Wind loads through roof gable diaphragm/drag truss.

StrEng007 · Sep 19, 2017

I know there are many threads regarding this question... but I can't seem to pin down a final answer on this one.

While tracing out the load path for MWFRS wind, into a diaphragm then lateral system, the question about how these loads make their way to supporting shear walls came up.

My general question here is how loads travel through a diaphragm that is not flat. There are (7) questions numbered below.

Let's start with the windward and leeward walls of a typical rectangular structure with a flat roof.
The half wall height will lend itself two (2) loads, one positive (towards) the diaphragm and one negative (away from) the diaphragm. The generic textbook method sums these two loads as a linear load and applies it directly to the diaphragm of a flat roof. No issues there so far. Since the diaphragm's plane is at a 0° angle, I see this load being transferred through the diaphragm, where the w(diaphragm) = (WW Pressure)x(1/2 wall height) + (LW pressure) x (1/2 wall height). [I'm not making reference to any internal pressure coefficients to keep this as straightforward as possible].

Example
(WW Pressure)x(1/2 wall height) = 300 lb/ft
(LW pressure) x (1/2 wall height) = 300 lb/ft
w(diaphragm) = 600 lb/ft

Now let's suppose the roof was not flat, but instead a gable with a 4:12 roof pitch (18.4°). Plywood sheathing is used on the top of the roof trusses and I'm assuming no ceiling diaphragm action below the truss bottom chords. Load is intended to travel through the roof sheathing, into a lateral resisting system (i.e. drag truss to shear wall, etc.).

Here is where most textbooks don't go into detail. Since the roof is no longer flat, I don't see how the w(diaphragm) can be determined as previously calculated. Now the loads on the system are travelling through a plane that is inclined and will have (2) force components associated with it (x-horizontal and y-vertical). The actual projection of the diaphragm will be the resultant... Therefore, in order to resist the overall x-horizontal movement of both walls, the linear diaphragm load through the windward portion of the roof diaphragm is:
w'(WW)= [600lb/ft]/[2cos18.4°]

and the leeward wall,
w'(LW)= [600lb/ft]/[2cos18.4°]

Here, the overall roof is split into separate planes to illustrate the resultant analogy. In reality, these should act as one combined unit with proper blocking etc... That is a whole separate topic of its own.

Over a wall length of 20 ft (the structure is 20 ft long parallel to the ridge, with a lateral system at each end) the diaphragm will have the resulting loads:
x-component= (20ft/2)x (2[600lb/ft]/[2cos18.4°])x(cos18.4)= 6000lb

Notice how this is equal to = (600lb/ft)x(20ft/2)= 6000lb

So far so good. By comparison, the values for the x-horizontal force are the same for both flat roof and gable roofs.

HOWEVER:
There will be a y-component from the WW panel=(20ft/2)x(1[600lb/ft]/[2cos18.4°])x(sin18.4)=+1000 lb

and the LW panel = (20ft/2)x(1[-600lb/ft]/[2cos18.4°])x(sin18.4)=-1000 lb

1.Where does this get distributed along the length of the roof? For a drag truss, these loads would be added as a couple at the ends of the truss down into the vertical portion of the lateral resisting system. What is done here?
2. Is this vertical component of the force making it's way into each supporting truss as a vertical reaction?
3. If that is the case, then is every truss by nature a drag truss of sorts? Since the horizontal reaction at the truss is inadvertently being dragged through the chords to resolve the forces.
4. Is this component of the force just ignored?

Now, for the next component of loading... the wind normal to the roof's surface. The normal load on each side of the truss can be split into a horizontal and vertical force. For a POSITIVE Windward and NEGATIVE Leeward scenario, the roof will see the following (wind load perpendicular to ridge).

Windward roof:
Horizontal wind from west to east
Vertical wind pushing down

Leeward roof:
Horizontal wind from west to east
Vertical uplift reaction

Here, I would take the vertical reactions out in the vertical system of the structure. However, there is still a horizontal component that wants to move the roof truss from west to east.

5. Is this horizontal load to be added to the horizontal reactions from the windward and leeward walls, calculated with the same procedure above?
6. Will the roof have uplift from wind normal to the surface IN ADDITION TO an uplift component from the portion of the load (question 5) added to the procedure I described above.
7. Why is this not discussed more?

