Chord force adjacent to CMU wall 3

[rrmiv]

In reading thread507-104685, it got me wondering about the necessity of diaphragm chords being continuous. Suppose you have a steel deck diaphragm attached to a CMU wall (200' long) via a “continuous” angle bolted to the wall. The wall is designed as a shear wall when the shear force is parallel with it. If the wall has control joints (say every 20') and all horizontal reinforcement (including bond beam) stops at these joints, then the long wall acts as ten individual shear walls. The angle doesn’t even have to be truly continuous.

However when the shear force is in the other direction, the wall itself can act as a chord. It seems to me the same ten individual walls can serve as the chord (again resisting in-plane shear forces), although not continuous. The forces into these walls are not equal - the force increases as you approach the point of maximum moment in the diaphragm.

Is my thinking correct?

 

[JAE]

For the case where your wall is parallel with the tension diaphragm chord, what prevents the diaphragm from tearing at the point of max. moment? Tbat is the reason the chord should be continuous.

Think Hooke's Law. When the diaphragm resists lateral forces, it deflects not only through shear deflection, but also in flexural deflection. So the outer "midspan" edge of the diaphragm has stretched because the diaphragm has deflected in a large, sweeping, but shallow, "U" shape. This stretching (via Hooke's Law) means that the deck, or sheathing, is being placed in tension. With deep diaphragms the tension isn't all that large, but sometimes it can be with shallow diaphragms. Thus, the need for a chord. The presence of the wall and connection to it doesn't change this tension condition in the diaphragm.

 

[jike]

The diaphragm chord needs to be continuous! This may be the continuous bond beam reinforcing, the continuous angle or a continuous structural member(joist) close to and parallel to the wall.

I suppose for a small enough building, it might even be a portion of the metal deck spanning between joists immediately adjacent to the wall. Obviously, this needs to be in the strong direction of the deck.

 

[UcfSE]

Think of what would happen if you cut the flanges on a wide flange you're using as a beam, say cut a 1-inch long notch every foot of length but left the web intact and continuous. You would have individual little "beams" every foot each connected by the "diaphragm" or web. How would that beam behave? I wouldn't walk under it!

 

[rrmiv]

UcfSE, interesting analogy. However, in my scenario, the individual little "beams" are each horizontally supported by the individual shear walls. In other words, each shear wall provides a reaction equal and opposite to the chord force at that location, which does not allow the force to accumulate as it does in a “beam analogy”. In typical diaphragm analysis, these reactions are not present, so the chord force accumulates and therefore must be continuous.

JAE, interesting comment about Hooke’s Law – I’m not sure. But I believe the force is taken by the walls and is not allowed to accumulate in the decking.

 

[JAE]

rrmiv - if the decking distorts, there is stress....that is what Hooke's law represents. You cannot have strain without an associated stress.

If your wall is continuous, with a bond beam, then the diaphragm now looks more like a dumbell cross section (thin web = deck and fat flanges = bond beams) and the moment of inertia goes up, so the lateral "bending" of the diaphragm is significantly reduced - so the stress in the thin web (deck) is reduced at the edge.

If you don't have a continuous wall, as you described above, there are abrupt areas where the flange (the bond beam) is cut (per UcfSE's analogy) and the web is exposed to a concentrated stress at the cut. With the cuts (the control/expansion joints) there would be less stiffness in the dumbell "beam" and more deflection in the diaphragm. Thus more strain = more stress in the decking at concentrated locations....thus the concern over tearing of the sheathing/decking.

It may not be a significant amount of stress, but it is a concern non-the-less.

So with no collector, you have to at least consider/worry about:

1. Tearing stress in the deck at locations of masonry control joints.
2. Higher flexibility of the diaphragm and thus more lateral sway in your building.

 

[DaveAtkins]

rrmiv,

I agree with you and disagree with everyone else in this thread. If you have no continuous chord, the chord force can be resisted by the series of shear walls. The shear walls near the ends of the diaphragm will take the most force, while the ones near the middle of the diaphragm will take the least force.

But I think you may be worrying about nothing. Most of the time, in my experience, the control joint does not extend through the bond beam at the top of the wall.

DaveAtkins

 

[rholder98]

Another twist on UcfSE's analogy: if you cut the bottom chord of a joist girder, what would happen? Diaphragm chords work together--one in tension, one in compression--much like a flanges of a beam. Like JAE says, the force will be there, and it will have to go through the deck if the chord is not there.

 

[UcfSE]

Dave, how do you calculate your chord force for a typical simple-span diaphragm?

 

[haynewp]

I have never thought of it this way before but I understand what you are suggesting. You are treating the 10 individual shear wall pieces like rollers preventing curvature of the diaphragm beam, each wall piece has a horizontal reaction at the top and the bottom of the diaphragm giving 10 individual couples that are allowing the diaphragm to translate instead of bend like a normal beam. And without curvature there will be no moment (M=EI*curvature).

