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Re: Rigid Diaphragms

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I have been asked to pass this test or face the consequence of being packed
off to a smaller cubicle. So here I go...

Q.1 The classical definition says that a diaphragm is fully rigid in its
plane and fully flexible out of its plane. So what happens to the
out-of-plane forces and moments ?

A.1 They are resisted by shears, moments and torsions in *real* beams (or
column strips in case of flat slabs) connecting the nodes.
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Q.2 There is another definition doing the rounds that a rigid diaphragm has
infinite in *and* out-of-plane rigidity. What's wrong with it?
 
A.2 It is incorrect to assign infinite out-of-plane rigidity to the
diaphragm as this will result in ~zero out-of-plane rotations and ~equal
out-of-plane displacements. Beams will behave as ~fixed ended while axial
forces in columns will be ~proportional to their cross-sectional areas - an
obviously wrong result if floor slabs are modeled thus but not so wrong for
massive foundations!
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Q.3 Can condensation be used to selectively remove the dependant in-plane
DOF's of a diaphragm?

A.3 No it can't be. The aim is to *tranfer* the actions and stiffness
matrices corresponding to the dependant DOF's to any one node in the plane
of the diaphragm. Condensation is nothing but selective Gaussian
elimination. By this technique one eliminates the "uninteresting" DOF's
which in a static case might be the internal DOF's of an element and in a
dynamic case, the massless DOF's.
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Q.4 It is proposed that the master-slave relationship be redefined as the
one which assures the same displacement and rotation for all master-slave
nodes. Why not?

A.4 Only one situation admits this possibility and that is when the master
and slave nodes coincide!
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Do I pass?

Rudra Nevatia
Central Computing Facility