Shear Induced by Roof Diaphragm in Balloon Framed Walls with No Second Floor Diaphragm, Hot Roof

[the Paper Owl]

Good Morning everyone,
I am in the process of the shear design for an A-Frame residential unit and am wanting to model the shear response of the structure properly. At one end of the unit (Elevation A), the gable end wall is balloon framed and is not connected to the second floor platform (as it is the area where the stairwell is accessed and showcases the hot-roof volume ceiling). My questions are as follows:

1. When modeling the response of the structure from the lateral wind on Elevation A, there is no floor diaphragm to cause racking. There are however the two perpendicular roof diaphragms (each terminating at the first floor sill plate). This wall will be fully designed for a deflection failure state in which it will follow suit with the qualms of the dreaded window gable end wall but I am however unclear if each roof diaphragm (18:12 slope - 2x12 rafters, blocked) will essentially act in the same regards as a floor diaphragm and cause point loads at the locations that are resisted by the diaphragm (the top of each perpendicular dropped beam where the rafters are lapped and spliced). I have been assuming this as the case, and designing the connection at each dropped beam to withstand the shear induced by each point load as well as the desire for the beam to withstand being pushed out of plane (shear transfer at the PSL column supporting it and PSL column bracing for the bending that would be caused).

2. Elevation B has a second floor platform intersecting the "gable / salt box" end wall, but has a large volume / cathedral ceiling. My preliminary design is using the area for the lateral wind load - with a lower boundary line at the midpoint of the first floor wall, extending to the entire ridge of the second floor. This is assuming that given a strong wind event, each cathedral roof diaphragm, along with one perpendicular wall will "be along for the ride" and place a lateral point load at the connection of my top plate (at the second story platform). My design follows ( B ) on the sketch. See sketch for the visualization.

Thank you in advance.

 

[KootK]

For what it's worth, I feel as though you've done a pretty great job of analyzing a very complex situation here.

This wall will be fully designed for a deflection failure state in which it will follow suit with the qualms of the dreaded window gable end wall but I am however unclear if each roof diaphragm (18:12 slope - 2x12 rafters, blocked) will essentially act in the same regards as a floor diaphragm and cause point loads at the locations that are resisted by the diaphragm (the top of each perpendicular dropped beam where the rafters are lapped and spliced).

The roof certainly will act as a diaphragm. Whether or not we label that a roof diaphragm, a flood diaphragm, or a tilted shear wall is immaterial: the fundamental mechanics of it's behavior remains the same.

If the dropped beam lines will be stabilized laterally by attachment to the second floor deck beyond, then I agree that they will act as point loads / supports on the roof diaphragms.

My preliminary design is using the area for the lateral wind load - with a lower boundary line at the midpoint of the first floor wall, extending to the entire ridge of the second floor. This is assuming that given a strong wind event, each cathedral roof diaphragm, along with one perpendicular wall will "be along for the ride" and place a lateral point load at the connection of my top plate (at the second story platform).

Yes, I think that you have that right. That said, I'd probably state it a bit differently as:

1) I would use model A to get the wind induced line load applied to the second floor deck by the end walls.

2) I would use model A to get the "point load" that the roof diaphragm applies to the second floor deck where it touches down. That point load will also be a line load running perpendicular to the diaphragm span but I get your meaning when you call it a point load.

If you have an isometric view of the building, or at least some building elevations, that would probably be a help to folks trying to understand this setup. Your sketches are excellent but its a pretty complex, 3D thing.

 

[the Paper Owl]

I appreciate the response KootK, I have spent a substantially amount of time within this thread over the past few years and will say that I have learned much from your posts / answers in various other structural discussions. The design in all of its glory (attached below), both 3D and Structural. Note that there are aspects of the structural model that are misrepresented (sill / header plates for skylights will be plumb and not tilted as shown - hopefully preempting any quick fire weak axis bending comments ). I have to say that this home (and its little brother being built next door) have been great teaching projects where I find my time split during the day either reading / researching and detailing.

In regards to your response. Each beam will be stabilized through a combination of the connection to the second floor deck / diaphragm (making sure that each bolt & nail can withstand the unit shear being transferred) as well as internally braced within the wall. I am treating the top end of the PSL column (where the point load / shear line load begins) as a cantilevered beam in need of bracing and proper restraint to the grout filled CMU wall below.

 

[KootK]

Thanks for the isometrics, they are a great help. I think that we are substantially on the same page with this.

...and will say that I have learned much from your posts / answers in various other structural discussions.

And thanks for that as well. Hearing it made my day. Sometimes I shudder to contemplate the number of words / sketches that I've probably typed here over the last two decades. It feels better hearing that the effort may have benefitted more people than just the OP's of those threads.