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Chord Force in a Concrete Filled Diaphragm
6

Chord Force in a Concrete Filled Diaphragm

Chord Force in a Concrete Filled Diaphragm

(OP)
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.

RE: Chord Force in a Concrete Filled Diaphragm

Design perimeter angle for chord force or put extra rebar in diaphragm for chord forces.

RE: Chord Force in a Concrete Filled Diaphragm

Just check.  treat the diphragm like a simply supported beam and check the stresses.  I interned at a pretty big precaster while in college and they always used chord steel (even when not needed by analysis, just for some belt and suspenders).  It wasn't a big deal with that because they had to pour a wash around the perimeter anyway.

RE: Chord Force in a Concrete Filled Diaphragm

That is a good question that I wondered before too because it kind of goes against the assumptions of a rigid diaphragm. But, I design for bending in the diaphragm and add chords whether it is assumed rigid or not. There is no such thing as an infinitely rigid diaphragm so there will be some amount of bending. If you go ahead and design for the worst case of a flexible diaphragm then you are covered and don't have to try and analyze what chord force actually exists in a rigid diaphragm.

RE: Chord Force in a Concrete Filled Diaphragm

The chord connection at the tilt-up wall connections does present a problem.  The panels must be allowed to move for temperature reasons, and the chord tie must be able to develop a tension.  This is a dichotomy.

The solution is to provide a number of grade 4o rebar across the joint that are welded to steel plates embedded into the walls at 2 to 3 feet from the joint.  You would want to weld the bars at the during the average temperature for the region.  The result would be a compromise, allowing the panels to get longer with increase in temperature above the normal - the bars will just bend to the inside - and the chord tie will be maintained.  The chord bars will have to be increased to allow for greater stresses due to the tension in the bars when the temperature drops below normal though.

Mike McCann
McCann Engineering

RE: Chord Force in a Concrete Filled Diaphragm

I worked at a place that literally did hundreds of big box tilt panel buildings and I think the standard detail was just a continuous L3x3 or L4x4 welded to embeds along the panels to support the roof deck. This was wal-mart and home depot type buildings. Not that there ever wasn't a shrinkage restraint issue using that detail, but there was not one over the years I was there that I recall.  

RE: Chord Force in a Concrete Filled Diaphragm

Well, I just wonder how much thermal expansion really takes place - most tilt-up panels have an exterior skin exposed to the thermal swings and an internal skin that isn't.  And over the width of a single panel, how much total movement is there really going to occur?  

The embeds are usually what - 6 feet on center or less so the angle doesn't even see the full panel width thermal movement, and being on the inside, may not see much at all.

RE: Chord Force in a Concrete Filled Diaphragm

Well, the gap between panels is usually 3/4" with a 1/2" diameter grade 40 rebar inserted in the panel to panel connections, leaving 1/4" for expansion/contraction.  For a 20 foot panel seeing 100 degree temperature swings (common in my area), this converts to a little over 1/8" or .15" in lateral movement per panel, under the .25" designed for.  

Mike McCann
McCann Engineering

RE: Chord Force in a Concrete Filled Diaphragm

We never used panel to panel connections other than what was provided by the continuous chord, there was only sealant between the panel gaps. Unless additional connections between the panels were required for overturning resistance.

RE: Chord Force in a Concrete Filled Diaphragm

(OP)
Mike,
I like your idea of the rebar across the joint but what about in the case where you have to have the perimeter angle pick up the deck? (i.e. wall running parallel to joists)  Would you then just provide slotted holes in the angle to allow the panels to expand?  You could also add a joist a few inches away from the wall to pick up the deck, but that's not always an option.

RE: Chord Force in a Concrete Filled Diaphragm

I would either stop the angle at the joint, or use slotted holes as you suggest.  However, I would NOT use the angle as the chord member.  I would still use the rebar.

I have seen too many chord connections and side panel connections that have failed from being too rigid in these buildings.  They need some flexibility in their connections.

Haynewp:  Yes, I have seen that too, but in general, not here. We are in a high seismic area and it is better to tie things together allowing more possible load paths.  We even tie the panels to the strip footing so they will not "walk" under seismic loading.

Mike McCann
McCann Engineering

RE: Chord Force in a Concrete Filled Diaphragm

(OP)
Thank you all for the GREAT responses and feedback, it's great to have a place like this to bounce ideas off one another .  
Thank you.

RE: Chord Force in a Concrete Filled Diaphragm

2
If you want one more opinion from somebody who's been designing tilt-up buildings for more than 25 years... the tilt-up panels themselves are the chord of the diaphragm. The "chord forces" dump out of the deck into the edge angle, but the edge angle is connected to the tilt-up intermittently (either directly or indirectly), and never sees a build-up of forces, because it dumps it's load into the tilt-up. Since each tilt-up panel is hooked up to the ground in some fashion, and can tranfer this load to the ground, there is not a build-up of chord forces in the panels either. As a result, you don't need big edge angles, and you do not need to design for accumulated chord forces in the tilt-up either.

RE: Chord Force in a Concrete Filled Diaphragm

Interesting concept - I'll have to think about that one though.

