Determine Rigid or Flexible Diaphragm Story Drift

[CorporalToe]

Hello, I have a question, according to ASCE 7 12.3.1.3 a diaphragm can be idealized as flexible if maximum diaphragm deflection is greater then 2 times average story drift. Assuming my building has multiple shear walls as its LFRS. I can calculate the story drift by finding the vertical deflection of the walls and averaging them if I am give a horizontal load. However how do I know how to distribute the horizontal load onto the walls if I haven't figured if the diaphragm is rigid or flexible.

I might sound confusing but to my understanding, in a flexible diaphragm you can use the tributary area of the diaphragm assigned to each wall as a method to calculate the lateral force each shear wall will resist. And for a rigid diaphragm you use the rigidities of the walls to calculate the lateral force each wall will resist.

However both these methods will give me a different story drift. How do I initially determine what type of diaphragm I have? Sorry if I sound confusing please let me know if you need clarification.

 

[driftLimiter]

Use the flexible diaphragm approach for your first pass. Afterall if you are comparing the diaphragm deflection to the wall deflection this implies that your diaphragm is flexible.

Also, a little caveat to what you are saying.

Each line of wall resistance gets horizontal loads that are tributary to it. But all the walls on a single line should be designed using equal deflection.
NDS requires we do it that way. I have seen some people try to take a tributary width in two directions to a single shear wall but thats not how it works.

 

[hardbutmild]

I dissagree. It makes no sense to me to compare the actual deflection with the flexible variant. For example. Imagine three lines of lateral force resisting systems. If you consider the diaphragm to be completely flexible it would distribute the load by tributary area, meaning that the middle LFRS gets the highest load. Now, if you say "I'll make the outer LFRS significantly stiffer than the middle one" you could get that the middle LFRS has somewhat larger drift than the outer ones. Add to this the flexibility of the plate end it could seem that This would mean that the diaphragm just translates and deflection of all the walls is the same.
Let's imagine a very flexible diaphragm. See the photo below. I don't know if you could see this but using a very flexible diaphragm I got max deflection of 4 mm and average of 3 mm. This means that numerically I'd get that it's not flexible. When you look at the forces it's obvious that they transfer by tributary area (outer walls are significantly stiffer from the leftmost picture).

Now let's compare this to the rigid solution.

You'd get a deflection of 1 mm. This means that the actual diaphragm (top) has 4 times larger deflection. Force distribution is quite different as you can see.

In conclusion if you compare the value of deflection to the average it should be comparing the actual diaphragm with an ideally rigid one (so top with bottom... 4 mm with 1 mm, not top with top or 4 mm with 3 mm).

 

[driftLimiter]

@hardbutmild, you make a fair assessment here. I am curious about one thing and I can't really read the specific values to check it from your pictures.

If you only consider 1 bay of the flexible diaphragm at a time for the average calculation how does it come out?

Either way I suppose your correct about this, the figure in ASCE 7 does appear to show a rigid behavior compared to the diaphragm deflection.

 

[hardbutmild]

If you only consider 1 bay of the flexible diaphragm at a time for the average calculation how does it come out?

Unfortunately I did not save that model, it was a quick check... I guess it should come out the same since deflections are symmetric. Even if it did not, clearly some combination of wall rigidities would lead to the wrong conclusion even if you check it span by span.

Yeah, it's hard to see the values but I did not want to attach 7 large photos. For top case (actual flexible diaphragm) max deflection is 4 mm and average is 3 mm, you can see the deflected shape I believe. Forces are 2393,84 kN for the middle wall and 1275,65 kN for the outer walls. I guess that you can see the values on the bottom picture.