Rigid Diaphragms

[EngTipper.]

Lets say we have a 2-bay diaphragm width (two wide in E-W direction), shear walls at each grid (3 total) and a seismic force in the N-S direction. In a flexible diaphragm, the diaphragm acts as a deep beam with fully rigid supports. So the end walls take approx. 25% of the load and the middle wall would take approx. 50%.

Assuming a rigid diaphragm, which would you say is the correct method/logic to determine the wall direct shears? Torsional shears would calculated separately, each wall has the same stiffness, and the mass distribution is uniform (UDL only).

a) Take the total load and distribute it according to the wall stiffness. Each wall would therefore take one third of the total load.
b) Using a beam model apply the uniform load and use spring supports all with equal stiffness. In this case, each wall would also take one third of the load since the load is uniform.

a) and b) provide the same result in this case since the load is uniform, but say there is a point load, a small cantilever for the diaphragm, or different bay lengths, they would provide different results.

Thanks,

 

[phamENG]

Your 'a' is a rigid diaphragm analysis. Your 'b' is called semi-rigid. Semi-rigid is by far the most accurate, but is also the most analysis intensive. No diaphragm is 100% rigid and no diaphragm is as flexible as a wet noodle, so they are all 'semi-rigid' in the real world. But for simple structures it's sufficiently conservative to make the simplifying assumptions.

 

[structSU10]

option a is what a rigid diaphragm analysis does if the load is perfectly at the center of rigidity. option b is closer to a semi rigid diaphragm analysis taking the diaphragm stiffness into account unless it was an infinitely rigid beam.

 

[SJBombero]

Option b isn't a semirigid analysis unless the beam/diaphragm stiffness is modeled.

 

[EngTipper.]

SJBombero that is my understanding as well. In option b) if the beam is just any random beam, and does not necessarily replicate the actual diaphragm stiffness, is this ever a recommended model to find the direct shears?

 

[phamENG]

if the beam is just any random beam

What? Why would you pick "any random beam"?

When you said "using a beam model" I assumed you meant considering shear stiffness and calculated deflection of the diaphragm.

 

[EngTipper.]

phamENG understood, what I think I was missing is that since the diaphragm is statically indeterminant (3 supports), the beam stiffness impacts the support reactions, and therefore the beam stiffness must be accurate. So b) would be semi-rigid diaphragm.

A rigid diaphragm would mean that the direct shear wall forces are just a function of the total force based off the wall stiffnesses, not the locations of the walls or diaphragm shape. The wall forces due to torsion is what takes into account the mass offset. Whether the diaphragm is statically determinant or not does not matter for a rigid diaphragm.

What i take from this is that if you have a statically determinant diaphragm, such as a simply supported beam, the stiffness of the diaphragm does not impact the forces on the walls. A rigid or semi-rigid diaphragm would give you the same result in this case.

 

[phamENG]

A rigid or semi-rigid diaphragm would give you the same result in this case.

For resistance of forces parallel to the walls in question and leaving torsion for another discussion, yes.

 

[Alistair_Heaton]

I have similar issues in a nonseismic zone and the local architects are fecking clueless about diaphragms. IN fact they are more clueless than 20 years ago in the uk. this is the abortion of the preferred roof design.

they are wanting 8 raw bolt 12mm anchors every 600mm.. Fecking gimps

 

[Once20036]

I agree that option a is a traditional rigid diaphragm analysis.

I don't think that option b is a valid option, as its not appropriate to assume that all of the walls would have the same stiffness.
A semi rigid analysis would need to accurately account for both the relative wall stiffness and the diaphragm stiffness.

If you have equal wall stiffnesses and equal spans and a very flexible diaphragm, I`d expect that semi rigid analysis to predict something close to the flexible 25/50/25.
If you have equal wall stiffnesses and equal spans and a very rigid diaphragm, I`d expect 19% on the outside, and 62% in the middle.

Edit: I just ran a quick elements model.
With a very flexible beam, I got 28/44/28
With a very rigid beam, I got 33/33/33