Seismic Base Shear Question

[LoneStarEngineer]

I have a building which has a vertical combination of seismic force resisting system. The lower structure has a R=3.25 and upper structure has R=5.
Per 12.2.3.1 (ASCE 7-10), the R value for upper can be used for the upper portion and R value for lower can be used for the lower portion. The forces from the upper to lower need to be increase by (R-High/ R-low). 2- stage analysis cannot be used since the period factor is 1.25.

So if Cs is calculated for the upper portion and the lower portion separately, how is the base shear calculated for the lower portion?
I calculated the base shear for the upper portion which would act at the 2nd floor level (Taking 2nd floor as base). I guess I am a little confused since the code already amplifies the forces at the 2nd floor which is base for the upper portion.

 

[EngineerRam]

Wouldn't the base shear for the lower portion be: (base shear for upper portion)(R upper / R lower) + (base shear due to weight tributary to lower diaphragm, using lower R)

 

[LoneStarEngineer]

So normally, if there is no vertical combination, the shear at the 2nd floor level is the same as the base shear and you would distribute your story shears accordingly. But in this case since the code says to analyze the two portions separately, you have a Base shear value at the 2nd floor level from the upper portion and you also have a base shear value for the lower portion. The Lower portions base shear value is greater than the amplified shear at the 2nd floor (say 602 kips at ground level and 408 kips at 2nd floor level).

So do you take the Ground base shear value to distribute the story seismic forces for the whole structure?
Or do you again separate the two structures and distribute the story forces for the upper and lower individually?
If doing it individually, what shear would the 2nd floor level need to be designed for? The amplified base shear (408k) or the ground base shear (602k)?

 

[EngineerRam]

This is a really good question. To me, it wouldn't make sense to distribute the "amplified" portions of the base shear to the lower levels, as they originated from the higher levels. This does not seem to be covered in the code, but rationally I would think that the base shear at the ground level can be distributed by multiplying the effective seismic weights of the stories above (where there is a higher R value) by the ratio of R values.

 

[JAE]

Could it be like this:
1. Use the upper design coefficients to determine Cs.
2. With Cs you determine base shear V (base shear at the bottom of the whole structure)
3. With base shear V you use section 12.8.3 to vertically distribute the story forces up the whole building.
4. With these story forces, you analyze the whole structure but design only the upper portion elements.

5. Now change the design coefficients to that of the lower section and determine a second Cs value (call it Cs2)
6. Cs2 is simply an elevated number directly proportional to R.
7. Determine a second base shear value V2 (base shear at the bottom of the whole structure)
8. With V2, distribute story forces up the whole building per 12.8.3. Note again that these forces are simply directly proportional to the R values - Fx(R(upper)/R(lower))
9. With these elevated story forces, you analyze the whole structure again but only design the lower portion elements.

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[LoneStarEngineer]

Thanks EngineerRam and JAE.

JAE- That is a very good interpretation of the code and it makes sense. So, the code requirement to amplify the lower structure forces are already taken into account when carrying out the second story seismic distribution and there would be no further need to amplify the forces. I think the code should just eliminate the statement where it tells you to scale the forces from the upper portion as it already tells you to use the lower systems coefficients to design the the lower system.

 

[SAIL3]

this sounds like a soft-story problem...not a good condition in a seismic event.....I guess the question is how much amplification of seismic forces would this cause in the lower structure and does this amplification carry over to the second story......IHMO, the first(soft) story would drive(affect) the whole structure and this amplification would carry over into the second story....

 

[JAE]

The R was smaller for the lower section - so not a soft lower story.

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[DETstru]

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)

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.

 

[JAE]

DETstru,
You can't do a two-stage analysis like you suggest - per the OP, that wasn't allowed.

And per 12.2.3.1 (which is NOT a two-stage analysis) you simply are using two full analyses each with two different R values to get design forces for the separate portions of the building.

A building's response fully depends on the WHOLE building behavior under a static load - whole building period, whole building stiffness interaction, relative values of mass and height (vert. distribution).

What you are suggesting is dividing the building into different analyses which turn it into a two stage process - not allowed unless you meet specific requirements of 12.2.3.2.

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[DETstru]

Whoops... missed that line about no 2 stage allowed. I'll edit. thanks!

 

[LoneStarEngineer]

Thanks everyone.

Here is another code requirement that I am trying to verify. My building is a 4 stories of wood over Non-composite steel 2nd level Podium. I have an out of plane offset irregularity (Type-4) as the vertical LFRS is not continuous (which is typical in podium type structures).

Per 12.3.3.3, the seismic shear at the 2nd level needs to be increased by the over strength factor (in my case it being 2.5).
Is this requirement applicable if my forces are already being amplified per the requirements of 12.2.3.1?

Appreciate your responses.

 

[DETstru]

12.3.3.3 is for "Elements Supporting Discontinuous Walls or Frames", keyword "Elements".

The commentary for 12.3.3.3 is very good and has the answer you're looking for.

 

[LoneStarEngineer]

Thanks.

Correct and I have read the commentary.. But my shear walls from the upper portion are supported by the 2nd floor podium slab which is supported by steel beams. So, in this case the slab and the supporting framing needs to be designed for over strength and ultimately increasing the shear at the 2nd level by the over strength factor would achieve this. Unless I am missing something here?

 

[DETstru]

The beam is designed for the load transmitted to it by the shear wall that rests on it using the overstrength load combinations.

The forces coming from the wall to the beam are these forces that JAE noted:

1. Use the upper design coefficients to determine Cs.
2. With Cs you determine base shear V (base shear at the bottom of the whole structure)
3. With base shear V you use section 12.8.3 to vertically distribute the story forces up the whole building.
4. With these story forces, you analyze the whole structure but design only the upper portion elements.

So the forces at the base of the wall that you determined from JAE's step #4 are inputted into load combinations with overstrength and used to design the beam.