chord force adjacent to cmu wall

huangyhg

chord force adjacent to cmu wall
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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.
the diaphragm chord needs to be continuous! this may be the continuous bond beam reinforcing, the continuous angle or a continuous structural   
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!
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 鈥渂eam analogy鈥?  in typical diaphragm analysis, these reactions are not present, so the chord force accumulates and therefore must be continuous.
jae, interesting comment about hooke鈥檚 law 鈥?i鈥檓 not sure.  but i believe the force is taken by the walls and is not allowed to accumulate in the decking.   
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.
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
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.
dave, how do you calculate your chord force for a typical simple-span diaphragm?
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
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