KootK · Sep 19, 2017

OP said:
1.Where does this get distributed along the length of the roof? For a drag truss, these loads would be added as a couple at the ends of the truss down into the vertical portion of the lateral resisting system. What is done here?

I believe that a couple is required at each truss in order for each truss to be in equilibrium.

OP said:
2. Is this vertical component of the force making it's way into each supporting truss as a vertical reaction?

Yes.

OP said:
3. If that is the case, then is every truss by nature a drag truss of sorts? Since the horizontal reaction at the truss is inadvertently being dragged through the chords to resolve the forces.

I don't see how the horizontal forces would be dragged through the chords. I see the horizontal getting absorbed bye the sheathing.

OP said:
4. Is this component of the force just ignored?

The vertical force couple on common trusses is often ignored. It usually pales in comparison to the demands from other load combos and general wind uplift.

OP said:
5. Is this horizontal load to be added to the horizontal reactions from the windward and leeward walls, calculated with the same procedure above?

Yes

OP said:
6. Will the roof have uplift from wind normal to the surface IN ADDITION TO an uplift component from the portion of the load (question 5) added to the procedure I described above.

Yes

OP said:
7. Why is this not discussed more?

The accounting's pretty tedious.

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.

StrEng007 · Sep 20, 2017

1.Where does this get distributed along the length of the roof? For a drag truss, these loads would be added as a couple at the ends of the truss down into the vertical portion of the lateral resisting system. What is done here?

KootK said:
I believe that a couple is required at each truss in order for each truss to be in equilibrium.

Will the truss manufacturer account for this couple? I believe most engineers do not add this additional load back into their structure. It's a "belt & suspenders" kind of thing... The wall-supported-truss is loaded by the horizontal reaction from the wall, where the load travels through the truss and is taken back out as a vertical couple into the wall...

2. Is this vertical component of the force making it's way into each supporting truss as a vertical reaction?

KootK said:
Yes.

Does this mean that the fastening tables for block & unblocked diaphragms have been analyzed at a range of angles, since this would induce tension and shear in the fasteners?

3. If that is the case, then is every truss by nature a drag truss of sorts? Since the horizontal reaction at the truss is inadvertently being dragged through the chords to resolve the forces.

KootK said:
I don't see how the horizontal forces would be dragged through the chords. I see the horizontal getting absorbed bye the sheathing.

OK, the sheathing takes in plane loads. The fastening to the truss distributes the out of plane from the diaphragm.

4. Is this component of the force just ignored?

KootK said:
The vertical force couple on common trusses is often ignored. It usually pales in comparison to the demands from other load combos and general wind uplift.

That makes sense.

5. Is this horizontal load to be added to the horizontal reactions from the windward and leeward walls, calculated with the same procedure above?

KootK said:
Yes

I see many engineers use the wall pressure and apply it to the vertical projection of the roof. I guess they figure it's better than having to separate the horizontal components from their roof wind loads. I would check this method to make sure I wasn't under-calculating my horizontal pressure demands.

6. Will the roof have uplift from wind normal to the surface IN ADDITION TO an uplift component from the portion of the load (question 5) added to the procedure I described above.

KootK said:
Yes

I believe this part doesn't matter as much, because tie-downs are specified for the C&C pressures. I wouldn't apply the C&C load from a wall to the C&C load uplift load for a truss using the procedure described above.

7. Why is this not discussed more?

KootK said:
The accounting's pretty tedious.

In the end, if the horizontal load calculates out to be the same value as the typical methodologies, then running through all these numbers is more time spent on a similar answer. Still, it would be nice to see some publication on what happens here versus how we typically calculate it. Or perhaps the load path is far to redundant to come close to assigning numbers to this... which is why we do it the simple way.

KootK, how much of this do you implement if you don't mind me asking?

KootK · Sep 20, 2017

OP said:
Will the truss manufacturer account for this couple?

Unlikely in most markets unless you specifically tell them to do this.

OP said:
Does this mean that the fastening tables for block & unblocked diaphragms have been analyzed at a range of angles, since this would induce tension and shear in the fasteners?

I don't believe that it does induce tension in the fasteners. And no, I'm not aware of any testing on pitched diaphragms. I would like to see some for other reasons though.

