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.

 

[jike]

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

 

[Lion06]

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.

 

[haynewp]

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.

 

[msquared48]

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

 

[haynewp]

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.

 

[JAE]

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.

 

[msquared48]

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

 

[haynewp]

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.

 

[kmead]

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.

 

[msquared48]

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

 

[kmead]

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.

 

[spats]

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.

 

[msquared48]

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

Mike McCann
McCann Engineering

 

[haynewp]

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.

 

[msquared48]

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

 

[hokie66]

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.

 

[haynewp]

OK, I am not saying you don't need a chord. If you {idealize} the shearwall segments as rollers restraining the chord you will not get chord forces. This is what spats was describing, but I know this is not reality.

 

[spats]

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.

 

[hokie66]

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