Period Calculation with Flexible Diaphragms 1

[ash060]

Working on calculating the modes for a building that is stepped with a low roof and a high roof. There is only one story difference between the low roof and the high roof. Modeling the building in RISA 3D and currently using the rigid diaphragm feature of the program for the flexible roof diaphragms. If I don't use the rigid feature get a ton of local modes and can't get the mass participation up. Looking for some guidance on this. I don't think that the rigid diaphragm will have a huge effect on period calculation, but would like opinions.

 

[JAE]

If the building isn't large with respect to the plan then perhaps rigid diaphragms would be OK. In fact, some "flexible" deck diaphragms sometimes qualify as rigid under ASCE 7 criteria.

If the building is larger plan-wise then you get flex in the overall diaphragm that affects the mode shapes significantly - i.e. a large flat roofed warehouse.

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[ash060]

The spans for the diaphragm are relatively small. The max span between frames is 70'. The period I was getting used the rigid diaphragms was pretty close to the approximate period I was getting from the ASCE 7 calculations, so I considered that a plus in favor of using the rigid diaphragms.

If you were trying to calculate the period using the flexible diaphragm what would be a good way to go about it?

 

[KootK]

This will probably be of interest even if you don't decide to adopt the methodology: FEMA P1026

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[JAE]

ash060 - I'm not sure how I would model/include the diaphragm. In RISA we can add the diaphragm stiffness to the model using equivalent plane stress plates with a material & thickness that mimics the behavior of, say, a metal deck. Or we can use layouts of "X" braces in plane that also mimic the stiffness.



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[bones206]

You could try changing the dynamic solver to the Ritz solver by going to Global Settings >> Solution >> Advanced. Then run the response spectra analysis in the direction of interest (X, Y or Z). This approach should reduce the amount of local modes you see and give you a good idea of the dominant frequencies.

 

[ash060]

What would be a good way of calculating the stiffnesses of the bracing to accurately represent the diaphragm?

 

[JAE]

What I've done in the past is something like this:

1. Take my general diaphragm size and dimensions and determine a trial deck/attachment design. i.e. 1 1/2" type B - 20 gage deck with #12 screws @ 12" o.c. (36/4) and 2 sidelaps.
2. From this design I can get a G' from SDI or Vulcraft diaphragm tables.
3. Using the general diaphragm size/dimensions (doesn't have to match your building exactly - just be close to the overall dimensions) I then apply a uniform load on the diaphragm based on a close magnitude of wind that will occur on my real diaphragm.
4. With that I can calculate a diaphragm deflection based on my G' value. There are formulas out there that relate the uniform force, q (plf) to diaphragm width, L, diaphragm depth, B, stiffness, G' and deflection.
5. Then in my analysis model I try to lay out a series of uniform X's with a set area and modulus of inertia, E using the same general diaphragm dimensions I used above.
6. I apply the same wind force to this X'd model and see what the deflection is.
7. I adjust the area of the X braces uniformly until my X-diaphragm deflection matches my hand-calculated deflection based on G'.
8. I then use that area and E value for the X's for that direction of wind.

Note that for different B and L values (dimensions of your diaphragm) the deflections and resulting brace sizes will differ so you really may have two different models to work with for the two orthogonal wind directions.



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[KootK]

Your diaphragm has a calculable bending stiffness and and a calculable shear stiffness. Similar to JAE's approach, I'd simulate it with a truss having matching bending and shear stiffnesses.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[bones206]

Couldn't you also use plate elements in the model to approximate the diaphragm stiffness and mass? I think RISA Floor ES has this capability.

Did you try the Ritz vectors? I just tested a large, complicated model where I had 20% mass participation in the X-direction in the first 100 eigen modes. Same structure got 85% mass participation in the X direction with only 20 Ritz modes.

 

[JAE]

bones206 - yes the steps I listed above can be used with member X's or with plane stress plate elements.

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