Note: this is actually a 2-stage analysis. See JAE's response below.
Here's my typical approach:
I'm going to assume you have 5 stories or R=5 built on 2 stories of R=3.25
1) Perform the ELF calc for the top 5 stories with R=5.
Only consider those 5 stories in your calculation.
[Note: The story forces you generate with this ELF are used to design the upper portion.]
2) Find the base shear at the "base" of that "5-story building".
3) Multiply by (5/3.25) and set it aside.
4) Perform the ELF calc for the bottom 2 stories with R=3.25.
Only consider those 2 stories in your calculation.
[Note: These story forces (along with the amplified base shear from above) are what you design the lower portion with.]
5) Find the base shear at the "base" of that "2-story building". (this is the actual base of your combined building)
6) Add the amplified base shear from above to this base shear. That's your full building base shear.
JAE,
I don't believe your last line is correct (#9)
JAE said:
9. With these elevated story forces, you analyze the whole structure again but only design the lower portion elements.
Doing it that way doesn't change the base shear but it changes how the load gets to the lateral load resisting system in the lower system. Doing the ELF for the full building with the lower R "sends" some of the force that would have originated from the mass of the lower system diaphragms to the upper system diaphragms. Then it comes back to the lower system from the upper system as the amplified load. Though you're not designing the upper system with those forces, it changes how that load is distributed in the lower system diaphragms.
Imagine offset shear walls or braces that don't stack on whatever lateral load resisting elements are in the lower system. Instead of that story force coming from the mass of the lower system, it comes from the upper system and has to be transferred to the lower system.