₄*(v/0.00290*[β])²

I am assuming the omega, rho, and beta factors are present because of the way Plywood and OSB are graded. A quick look at the omega factors show they are less than or equal to one, so ignoring them would be conservative (for wood sheathing applications). I haven't found the values of the shear modulus for gypsum and fastener deformations under load.

Juston Fluckey, E.I.
Engineering Consultant

 

[a2mfk]

No way you can use that same light-gage deck for your walls for a better diaphragm than gyp board? Or diagonal metal straps? I'd want some redundancy at a minimum... What is your exterior wall cladding?

A little bit of moisture/water and gyp assemblies fall apart (ie storm events with lots of rain that can last 24 hours+). I would be reticent to ever use them except maybe for the lightest of interior shear walls, I would run away from using them as my primary MWFRS for a hazardous material storage building!

Just my two cents.

 

[P1ENG]

@a2mfk The problem is the fire-rated assembly. I can't add or remove members or the assembly is void (I will double check if adding steel does in fact make the assembly void because logically it should be o.k.). Again, this is going to be a light shear wall (V=90 mph and low seismic). The exterior is light gauge steel over 3/4" gyp then light gauge studs.

A little off topic here as I was looking for suggestions for calculating the drift of a gypsum on light gauge framing shear wall.

Juston Fluckey, E.I.
Engineering Consultant

 

[a2mfk]

My point being you can calculate the drift of a cardboard box but that doesn't mean I would sign and seal it... And if you have light gauge steel cladding over the gyp this may dominate the stiffness of the system and collect the shear anyway. I understand your hands being tied as far as fire assemblies, and that is low shear, but it is also hazardous materials..

 

[P1ENG]

I thought about the steel cladding too, but then how to determine the fastener deformation because you must assume a void where the gyp is present.

I have discovered that the studs are welded to the tracks instead of being pinned, so I have decided to use the studs as an ordinary moment frame (this oversight will be reflected in their bill, so hopefully they will decide analysis shouldn't be demanded until their drawings are complete). Redundancy is accounted for and construction doesn't need to change. Thanks for participating in my thread.

Juston Fluckey, E.I.
Engineering Consultant

 

[NITTANYRAY]

If you need a fire-resistant sheathing with reasonable structural properties use DensGlass Fireguard made by Georgia Pacific. It has an ultimate racking strength of 654 PLF.
With a safety factor of 3 it has an allowable racking strength of 218 PLF when used with 18 Ga. steel studs at 16"c/c.

It is a fiberglass reinforced gypsum sheathing.
Obviously you can get higher values with OSB sheathing but the DensGlass is about twice as strong as regular gypsum sheathing. IBC allows 90 PLF for 1/2" gypsum board for wind but only 45 PLF for seismic.

 

[ash060]

According to the commentary in AISI S213 there are currently no provisions for the deflection calculation of gyp. shearwalls. It also says that due to the low R value that deflection is unlikely to control design.

 

[P1ENG]

@ash060 I don't know why I always fail to look at the commentaries. Thanks for pointing that out.

Juston Fluckey, E.I.
Engineering Consultant

 

[NITTANYRAY]

If you are Seismic Design Category A and have a 90 MPH wind, I doubt if seismic design governs. If wind design governs, The seismic R Value is irrelevant.