Seismic Force Distribution - Flexible Diaphragm

[WiSEiwish]

Hello,

I have a question regarding seismic force distribution to vertical elements in which the the diaphragm is flexible and the plan is irregular. I have attached a sketch as to what I am referring to. My goal is to determine the forces in the three shear walls shown. I am concerned with the forces in the N-S direction.

I understand how to calculate the base shear and then distribute it vertically to the different levels. However, with a flexible diaphragm, the loads are distributed based on tributary area rather than the rigidity of the vertical elements. When calculating the force using the equations in ASCE 7-05 the units are not distributed (k rather than k/ft) therefore I can calculate the seismic force, but, in this example, it doesn't make sense to divide that load by L_T because it would seem that the distributed load between the western edge of the building and the middle wall should be less than between the middle wall and the eastern edge.

In this case, would I calculate 2 different base shears? One would be along the length L_A and the other along the length L_B? I would then be able to transfer those loads across the respective tributary areas and have results that would seem a bit more accurate. If I simply took the force at the level and divided it by L_T and applied it to the whole structure it would seem that the western wall would have an applied force that is higher than it should be and the eastern wall would have an applied force that is less than it should be.

Any thoughts or comments or references to literature that I could look into would be very helpful.

Thank you.

 

[structSU10]

I've looked at is as if the seismic load was an area load, as it is derived from the moving mass of the building, which is usually pretty well distributed. What that would give me is a line load applied to the diaphragm that would be different for the east and west sides in your sketch. I would take the seismic force for the level, divide it by the total area, and multiply it by the depth of the diaphragm in each segment to get the line load on that region.

 

[msquared48]

I agree with structSU10. Same effect as just proportioning the force at that level by the % of the total area for each individual floor diaphragm. Done that before many times.

Mike McCann
MMC Engineering

 

[WiSEiwish]

Thanks. That seems like a very simple solution, and the numbers work out to what I was anticipating that they should be. I guess I was over thinking this one.

 

[mike20793]

So are you saying that for the western shear wall, you would take the distributed area load and multiply it by its tributary area, bA*LA/2 to get the load on the wall? What if there were two segmented shear walls instead of one? Are you just looking at the tributary area of each wall within the wall line or the total depth of the region? Thanks.

 

[mike20793]

I attached an example. Am I understanding this correctly? The force on SW1 would be Few distributed across the total building area multiplied by (16 ft + 7 ft/2)*(5 ft + 13 ft/2). Basically your just looking at the tributary area of the supported diaphragm for each shear wall. Is that correct? Thanks for the help.