Can a 'U' shaped flexible even stan up? 1

[jnichol]

I'm hoping someone out there wiser than myself can help me finally put this question to rest.

I work for a mid-sized structural firm doing work across the country. Often times the buildings we design have steel roof decks, and (3) long shearwalls along the perimeter. One side will have no lateral support what so ever. This can be because one side of the building is constructed entirely of storefront glass, or it may be because there is an expansion joint in the middle of the deck.

My understanding is that flexible diaphragms distribute forces base on tributary area (an are unable to transmit torsion forces), rigid diaphragm on the other hand transmit forces based upon rigidities (and can take torsion). Semi-rigid fall in between these two extremes.

When a building is 'U' shaped, and wind/seismic forces are going in the direction parallel to the lone wall, can a flexible diaphragm even stand up? Because the center of rigidity and the center of force are at different locations, torsion is required for stability, but a flexible diaphragm can not transmit such force (or can it). Does that mean that my diaphragm always has to have (4) sides if it is flexible?

Then, should I treat this condition as semi-rigid or rigid? Best I can tell SEOC say do both (semi-rigid). Great concept, but if there needs to be (4) sides for a flexible diaphragm to work since it can not transfer torsion, and I dont have it, what should be done?

Also, if a flexible diaphragm can indeed take torsion than what would be the difference between a flexible and rigid analysis for loading in this direction?

Reason for the question, we have just completed two CA jobs in the last 3 months. One code reviewer says prove the diaphragm is rigid, the other says prove its flexible. Cant win for loosing!

Thanks in advance for all your comments on this condition!

 

[DaveAtkins]

I have the benefit of working in an area with no seismic concerns, so my answer may not fly with you California engineers. I have designed three sided steel deck diaphragms, on occasion, and yes, that means I assumed the deck was rigid.

DaveAtkins

 

[doejohn]

Well, I think it's an over-extension of the the flexible diaphragm concept to say that they are theoretically incapable of resisting eccentric load. But even if the theory (as I understand it) doesn't really rule out being able to resist eccentric load, as a practical matter, buildings such as yours never give me a good feeling.

As far as the theory goes, I think the right way to think about it is that in the spectrum of possible distributions of stiffness between the diaphragm and the shear walls, "flexible diaphragm" really means the extreme of shear walls that are infinitely rigid compared with the diaphragm (like the classic idealized beam on pinned or roller supports we all learn early on in Engineering education), and "rigid diaphragm" means it's the walls that undergo all the deformation to resist the load (like a rigid beam on spring supports). Either way, the correct distribution of force/deformation to the non-rigid components must satisfy equilibrium; and if it's statically indeterminate, the theoretically-correct solution must also involve the stiffness(es), either EI for the "flexible" beam, or the distribution of spring constants K for the "rigid" beam.

Now a better analogy to a diaphragm would be a shear beam (deformed slope proportional to shear, instead of curvature proportional to moment, if memory serves), so GA instead of EI. And tributatry span is a better approximator of load distribution for a shear beam than an Euler(?) beam, hence its use for flexible diaphragms. So if you've been curious why your calculated wall shears don't quite satisfy equilibrium, it's because you're (appropriatly) approximating the theoretically-correct "shear beam" solution with tributary area.

Where this all leads is that yes, you can have torsion in flexible diaphragm, just like you can have moment in a shear beam. And a three-sided building such as yours (with the infinitely-rigid shear walls, of course) is like a cantilevered beam. It's statically-determinate too, so it's just like you thought: the single parallel wall takes all the applied lateral load, and a couple is produced in the two perpendicular walls to resist the resulting torsion.

Of course, analysis of your buiding faces the same question as any diaphragm building: which (if either) diaphragm or shear walls, may be consisdered essentially rigid compared to the other? But flexible diaphragm "theory" doesn't prevent you from getting a "correct" force distribution solution, so the SEOC "bracketing" method should always be available.

That's my take on it, FWIW

 

[jnichol]

doejohn/dave atkins - Thanks for y'alls take on it. The shearbeam concept does seem to make some sence to me. And I guess I can see why this type of diaphragm can take moment. Its somewhat similiar to the force distribution in a wide flange beam, where the flanges in essence resist 99% of the bending force. Also explains why we need to design closure angles for chord forces.

Thanks for your help

 

[Ron]

jnichol...it sometimes helps to visualize the potential failure mechanism. Take one of your business cards. Fold it in half, but leave 1/2 flopping down (you now have an "L" shape, upside down). Now take the free ends of the horizontal leg of the "L" and push them together. Do this a couple of times. You will see that the free edge can go up or down, but that the edge by the vertical leg shows almost no movement. This approximates your diaphragm deflection pattern. You can see from this that a shear beam would solve the problem, or you can increase the rigidity of the deck sufficiently to solve. Consider the flexible condition, since you can't guarantee that vertical loads will not force the diaphragm out of its rigid plane.