Double Notched Diaphragm, Force at 2nd Transfer Diaphragm

[CLT49er]

I have a metal deck diaphragm that has a double notch on one end. I am using the methodology in "The Analysis of Irregular Shaped Structures" by Malone and Rice for determining the shear and chord forces in the diaphragm (I know the book was written for wood structures but the analysis to determine the forces should be similar). Example 3.1 in the book outlines the process for a diaphragm with a single notch on one side. However, the diaphragm I am analyzing has a double notch and the author does not provide any examples for this condition. I have calculated the chord force at line B and analyzed the first transfer diaphragm to determine the reaction force at line C. What is not clear to me is how to determine the load on the 2nd transfer diaphragm. Is it just the chord force at line C or is it the chord force plus the reaction from the first transfer diaphragm? I am thinking that it would be the chord force plus the reaction from the first transfer diaphragm. Does anyone who is familiar with this book have any insight on this? I have attached a sketch of my specific case.

http://files.engineering.com/getfil...2-bd6e-41b6-9d3a-bc01e211a75f&file=Sketch.pdf

 

[XR250]

Which way are the joists running? If left to right, I would try to use them as a chord at the edge of the rectangular area (72' x 153' +/-) and forget the rest of the deck except as a straight load transfer to the rectangular diaphragm.

 

[CLT49er]

The joists span from A to D (there are a couple of interior bearing walls not shown). The joists are parallel to the shear walls shown as SW. What is left to right to you just to make sure I am interpreting your response correctly?

 

[KootK]

If there's an interior framing line that can serve as the boundary element for the simplified diaphragm then XR250's method becomes very attractive in my opinion.

The sketch below is my attempt to handle it the Malone way. Note:

1) I simplified things by assuming 100%V is carried all the way back to the full depth diaphragm. You can step V as you go if you're up for a little more math.

2) I imagine things as little trussed panels. That helps me for some reason.

3) With the forces as shown, you should be able to work out the horizontal shear in each trusseed panel and then, via the complrmemtary shear stress principle, the vertical and horiziontal shear stresses in each panel.

4) Once you know the shear panel stresses, you can load up your drag struts like Malone does.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[CLT49er]

KootK,

So it sounds like you simplified the analysis by assuming that the shear diagram is rectangular vs triangular. With the actual triangular diagram the V you show at the bottom left corner of panels 2 and 3 would become a function of the distance from the shear wall (V@notch = V@shearwall - w*x), similar to the example in the Malone book, correct? The reaction force from the first panel is the chord force in the diaphragm at the notch. This force loads the 2nd panel in your sketch. The reaction from the 2nd panel shown in your sketch, (V*B+V*A*D/D)/(D+E), can be broken up into two pieces. The first part is V*B/(D+E), which is the chord force in the original diaphragm at the 2nd notch (when calculating the V from the correct location on the triangular shear diagram), and the second part is (V*A*D/D)/(D+E), which is the reaction force from the transfer diaphragm under V*A/D only. This sounds like what I was thinking, albeit in maybe a slightly different way since I was breaking the analysis into two separate pieces and then putting them back together the way the book does. The result appears to be the same although I think your diagram illustrates it better. I just wanted to confirm that my thinking was correct before going through all the math.

I thought about XR205's way but I don't really have any framing at that location that can act as a proper chord. There are several interior CMU bearing walls that will have a bond beam at the top that in theory could act as a chord. However, since the shear force in each interior shear wall is so low in the longitudinal direction I was planning on transferring the shear from the diaphragm through rollover in the joist seats. Without a continuous connection between the diaphragm and the CMU (more than just the seats which are about 6 ft apart) I feel like if a rip started at one of the notches in the diaphragm south of the chord it could still propagate past the CMU bond beam chord and through the rest of the diaphragm.

 

[KootK]

So it sounds like you simplified the analysis by assuming that the shear diagram is rectangular vs triangular.

More or less I guess. I assumed that the peak value of diaphragm shear would be maintained from the edge of the diaphragm through the steps. I usually find that additional accuracy is unwarranted. That said, it's easy to be more accurate if you wish. Just do this:

1) Change V on the right edge of panel three to the actual value of the diaphragm shear there.

2) Add point loads to the right sides of panels one and two to represent the additional shear being delivered there.

Often, I'll just go and model the truss assembly as I've shown it in SAP, RISA, etc. It takes no time at all and, once modeled, you can just pull your panel shear values out of the model directly. The shear stress in each panel winds up being F_diagonal / L_diagonal.

With the actual triangular diagram the V you show at the bottom left corner of panels 2 and 3 would become a function of the distance from the shear wall (V@notch = V@shearwall - w*x), similar to the example in the Malone book, correct?

Sounds about right. As long as you wind up with a complete set of forces that's statically admissible, I think that you're good to go.

I thought about XR205's way but I don't really have any framing at that location that can act as a proper chord.

You may be right. If you post a more detailed sketch of your framing plan, we'll happily review the situation with you.

Without a continuous connection between the diaphragm and the CMU (more than just the seats which are about 6 ft apart)

The rollover business doesn't bother me. Again though, we'd need a better feel for what's going on. There's a pretty good chance that the interior CMU walls are going to alter what's going with your diaphragm whether you choose to acknowledge it or not.

I feel like if a rip started at one of the notches in the diaphragm south of the chord it could still propagate past the CMU bond beam chord and through the rest of the diaphragm

Yeah, I hear 'ya. And, to some extent, I agree. There's a tendency these days to try to design complex diaphragms to the same level of detail that one might design a notched steel beam etc. I feel like we're taking it too far in many instances. There are many aspects of "real" diaphragm behavior that even the Malone methods don't account for explicitly. Diaphragm design is and will always be a rough approximation. As long as I can demonstrate a reasonable expectation of global diaphragm strength and stiffness, I don't sweat the small stuff.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[XR250]

What about adding a 4x2 tube steel chord in the valley of the roof deck?