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Flexible diaphragm and rotation
2

Flexible diaphragm and rotation

Flexible diaphragm and rotation

(OP)
I have seen several single story steel roof deck buildings with a brace at one end wall and one at one side wall. I realize that many people must assume that there will be enough deformation of the deck during the short term lateral load that you can disregard diaph. rotation. Is this always a pretty safe assumption after concluding that a diaphragm can truly be treated as flexible?

RE: Flexible diaphragm and rotation

haynewp,

I have seen buildings with vertical bracing on three walls.   In those cases, the roof has to act as a diaphram or have horizontal bracing.  The theory is that one wall takes the total shear, while the othe two opposite walls tke the moment due to the eccentricity of the load.
There is a small rotation of the roof and deformation of the structure.  

Regards

RE: Flexible diaphragm and rotation

(OP)
I have been looking over a building this week, it was given to us by the owner to review the structural work. It only has braces on 2 of the walls. Would this be unsafe due to some slight rotation?

RE: Flexible diaphragm and rotation

(OP)
I have always put at least 3 braced walls myself.

RE: Flexible diaphragm and rotation

haynewp,

I believe that with only 2 walls resisting the horizontal loads, the building would deform excessive and could fail.    Could some of the walls be acting as shear walls?



RE: Flexible diaphragm and rotation

(OP)
No, only storefront on other sides.

RE: Flexible diaphragm and rotation

steel deck without concrete has been considered flexible traditionally.

in california, we have a lot of wood structures.  wood diaphragm, also, has been considered flexible, however, we now recommend that flexibility of the diaphragm be verified by calculations.

if the maximum diaphragm deflection is more than double the deflection of the lateral system, it is considered a flexible diaphragm.  using this approach, many wood framed homes and low rise wood structures will be rigid diaphragm (contrary to original assumption).  it is recommended that engineers use the envelope approach - using both the flexible diaphragm approach and rigid approach and design for the greater of the two.  this has caused alot of grief to smaller firms since the amount of engineering "doubled" and they can not increase the design fee.

going back to your building, if it is a metal deck without concrete, and the lateral elements are only at the perimeter, it is reasonable to assume a flexible diaphragm.

flexible or rigid diaphragm approachs are just simplified methods available to us for designing.  nothing is infinitely rigid or purely flexible in reality.

RE: Flexible diaphragm and rotation

I believe that your diaphragm could be considered rigid enough to transfer all the lateral load to one braced frame; HOWEVER YOU MUST HAVE LATERAL LOAD RESISTING ELEMENTS ON AT LEAST THREE WALLS!  It is impossible to satisfy statics with braced frames on only two walls.

DaveAtkins

RE: Flexible diaphragm and rotation

(OP)
Thanks, and I will bring this to the attention of the owner!

RE: Flexible diaphragm and rotation

DaveAtkins points out an interesting thought.  Yes, three walls must be present for diaphragm stability.  The moment caused by the load parallel to the single line of brace can be taken by the "coupling" effect to the other two.

I am not sure which code is the adopted code in haynewp's area but having just a single brace at each ends may be not redundant enough.  of course this will depend on the total area of the building.  if your governing code is based on 97UBC, please check the rho factor to see if you get penalized for a non-redundant system.

DaveAtkins, any thoughts on redundancy factor for a three sided braced frame structure?

RE: Flexible diaphragm and rotation

Whyun,
Interesting question, and worthy of some discussion...in my limited experience with the UBC and IBC, the rho factor would be calculated assuming that no redundancy to the system.  This would be because if any one brace failed, the system would fail - therefore no redundancy.
Now for the original question about steel deck - rigid or flexible.  I have done some theoretical research (using FE SAP models) to model steel deck diaphragms.  What I found was rather shocking.
The building I modeled was 1000 ft by 400 ft, with an expansion joint at 500 ft.  The building was a tilt up building (concrete shear walls) with a braced frame at the expansion joint.  
Here is what I found.  The steel deck diaphragm (1 1/2" 22 ga, with 36/4 pattern and 4 sidelaps) was stiff enough to act as a three sided box, even though there was a braced frame on the fourth side.  By the time the diaphragm deflected enought to where the braced frame took load, the rotational stiffness of the diaphragm had transfered the load to the transverse shear walls.
This is of course a model, and not reality.  But as I played around with the stiffness of the diaphragm, I found that if the diaphragm deflection was up to 100 times that of the resisting element, that it was still stiff enough to act as a rigid diaphragm to re-distribute the loads.
Of course I haven't been able to get funding to try this on a full scale building...but if I were designing a structure with multiple kinds of lateral resisting elements, I would design the diaphragm for the higher shear because of the torsional redistribution, and also check the shear walls for the higher load, but also design the braced frame for a flexible diaphragm.
Just food for thought.

RE: Flexible diaphragm and rotation

whyun,

I work in Wisconsin, which almost always results in Seismic Design Category A.  However, I reviewed IBC Section 1617.2, and rho is definitely higher when only one brace resists lateral loads, because r max is equal to 1.  So you are indeed penalized in one direction when only three braced frames are used.

DaveAtkins

RE: Flexible diaphragm and rotation

Thank you both for the follow up.

It is interesting to see douganthols' metal deck of a tilt up building acting like a three sided structure.  whats shocking is not that the brace really isnt effective at all.  traditionally, and even today, this type of building will be designed as having a purely flexible diaphragm.  brace taking exactly the same shear as the parallel concrete wall on the other side.

I do agree with your envelope approach similar to the wood diaphragm design recommendation from SEAOC.

For Dave, Did wisconsin adopt IBC2000 already?  Where i am at, it is going to be 1997UBC for 3 more years.  1617.2 in the IBC appear to be no different from the 1997 definition of rho, r max, etc.  I think if you have a small enough structure, rho will not exceed one, even for a three sided structure.  I am not sure how small a structure... perhaps garage size.  Anything bigger, you may be penalized upto 50%.

Thank you for your discussion.

RE: Flexible diaphragm and rotation

Actually, a building with 1 LLRS on each of 2 walls is probably REALLY FLEXIBLE...

Can this be said of metal deck with concrete?

I agree with this statement only for the condition presented by haynewp (non-composite metal deck roof).

RE: Flexible diaphragm and rotation

whyun,

Yes, Wisconsin adopted IBC (with a few "Wisconsinisms") in July of this year.  Rho is equal to one in Seismic Design Categories A, B, and C (no penalty).  I was referring to Categories D, E, and F, and a "typical" size building (say, 100'x100').

In response to your other question, statics must be satisfied regardless of whether or not the diaphragm is flexible or rigid.  You cannot satisfy statics with two braced frames on two perpendicular walls.  You must have braced frames on three walls.

DaveAtkins

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