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Rudra Nevatia ...
Joined: 26 Jan 2003 Posts: 215
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Posted: Tue Dec 28, 2004 5:14 am Post subject: Dilemma |
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Thank you Mr. Barua. As expected, the response came from an old timer who would have gone through many such discussions on ill-conditioning in the early seventies.
As you rightly pointed out, the problem can be solved by using higher precision math though I would not bet on 16 bits. Pivot exchange strategy is perhaps another way.
The point I would like to make is this: There is a possibility of error when out of plane stiffness is increased arbitrarily to model a rigid diaphragm. It is better to use a master-slave model.
Regards, Rudra Nevatia
--- ibarua@deguild.com wrote:
Quote: | Re.: Mr Nevatia's dilemma --------------------
Ill-conditioned equations, which occur frequently in real life, can be solved only by so-called 'exact' or rigorous methods such as matrix inversion and not by iterative methods. Even in matrix inversion, it becomes necessary to use double precision. Our computer programs noramally work in single precision, that is, up to 8 significant places. If double precision is declared for the variables involved,then the calculations extend up to 16 significant places, precluding round-off errors so common in ill-conditioned equations.
I thought that increase in the stiffnes of the horizontal diaphragms, the slabs, will enhance diaphragm action and help to transfer lateral forces to the stiffer elements in the building, such as the shear walls or the braced frames.
Indrajit Barua.
Message From rudra_nevatia@yahoo.com Subject: permissible limit of drift Date: 27/12/04 Time: 20:46:24
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Quote: | -- I am confused.
I was taught that arbitrarily increasing out-of-plane stiffness of beams to account for diaphragm action results in large off-diagonal elements in the global stiffness matrix and the resulting system of equations can be ill-coditioned giving wrong results from an otherwise well behaved software.
But then this was thirty five years ago.
Rudra Nevatia
--- ishacon@vsnl.net wrote: You may want to increase IY & IZ of beams to account for diaphragm action of slab.
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