Mike McCann
McCann Engineering

RE: Chord Force in a Concrete Filled Diaphragm


 spats-

Using that idea you could apply it to any shear wall building with walls around the perimeter and say there are no chord forces.

This is similar to an argument I made here about a year ago regarding how a cantilevered diaphragm does not have built-up chord forces. If it did, what moment would you design the chords for, w*L^2/2? If so, where does this force go when the chord ties into the single wall that is parallel to the lateral force?

The problem I believe with this line of thinking is as JAE pointed out previously; that there is deflection in the diaphragm so there has to be force in the chords. I think some of the chord force actually does get absorbed into the shear walls it connects to but it would be difficult for me to quantify the amount, so we usually design chords for the worst case....as if none of the chord force goes directly into the connecting shear walls and it builds up in the chords.

RE: Chord Force in a Concrete Filled Diaphragm

I see apples and oranges here, the apples being the shear force, and the apple the chord force, and they are not related or interchangeable.  

I can see the shear gradually being taken into each panel, but not the chord force - that is reguiired to develop the diaphragm strength and must be unbroken - continuous.  It is max at the center of the diaphragm span, and zero at the ends.  Moreover, the chord force is developed by the force that is normal to the chord force - two different loading conditions.  Apples and oranges here.

Mike McCann
McCann Engineering

RE: Chord Force in a Concrete Filled Diaphragm

Mike is correct, if you have a diaphragm, or alternately if you use diagonal bracing (horizontal truss) in the roof, you must have a continuous chord.  As far as connections of the chord to the panels, connections should be avoided near the edges of the panels unless those connections are horizontally slotted.  

RE: Chord Force in a Concrete Filled Diaphragm

OK guys, to prove I'm right, here's my version of Diaphragm 101:

Remember your mechanics of solids? In order to be statically stable, any isolated "element" has to have shear acting in both directions (opposing couples). That means there is not only vertical shear in the diaphragm, there is horizontal shear as well. At the "chord" edge of the diaphragm (the edge of our "element"), this horizontal shear has to be resisted (by something) for stability. That is where the "chord" comes in.

For a simple span diaphragm, the vertical shear at the support would be wL/2d (lbs/ft), where d is the depth of the diaphragm. Again, for stability, the horizontal shear in the diaphragm at any given point has to equal to the vertical shear in the diaphragm. This means the horizontal shear diagram is exactly the same as the vertical shear diagram: it is wL/2d at the supports, and zero at L/2. The change in chord force over any given distance is the area under the shear diagram. This chord force is zero at the supports, and increases to a maximum at the center, increasing more over a given distance near the support than towards the middle (larger area under the shear diagram per unit length the closer you get to the support).

If this chord force is unresisted by anything but, say, an edge angle, then the chord force at the center of the span would be wL/2d*L/2* 1/2(area under the shear diagram) = wL^2/8d (sounds familiar?). However, if the edge angle is intermittently connected over it's length to a shear wall/tilt-up that's hooked up to the ground, this chord force can (and will) dump out of the edge angle at each connection.

Just for an example, say w=300 lbs/ft, L=200', d=75' and your first connection along the chord is 6' from the support. The horizontal shear at the end is wL/2d = 300*200/(2*75)= 400 lbs. per foot. The area under the horizontal shear diagram between the support and 6' away is (400+(400-300*6/75))*0.5*6=2328 lbs. This is the chord force in the edge angle at this point. If all of this load can dump out in the first connection, and it probably can, then the chord force won't accumulate. If all connections are at no more than 6' on center, and they're all strong enough to transfer the change in chord force, the maximum force in the edge angle will never be greater than 2328 lbs! Of course, the shear wall/tilt-up has to be capable of resisting these loads and sending them to the ground (probably so).

This totally explains haynewp's comments about a cantilevered diaphragm. It's not that there aren't any chord forces, it's just that they don't build up, and are gone by the time you get to the diaphragm support. If the cantilevered diaphragm did not have shear walls on the "chord" edges... say, just steel beam & column framing with a vertical x-brace each side, you would build up significant chord forces, depending on the distance to the resisting brace along the "chord" wall.

Shear and bending/chord forces are not "apples & oranges". They go hand-in-hand.

RE: Chord Force in a Concrete Filled Diaphragm

Spats, you have a convert.  And my compliments for how you thoroughly explained your design method.

RE: Chord Force in a Concrete Filled Diaphragm

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

RE: Chord Force in a Concrete Filled Diaphragm

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.

RE: Chord Force in a Concrete Filled Diaphragm

Quote:

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.

Quote:

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: Chord force adjacent to CMU wall.

RE: Chord Force in a Concrete Filled Diaphragm

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.

RE: Chord Force in a Concrete Filled Diaphragm

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.

RE: Chord Force in a Concrete Filled Diaphragm

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.

RE: Chord Force in a Concrete Filled Diaphragm

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.

RE: Chord Force in a Concrete Filled Diaphragm

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.

RE: Chord Force in a Concrete Filled Diaphragm

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.  



RE: Chord Force in a Concrete Filled Diaphragm

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?  

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