Chord Force in a Concrete Filled Diaphragm 7

[kmead]

I am designing a one story building with tilt-up shear walls and LW composite roof deck for blast resistance. My question is: since I have a concrete filled diaphragm, do I still need to design the perimeter angle for the chord force or is the concrete diaphragm so rigid that the perimeter angle doesn't even have much chord force? Any help would be appreciated.

 

[msquared48]

Spats... Thought about this off and on all day, and I can see how this would work too, but I also see two critical areas to check here:

The first concern would be the overturning on two of the four corner panels as two of the corners will see uplift from shear in both directions at the same time due to shear flow. Thus, all the corner panels would be the critical panels as the loads can reverse.

The second concern would be an increase in diaphragm deflection due to the discontinuity in the "chord" angle or reinforcing with this method. How much I do not have a feeling for, but the Plywood Diaphragm Construction Manual does add a "chord splice" factor for spliced double top plates double in their diaphragm deflection formula. Although this case is not the same, the idea is the same in that the panels are allowed to flex, or slip, between themselves. Due to the higher force at the corners, the corner panels will have a tendency to move more than the center panels.

I'll have to try a design example the next chance I get to get a better feeling for the concept.

For the record, if there were any stars left here, I'd have to give you one too.

Mike McCann
McCann Engineering

 

[spats]

Mike,

You don't necessarily have to assume that the higher shears at the corners are all resisted at the corners. In my example, I was basically doing a worst case senario for load in the edge angle.

When you design a composite steel beam, the AISC Code allows you to assume the transfer of horizontal shear by the welded studs to be uniformly distibuted between the point of maximum positive moment and points of zero moment. In the same way, the edge angle, which may be considered a "subchord", can transfer this load down the line if need be, at least to the point where it would be loaded to it's compressive capacity.

I'm one of these engineers that doesn't necessarily fret that much about strain compatabilities to determine where the load will theoretically go. If a mechanism exists whereby the loads can be safely resisted, then the system cannot fail. That means, in effect, if you have enough total potential resistance in a combination of the edge angle strength, the strength of it's connections to the shear wall, and the shear/overturning capacity of the wall itself, then the system cannot fail. If you like, you could assume something between my worst case senario, and the AISC senario.

I have to point out that I am not a experienced seismic and wood diaphragm guy (I'm in Florida), so I can't help you there. Not that I can't do it (recently did a manufacturing plant in Oklahoma with seismic), I'm just not experienced. I'll defer to others on that one.

 

[miecz]

At the "chord" edge of the diaphragm (the edge of our "element"), this horizontal shear has to be resisted (by something) for stability.

The shear at the cross section of any member is greatest at the mid depth of the member, and diminishes to zero at the edges. So there os no horizontal (or vertical) shear at the chord location.

This is where the chord comes in.

I don't think so; The chord is resisting tension, not shear.


The whole argument about the force dumping into the walls ignores strain compatibility. A vertical wall with a shear load at the top will deflect a distance proportional to the shear. Unless each individual wall takes the same lateral force, it will deflect differently from the adjacent wall. The difference in deflection between adjacent walls must result in the diaphragm as a crack, or series of cracks, between the points of attachment.

For the discussion, which discussed metal decks and masonry walls, see thread507-167171.

 

[spats]

Miecz,

Your missing the point... I made the statements you quote only to get the reader to look at it a liitle different way. Just like the tension in a beam flange is balanced/caused (whatever way you want to look at it) by the horizontal shear in the web at the flange interface, that is the way the interface between a deck diaphragm and it's chord acts. If you add the total VQ/I horizontal shear between the end support and mid-span, it will equal the flange force at the middle of the beam... simple mathematics.

As far as strain compatability, as I said in my last post, that does not concern me. If something, or a number of things, have to yield or deform a little for my mechanism to function, that's OK. It can't fail. I don't have time to look at the other thread right now... I'll look at it and comment later.

 

[cms1]

There must always be some element that picks up the tension that is normally carried by a continuous chord. If you are depending on the shear wall to transfer 'chord tension loads' (for lack of better terminology) to the foundation, then you are assuming that the foundation is going to provide the continuous "chord".

Here is where the relative stiffness of the shear walls/foundation vs. the stiffness of the diaphragm deck in tension matters. If you can assume the stiffness of the deck is significantly less than the wall/foundation system, then the walls would transfer the forces to the foundation. But if you can't justify that assumption and the deck cannot handle the tension force, then you need a continuous chord.


Note: I'd be wary of never considering strain compatibility or relative stiffnesses - especially when stiffest resisting element is brittle.

 

[spats]

I'm not saying to never consider strain compatibility, but sometimes we think too much, particularly in a case like this. Question: how does a roof expansion joint work in a tilt-up building at the wall? Talk about a strain compatibility problem!

I browsed a little of the thread referenced my meicz about, and I think this whole continuous chord thing is a little overanalyzed. As I said earlier, I consider the tilt-up to be the chord. It doesn't matter (for the most part) that there are joints between the panels. This does not make the chord discontinuous. That is because each individual panel is capable of resisting it's portion of the chord force, and carrying it directly to the ground. It does not have the transfer load to the next chord element to be stable, and the diaphragm will not “tear” at the joints as suggested by some in the other thread.

 

[spats]

Oops! As a follow-up, I missed reiterating one point I made earlier. I feel you must have a continuous edge angle, or "subchord", properly spliced. That way there is a continous chord that the deck attaches to, that collects the load. It just doesn't have to hold all the load by itelf.

