Shear wall fixity 1

[bouk715]

I am hoping someone can clear this up for me...

Let's say there is a 2-story building with a concrete-filled diaphragm 2nd floor and metal deck roof. Shear walls span from floor-to-floor and are connected to the underside of the steel floor/roof beams. Are the shear walls designed as fixed piers on both floors or are the shear walls spanning from the second floor to the roof considered cantilevered since the roof diaphragm is flexible? Also, is reinforcing sized based on overturning of the entire system (if the walls are vertically in the same plane from floor to floor-i.e. no vertical/plan offsets). I wouldn't think so, and the reinforcing is only sized for the moment in a fixed pier at each floor. Thanks.

 

[14159]

The shear walls should be designed like cantilevered columns, supported only at the foundation. For this, it makes no difference whether the diaphragms are rigid or flexible. A rigid diaphragm is rigid only for horizontal bending and shear, not for bending about a horizontal axis. The only way to restrain your shear for bending about a horizontal axis to add a link beam, outrigger, or other serious structural element that doesn't apply to your case.

Your question indicates that you need to start a thorough study of lateral load paths. There are many books on the subject. Breyer's wood book comes to mind immediately.

DBD

 

[strucsteel]

I think I understand something of what you're talking about, bouk715. I've seen books and pamphlets that talk about fixed-fixed and cantilevered shear walls, and they do seem to guide you in the direction that you're describing, where the top story is considered cantilevered and the others are fixed-fixed. It does appear that the thought may have something to do with a rigid vs. flexible diaphragm, but I don't think I've ever seen that said explicitly. I found something in "Design of Reinforced Masonry Structures" by Narendra Taly that may provide some guidance to your question. On page 7.4, it reads "In case of a reinforced masonry wall, the practice is to consider shear walls in one- or two-story buildings as cantilevered; whereas in a multistory building, the segments of the walls between stories above and the first story are fixed both at top and bottom."

On the other hand, I must respectfully disagree with Dr. Taly and say that I have always considered shear walls to be cantilevered on each level. I do not see how the lower stories can be considered to be fixed-fixed, since this analysis assumes that the top of the shear wall can develop a moment to resist the lateral load. If it can, then to what does it transmit the resisting moment? It could only transmit it to the story above, and that only leads up to the top of the building and a dead end.

Regarding your question about reinforcing, I usually consider each pier on each floor individually, with the shear wall at the top story designed as a cantilever with only a point load at its end, and all shear walls below designed for a point load (story shear) and a point moment (the moment developed at the base of the shear wall immediately above to resist overturning) at their ends. I hope this is of some use.

JS

 

[bouk715]

Thanks, strucsteel; that is basically what was confusing me. I had seen in some texts that they treated shear walls extending from floor to floor as fixed-fixed. But then that begs the question that you raised: where does this moment at the top of the wall go? I agree with your analysis (story shear and concentrated moment) and is what I have used in the past. I just wanted to know if I was missing something. Thanks again.

 

[jike]

Could it have something to do with the weight of the wall being heavy enough in the lower stories to develop the fixed fixed condition? The cantilever action is only for the upper stories of a tall building or for small buildings.

 

[strucsteel]

It is possible that the weight of the wall may have something to do with it, jike. Clearly, Dr. Taly (among others) feels confident enough in the validity of the approach to put it into print, but I just can't get past the roadblock of where the reisting moment at the top of the wall would go. If we were to make up a wall that had a 20 k/ft floor load along its length, and apply a moment which was equivalent to a maximum of 1 k/ft at each end of the wall, then it would probably be reasonable to say that the condition "appears" fixed at the top, since the loading by the transient moment is so small compared to the constant gravity effects and the resulting displacements at the ends of the wall are negligibly affected by the moment as opposed to the gravity loads. Even so, if we were to isolate the wall at the underside of the floor, we'd be looking at a uniform downward load from the floor with a centroid at the wall center, and the transient moment, and that's it. That just doesn't add up to me; it sounds unstable, like the floor must be rotating to expend the rotational energy of the moment. If that is true, however, then the top of the wall is in fact rotating anyway, and the fixed (by definition, no rotation) top condition has been invalidated. I guess that either there is not much in the way of a factual basis for this approach, and consequently Taly could only give it one sentence and say "the practice is...", or it is so obvious that it should not require explanation, and I am unfortunately too dense to be able to see it.