Stepped Shear Wall - Vertical Irregularity

[ChiEngr]

Hello,

Apologies if this question may be simple, but I am trying to wrap my head around the following concept.

I am working on a fairly complicated project. It is a 100 year old, single story building. The floor to roof height is just shy of 30 ft. The owner wants to add an adjacent 2 story building to the east of the existing building to be used for office space. The owner thus wants to convert the single story existing building into a two-story space. I am designing a new second floor within the existing building footprint, but keeping this second floor structure isolated from the perimeter brick masonry walls (multi-wythe). In order to integrate the new east building addition into the existing building footprint, the owner wants to demolish the existing east wall to create an open space and seamless integration between the two buildings.

The existing roof diaphragm is a solid precast concrete slab. Thus, the slab is a rigid diaphragm. By removing the existing east shear wall, the center of rigidity moves far west to the existing west brick masonry shear wall. In order to prevent the remaining walls from seeing an increase in load due to the east wall removal, we plan to introduce new concrete shear walls between the ground floor and new second floor and between the new second floor and the roof. The new shear walls will be worked into the architectural concept/programming.

The new shear walls are not of equal length however; the bottom run of wall is 15 ft, and the top run of wall above the second floor is 10 ft. After modeling this wall configuration, I found that the new shear wall is picking up as much load as the original east wall to be demolished. This is what I was hoping to achieve. I next tried to see if the shear wall could be cut down to 10 ft in length over its entire height. The amount of load going to this wall decreased significantly. I am trying to understand why this is the case. I am probably overthinking this, but why does the bottom run of wall influence the stiffness of the top run of wall given that the new second floor level is also a rigid diaphragm, tied to other lateral force resisting elements.

Thanks for your help; sorry if the above was wordy or unclear!

 

[KootK]

The key, I feel, is to recognize that the stiffness any element of your lateral system at the second level is a function of the stiffness of that lateral element at all of it's levels.

Imagine a simplified, 2D structure like the one shown below. Just columns sharing a lateral load with one of the columns stepping to a larger cross section at the second floor level. You can see that the load apportioned to the the top of the middle column will be affected by the stiffness of that column at the first floor, right? I would argue that your situation is analogous to this.

I've struggled with this at times too. Much of the literature that contains examples of hand calculated lateral load distributions tends to deal with simplified situations where it is appropriate to look at the lateral system one level at a time, in isolation. That can create the impression that you can do that will all building systems which is incorrect. Or, at the least, it did for me.

I actually find this to be quite difficult to explain well. If I've not managed to be helpful on this, let me know and I'll give it another go.

 

[ChiEngr]

Koot,

Thanks for your response and I am sorry it has taken me so long to reply (I have been on vacation). What you have provided makes a lot of sense and has cleared things up for me. Thanks again!

 

[KootK]

No worries ChiEngr. I'm glad to have been able to help and I hope that you had a fun vacation.