You could make a finite element model of the roof with element nodes restrained along the top and bottom of the diaphragm preventing curvature, and you would see reactions at each shear wall pointing left or right toward the middle of the beam. But personally, I would suggest leaving the chords continuous since it shouldn't be that much more work, and everyone else is doing it. (ie. Don't have to worry about proving your new theory in court).


Insanity in individuals is something rare - but in groups, parties, nations and epochs, it is the rule.
-Friedrich Nietzsche

 

[DaveAtkins]

Assuming uniform load, the chord force at midspan of a diaphragm is equal to the moment in the diaphragm divided by the depth of the diaphragm. But this chord force develops from the shear in the diaphragm from the support (where shear is maximum) to midspan (where shear is zero). So if this chord force cannot develop, because shear walls along the chord resist the shear forces, then there is no chord force. Imagine a simple span diaphragm is cut in half at midspan. You are left with two, open ended diaphragms, that in my opinion can still function.

DaveAtkins

 

[haynewp]

I think that is right. The difference in this situation and the other beam situations mentioned is that the shear walls are providing support reactions parallel with the tension and compression chords, so theoretically, translation without bending. I don't know what kind of drift you might end up with though...


Insanity in individuals is something rare - but in groups, parties, nations and epochs, it is the rule.
-Friedrich Nietzsche

 

[UcfSE]

If the chord force is equal to the moment divided by the depth, would it not seem reasonabble that the location of the maximum chord force should correspond to the location of the maximum moment, given a constant depth?

 

[JAE]

What DaveAtkins is describing is very similar to some of the "tensegrity" domes out there....such as the St. Petersburg dome in Florida, where radial "trusses" have no bottom chord but the normal chord force is taken out by circular hoops at each panel point.

I guess I can see this sort of thing working if you have a series of cut up shearwalls serving to take out the build-up in chord forces along the diaphragm tension edge, but I guess I'd ask....why would you?

A continuous angle is, or should be, used along this tension edge anyway to assist in connecting the exterior wall to the diaphragm for normal forces anyway. So if you have some sort of element there, why not utilize it as a simple chord collector? Why go the complicated route?

 

[haynewp]

I worked with an older engineer that never designed chords and said that others in the company he was with before he went on his own never did either. He always used these L2x2x3/16 angles where I was sizing L4x4x1/4 or 3/8 for the same sized box building. He saw what I was doing and thought it was overkill and I tried to explain how diaphragm chords worked to him. But he didn't think about the parallel shearwalls as we have been talking about, he just did it that way.

The point is that he and his friends probably designed hundreds of these buildings without considering chord forces and the reason they work is because of this parallel shearwall reaction effect. So I guess there are people like him that think designing chords is overkill?? But I believe that codes require a continuous chord in seismic areas anyway.


Insanity in individuals is something rare - but in groups, parties, nations and epochs, it is the rule.
-Friedrich Nietzsche

 

[JAE]

haynewp,

I also began my career under the wngs of some "older" engineers (mine started their careers in 1927, 1946 and 1947). After working with them for my first few years, I finally asked one of them why they never performed lateral analyses of some of their buildings, primarily for a grocery store client for which they designed dozens of structures.

The answer was sort of like...."ya, we probably should do that, but we never have in the past."

I just believe that as smart as some "older" engineers are, there were many who really didn't thoroughly analyze and design their buildings for the REAL loads, but were fortunate over time that many of the older construction techniques involved built-in redundancy that took care of their lack of concern.

 

[haynewp]

I agree, and another example is how P_DELTA was not even considered until what, 20 years ago? But I think there is validity to this shearwall interaction but I personally will continue to design chords for buildings surrounded by shear elements.


Insanity in individuals is something rare - but in groups, parties, nations and epochs, it is the rule.
-Friedrich Nietzsche

 

[DaveAtkins]

I agree with JAE--if you HAVE a chord of some sort--an angle or a continuous bond beam, then that is the best (and easiest) way to justify a diaphragm.

One thing I haven't seen much on other engineers' drawings is a splice for the angle at the edge of the diaphragm, if it is a chord. I use a plate to splice angle to angle, because if you don't, the chord is discontinuous. This detail is almost always needed, because the angle will not be one continous piece the whole length of the diaphragm.

DaveAtkins

 

[rrmiv]

Thanks to all for your input. I agree that ideally the chords should be continuous - and it is easier to design that way. However, the previously-mentioned thread got me thinking about some of the construction I've seen in the field. I've seen "continuous" angles butted together with no connection, CMU control joints where all reinforcement stops, etc. This all got me wondering about projects I've designed and not visited during this stage of construction. I'm sure similar construction errors have not been corrected in all cases. How do those diaphragms work? I think these walls serving as the chord help explain some of it, in addition to redundancies we don't rely on in design.

 

[UcfSE]

So how would you model this? Would you have a simple span with pinned ends, and supports along the span that are fixed in the longitudinal direction only, like a series of horizontal rollers between the pinned ends?