Seismic Force Distribution and Eccentricity

[jayson34]

Hi everyone,

Please let me know if my understanding below is correct. Assume the sketch is a one-story concrete building, and the relative rigidity of the walls parallel to the force is equal.

The seismic force should go through the center of mass tributary to the (roof) diaphragm level. For a layout like this, the center of the effective mass is skewed to the north as the walls normal to the force are located up there. Thus, there would be an (small) eccentricity between the center of mass and the center of rigidity.

Also, the weight of the walls parallel to the force should be excluded from the effective seismic weight in the direction under consideration - because the inertia force on these walls does not go through the diaphragm. To design these walls, I need to include the diaphragm shear located on the top of the wall and the inertia force (Cs x weight of wall) located at the mid-height of the wall.

Thanks,
Jayson

 

[KootK]

That sounds spot on to me with respect to how most engineers would handle this.

...because the inertia force on these walls does not go through the diaphragm.

That makes sense for this building and will make sense for many buildings. For more complex buildings, sometimes the inertial weight of the walls can move around the system a bit. The most general way to think of it is as if the shear from all sources gets reshared at every level based on the stiffness of the VLFRS stiffnesses at that level.

 

[ChorasDen]

I agree that your approach makes sense, but I'm a bit lost about how the shear walls dramatically affect the center of mass in your sketch? Is the rest of the system open without any wall weight?

Don't forget you also need to include the effects of accidental torsion per 12.8.4.2 of ASCE 7.

 

[WARose]

Also, the weight of the walls parallel to the force should be excluded from the effective seismic weight in the direction under consideration - because the inertia force on these walls does not go through the diaphragm.

I've never done this. I've always included everything that ties into the diaphragm as part of the seismic dead load. I have seen people do that....but not me.

 

[jayson34]

Thank you everyone for your input!

 

[lexpatrie]

Give one of the older SEOC Blue Books a scan. There are also the newer ICC Seismic Design Examples that contain "their" approach so you can at least refer to it.
Structural Seismic Design examples and whatnot

2019 SEAOC Blue Book
Yeah if you include the walls in with the floor weight, Center of Mass (CM) should be slightly up from the exact geometric center of the building. I'm not sure that's how it's usually done, but given you are asking about adding the weight of the walls to the center of mass, that's correct. To me, the walls resist the load so you'd add the wall seismic load directly into the wall, rather than having it go "upwards and downwards" to the diaphragm then back into the wall. It doesn't have to do that, physically.

Rigid Diaphragms by Louis Yaw at Walla Walla explains it pretty well, if you ask me. I emailed Louis a while back about the way differing wall thicknesses/strengths change the equations and he revised it after that.