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Reducing the number of degrees of freedom for dynamic anal
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kajal.chopra
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Joined: 26 Jan 2003
Posts: 102

PostPosted: Thu Sep 01, 2011 11:51 pm    Post subject: Reply with quote

Kumar_Abhishek_Singh wrote:
Dear Ms. Kajal,

Static condensation is done to make our lives easy. If we do not have some mass associated with a defined degree of freedom, we can reduce our computational effort by reducing the degrees of freedom and just playing with the quantities we are actually interested in.

Generally the rotational degree of freedoms are condensed. If vertical degrees of freedom are included in the dynamic analysis then they can also be removed because generally the ground motion is horizontal (with low fequency and high amplitude) and again to make our lives easier with pen, we assume that the ground motion will not have any component that will excite the vertical degree of freedom or in other words the inertial effect associated with the building's vertical degree of freedom will be small.


Abhishek Singhji,

Yes, this is given in Chopra's book.

But also give, besides static condensation is reduction in DOF by Rayleigh Ritz approach where J< N, N being the number of natural modes of vibraytion and J is the approximation considering Ritz vectors.

In this (Rayleigh Ritz or RR) is different approach than Static condensation- for static condensation we express a relation between ktt and koo wherein ktt are those terms associated with mass and koo terms associatred with 0 mass.Though, static condensation results in non banded stiffness matrix thus almost nullifying the gain obtained by dropping the non mass terms.

My question was associated with RR where J<N.

IS this approach used in computer software???

Kajal
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