Sloped Diaphragms

[abusementpark]

Has anyone seen a good textbook treatment of sloped/gabled diaphragms? It seems like they get analyzed the same as horizontal diaphragms, but when you sit down and think about the statics/equilibrium that must occur, it seems to me like there must be some vertical load that gets induced into the roof system for these sloped diaphragms to continuously transmit horizontal forces across ridges and valleys, also simply due to the angle of the diaphragm member itself.

Have these actions been historically neglected?

 

[a2mfk]

Funny, I was just pondering the same thing a few days ago. I don't ever remember seeing this discussed in any texts.

I think with pre-eng truss systems, there is a lot of redundancy in that some of the horizontal axial load (from the lateral wall loads) is taken into the ceiling diaphragm and the trusses themselves. Out-of-plane forces are resisted by the entire truss system, not just the diaphragm, though this is not considered in design. But the problem becomes a little clearer if you think of a ridge beam and rafter system, vaulted with no ceiling or no collar ties.

Since a diaphragm is modeled as a deep beam, you actually have a V-shaped deep beam (rotated 90 degree), a folded plate if you will. One side of the plate is essentially taking the positive pressure from the walls, the other the negative pressure from the opposite side. And this is where it gets a little complicated and foggy to me without sketching it out...

I have however seen gable end designs discussed. Since your diaphragm force is at an angle at the top of the gable, you have to derive the vert/horiz force components and design for overturning and uplift (usually only 1 ft of trib). In my calcs for most residential applications if you put straps at every vertical member (2ft oc) this is more than adequate.

 

[csd72]

I believe that when you add the component up of the wind pressure on the roof and the components of the sloped reaction you end up with basically the same reaction anyway.

Just remember that if your roof is 20 degrees off horizontal then your roof pressures are 20 degrees off vertical.

 

[msquared48]

I would negate the vertical carrying load capacity of the diaphragm when designing the ridge beam unless the pitch is extremely steep - like 1:1 or higher, but account for the vertical reactions in the rafters at the connections.

Mike McCann
MMC Engineering
Motto: KISS
Motivation: Don't ask

 

[BAretired]

I don't see any mystery about sloped roof diaphragms taking lateral load. The horizontal force has to be resolved into components, not unlike members of a truss.

BA

 

[abusementpark]

But the problem becomes a little clearer if you think of a ridge beam and rafter system, vaulted with no ceiling or no collar ties.

Since a diaphragm is modeled as a deep beam, you actually have a V-shaped deep beam (rotated 90 degree), a folded plate if you will. One side of the plate is essentially taking the positive pressure from the walls, the other the negative pressure from the opposite side. And this is where it gets a little complicated and foggy to me without sketching it out...

Exactly. It seems me for the case of a gabled diaphragm, since we must assume that the diaphragm is only taking in-plane loading, there must be some vertical load induced into the roof structure to accommodate the diaphragm force direction change at the ridge.

I have however seen gable end designs discussed. Since your diaphragm force is at an angle at the top of the gable, you have to derive the vert/horiz force components and design for overturning and uplift (usually only 1 ft of trib).

If you remember where you have seen this discussion, please share as I would be interesting in checking it out.