 

[hokie66]

spats,

While I gave you full marks for your explanation for how a diaphragm transfers the loads to the normal as well as the parallel wall panels, I wouldn't agree on a building with an expansion joint. We have had several discussions on this site about shear walls on only three sides and long buildings with expansion joints, and except for quite small buildings, I always argue against designing buildings which depend on this type of torsional resistance.

 

[southard2]

I agree with Spats that one can assume that the chord force is gradually collected in the tilt-up panels that the chord is attached to. This would also legitimize the three shear wall situation with torsion. Without heavy overturning resistant shear walls capable of resisting the chord force in a cantelevered diaphragm what other explanation could there be.

That said I always design my chords to be continuous. For floors I will use the ledger angle as my chord. Each angle is cut to panel length and than spliced with a steel plate at the panel joints. To prevent thermal stress and curing shrinkage from pre-loading my chord I place bolts thru horizontal slotted holes. At the middle of each panel I weld the chord angle to an embed plate or use a number of closely spaced expansion bolts. This connection at the center can transfer diaphragm shear to the wall when the wind is blowing in the other direction. Out of plane, and gravity loads can be resisted by all the expansion bolts including the ones thru the slotted holes.

One more point using an example of steel bar joists bearing on top of a CMU wall (without shear collectors between the joist seats). For CMU buildings most of us engineer's use a bond beam or tie beam at the top of the wall to act as the continous chord. Masonry control joints are placed in the wall but the bond beam steel is continous thru the joint and uncut. I often place shear collectors between my joist seats but for most buildings I've seen this is rare! It shouldn't be rare since the diaphragm design manual requires shear collectors where diaphragms can't meet the shear requirements with zero sidelap fasteners. That is a discussion for another time. For now assume there aren't any shear collectors which is usually the case. We could also assume this is a wood truss or light-gage truss building as well. Same situation.

If one were to picture the diaphragm as a deep truss or beam the top and bottom chords would be the bond beams at top of wall. The web would be the steel deck. Only problem is that the web isn't connected to the chords. The only connection in our case is through the joist seats. The joist seats must than be designed for a rollover force equal to the diaphragm shear times the joist spacing or the total chord force divided by the number of joist seats.

This implies that Spats is right on both accouts. One that the chord force can dumped out of the diaphragm into the walls and that yielding of the end materials or movement of a end tilt-up panel will result in the redistribution of forces thus avoiding failure.

At the top of the diaphragm the deck will be in compression trying to push inward. The deck's inward crumpeling movement however is restricted by the joist seats. They may move a bit but the total force is dumped out of the deck into the top of the walls thru the joist seats. Than the compression or tension is resisted by the bond beams.

So either Spats is right or most buildings have serious design flaws. One I think could also perhaps argue that a chord force does not exist unless the span to depth ratio is greater than 2.0. At less than 2.0 one could argue that arching action would load the diaphragm in compression only. No shear, No moment, No chord force.

One can also use joists, beams, and other members as chords if they need too.

Being a conservative engineer however I always provide a continous chord and always assume a chord force exist. Where roof joist bear on top of concrete walls I will either use the ledger angle at the end of the overhang as my chord (spliced with horizontal slots) or I will attach continous angle to the inside of the top of wall and splice using the same horizontal slot method as I do for a floor ledger angle.

I have a project now where I will try to use the ledger angle at the end of the overhang so I avoid the need for a ledger angle and a chord angle on the inside of the wall. Joist seats have a gap between them. Here I will bolt the overhang ledger angle to the chord. The deck will be welded to it so it will be braced in that direction. Vertically it will be braced by the joist extensions. The bolts will be thru horizontal slotted holes to allow panels to move independant of the angle. Key is that the angle can not be welded to the joist extensions as usual. If the overhang is 2ft or longer my feeling is that one can ignore the thermal movement of the panels since the joist seat extensions are weak in that direction and can flex a bit. Still being conservative I personally will not rely upon this. I only did for one project. So far so good but still.

Assuming Spats is right chord angles, continous chord reinforcement grade 40 at the top of walls may not really be necessary as long as the tilt-up panels will not overturn.

One more easy illistration to think about. The deck at the chord boundary wants to stretch or crumple but it can't because the joist seats won't let it. The joist seats don't move because the walls their attached to won't let them. If the walls can move than this doesn't work.

I want to say that ACI or the tilt-up manual might even allude to checking the panels for overturning due to chord forces being exerted on them. Spats I'm in Florida too where we have to think about this stuff a bit more. I do agree too with Hokie that I avoid torsion situations. So far I've always been able to avoid that situation.

My biggest grip is with light-gage truss and wood truss people never accounting for rollover forces.

 

[haynewp]

I have been extremely busy and just now have read through all this. I completely understand the concept behind all this since I mentioned it on the previous thread, but as also mentioned by others above, the chord force is not 100% resisted by the walls and the chord/diaphragm will feel some of it.

So the building should work using the wall segments, but 99.9% of other engineers are designing typical continuous chords and not counting on wall segments as resisting the shear. This is also exampled in every textbook, ICC, BSSC guide you will find. So past earthquake performance of tilt-up box buildings have been evaluated based on buildings that were {likely} designed with continuous angle chords at the boundary taking all the force and not just relying on the shear wall segments with a small continuous angle. So when the building is rocking inelasticaly, do you think it will behave the same having not designed a continuous angle or bond beam "chord" to resist all the force? I don't know.

I guess I am saying I know the shearwall segments are there and working (have to be for a cantilever diaphragm) but I personally do not feel comfortable not designing chords. How much cost is designing chords and using an L3x3 or L4x4 versus not desiging a continuous chord angle and using an L2x2 going to make anyway?