OP said:
KootK, how much of this do you implement if you don't mind me asking?

How dare you ask me this in public!?! I don't do any of it. I'll design/specify the diaphragm and collector trusses in the usual way and that's it. I consider it to be at too granular a level of detail for practical design assignments. I do realize that some engineers would argue that there's no such level. I feel that you and I are likely way ahead of the curve for having thought things through in even this much detail. Consequently, I feel that my/our negligence smells a little better than the negligence of others.

A related topic of great interest to me is just how a pitched diaphragms resists shear that is applied horizontally. It all comes down to one truss sliding past its neighbor. I think that I've got it figured out but, again, it's not something that's commonly talked about. And I feel that some research is probably warranted.

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 · Sep 20, 2017

KootK said:
How dare you ask me this in public!?! I don't do any of it. I'll design/specify the diaphragm and collector trusses in the usual way and that's it. I consider it to be at too granular a level of detail for practical design assignments. I do realize that some engineers would argue that there's no such level. I feel that you and I are likely way ahead of the curve for having thought things through in even this much detail. Consequently, I feel that my/our negligence smells a little better than the negligence of others.

Very well said!

StrEng007 · Sep 20, 2017

KootK said:
A related topic of great interest to me is just how a pitched diaphragms resists shear that is applied horizontally. It all comes down to one truss sliding past its neighbor. I think that I've got it figured out but, again, it's not something that's commonly talked about. And I feel that some research is probably warranted.

Isn't that what we have been discussing above? Application of force that travels through the horizontal flat plane of the diaphragm?

Or, are you talking about how a diaphragm acts as a deep beam web, transferring loads to the chords? If so, where are you at with it?

KootK · Sep 20, 2017

I was referring to how diaphragm in plane capacity resists translation that is not fully in plane.

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.

StrEng007 · Sep 20, 2017

OK, similar to my original question. Part of the component stays in plane. The other part resolves itself back into whatever member supports the diaphragm at intervals. Or else, you'd have a large plate element that would buckle out of plane. Obviously, I'm making it sound more simple that it actually is.

The transition at the ridge, now that's something...

KootK · Sep 21, 2017

OP said:
3. If that is the case, then is every truss by nature a drag truss of sorts? Since the horizontal reaction at the truss is inadvertently being dragged through the chords to resolve the forces.

I didn't fully understand what you were getting at here. Upon further consideration, I agree with this statement too. Each truss is acted upon by a lateral load which is resisted by truss pushing those "drag" loads into the diaphragm, thus inducing some axial loads in the truss chords. If any truss supplier has ever considered these forces, I'd be shocked.

OP said:
Does this mean that the fastening tables for block & unblocked diaphragms have been analyzed at a range of angles, since this would induce tension and shear in the fasteners?

I change my answer on this too and now agree that tension is induced in the fasteners. And I know of no accounting for this, neither in the research nor in practice. One saving grace may be that:

1) This is a force developed as a result of an imposed displacement and;
2) The particular load path is not very stiff (weak axis sheathing bending).

I feel that will steer things toward small -- although admittedly non-zero -- forces perpendicular to the plane of the diaphragm.

OP said:
The transition at the ridge, now that's something...

I've noodled on that a fair bit myself. What aspect bothers you? I got cosy with the whole folded plate business by way of some FBD's and comparison to steel beams with corrugated webs. Now, the only part that bothers me is the rather extreme need for blocking at a location that rarely receives it.

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.

StrEng007 · Oct 3, 2017

KootK said:
What aspect bothers you?

I suppose it's the location of the top chord ends & ridge. With the roof diaphragm having a drastic change in pitch, I imagine the ridge wants to act as a chord. However, with proper blocking, the load travels past the ridge and into the second diaphragm section (leeward roof).

Have you noticed that the directional procedure for MWFRS in ASCE 7-10 (Fig. 27.4-1) allows the horizontal shear from wind forces on applicable roof surfaces to be neglected? This doesn't apply to moment resisting frames.

Going back to question #5 in my original post... For a simple diaphragm building, this x-component can be neglected in accordance with this wind loading procedure. All you're left with is the vertical component of the roof pressure. Since the wind is normal to the roof, you just need to apply the pressure on the horizontal projection of the roof's surface. This vertical component gets resolved by the truss.

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