Lateral Load Distribution Per Floor

[runcc]

Assume a 2 story building. The roof is a flexible diaphragm and the second floor is a rigid diaphragm. There is a 50 kip lateral load at the roof and a 50 kip lateral load at the second floor. At the roof the diaphragm transfers half of the lateral load to a braced frame on each side of the building, so each braced frame resists 25 kips of lateral load at the roof elevation. Assume that the left side braced frame at the second floor level is 4 times stiffer than the right side braced frame so that the left side braced frame would take 80% of the lateral load and the right side braced frame would take 20% of the lateral load (ignore any torsion). Does the load from the roof stay in the braced frames so that the left side braced frame resists 25k + 40k = 65K and the right side braced frame resists 25k + 10K = 35k, or is the entire lateral load redistributed 80/20 so that the left side braced frame resists 80k and the right side braced frame resists 20k?

 

[KootK]

LFRS = Lateral Force Resisting System.

Technically, it's a do over at each level with all loads coming in from above getting dumped into the diaphragm where they land and redistributed to the LFRS below that level according to the stiffnesses of the load paths to those LRFS. This is the subtler version of the transfer diaphragm condition wherein the stiffness distribution of the LFRS changes even if no LFRS are discontinued entirely.

In practice, there will be connection flexibilities that make the draw off of LFRS demand less certain than our models would suggest. Many engineers will consequently take a conservative approach to estimating how much that draw off is when designing the LFRS below.

 

[r13]

The shear distributed from the upper floor becomes applied load on the bottom floor, it is in addition to the load on the lower floor, and then distributed according to the rigidity of the lower floor supports. It will be much clear, if you have identified the center of rigidity of the lower floor.

 

[runcc]

I appreciate the reply's, and they match what I have seen in design guides, but from a gut feeling perspective it just doesn't feel right to have less load in an upper story brace than in a lower story brace that is directly beneath it. There could be a direct load path from upper brace to lower brace to ground, but instead of taking that direct load path some of the load from the upper brace could transfer from the upper brace 200' across a diaphragm into another lower brace on the opposite side of the building and then into the ground. Its just hard to picture that happening in my head.

 

[r13]

In general, the effect of gravity is accumulated from top down. The weight/force can't climb, the force at the lower floor will be felt by the upper floor at the joint interface only. But in a sense, the upper floor might have suffered more force than if the lower floor doe not have stiffness irregularity. You can verify the phenomenon with a simple 3D computer model.

 

[KootK]

You'll see a lot less of this effect when diaphragms are modelled semi-rigid rather than rigid. The diaphragms themselves will add flexibility to the load paths that would cross the diaphragm.

 

[JLNJ]

It sounds like your gut is telling you that your diaphragm isn't ideally rigid, and since the one line is braced above and below, the force "stays" in that brace line. This is probably true where you have concentrically braced frames since they are so rigid.

The exact behavior is hard to predict. I suppose you could envelope both cases - whether the forces "stays" in the row or "leaves" and goes to a different row based on stiffness. You certainly don't want to under-design the other rows!

 

[runcc]

I am definitely leaning towards enveloping the solution as you have suggested JLNJ.

 

[KootK]

To be fair, I don't believe that your extreme example was set up accurately which is why I intentionally did not respond to it explicitly. As you have described the system, you'd still have a 50/50 distribution all the way down regardless of the relative stiffness of the left and right braces. The 80/20 business is fiction for this particular example. Obviously, I understood the real intent of your question and responded accordingly.

 

[KootK]

The only way that I can think of to get the 80/20 would be to have both a rigid diaphragm and a pair of rigid LFRS oriented perpendicular to the load and forming a rigid torsion couple. That would indeed be a pretty extreme setup.