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Seismic Wt. of Floors

 
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aswinpe
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Joined: 26 Jan 2003
Posts: 28

PostPosted: Sun Nov 09, 2003 10:37 pm    Post subject: Seismic Wt. of Floors Reply with quote

Without getting into complicated issue here is a simple explanation:
In a simply supported beam, 1/2 of the weight goes to each support at the
ends.  Now imagine the wall to be that beam in a vertical position and
supports at each floor. 1/2 wt goes to top floor and 1/2 to bottom.

Aswin Rangaswamy

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hsnagle
SEFI Member
SEFI Member


Joined: 26 Jan 2003
Posts: 7

PostPosted: Mon Nov 10, 2003 5:15 am    Post subject: Seismic Wt. of Floors Reply with quote

mr. upadhyay.
for gravity loads what you said is right but for horinatal load, it is a
lumped mass which is acting horizontlay, transfer of load is as suggested by
code. The point will be more clear if you compare this analogically with
wind load.

h.s.nagle(diensh)

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prof.arc
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Joined: 26 Jan 2003
Posts: 703

PostPosted: Mon Nov 10, 2003 12:29 pm    Post subject: Seismic Wt. of Floors Reply with quote

Dear Mr. Upadhyay
Your inference is based on "the reactive force" coming on the bottom floor
for static analysis.

However, it can be proved by energy methods, that in the case of cantilever,
with a uniformly distributed mass Md and a concentrated mass Mc at the free
end, the equivalent mass at the free end would be Mc+f*Md
[considering as an equivalent single degree of freedom system).
f= 0.33  if Md <<Mc
f=0.50  if Md >> Mc

Read Chapter  2 of the book by Jacobsen & Ayre on Vibrations for an
excellant treatment.

For dynamic analysis of buildings in which masses are lumped at nodes, the
method suggested of 50% distribution to top and bottom mass is more correct.

Interestingly, even in Static Analysis, the equivalent loads at the nodes of
a eight noded 2D FEM element would
indicate W/3 at midside nodes and negative W/12 at corner ends !!

Sincerely
ARC

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prof.arc
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Joined: 26 Jan 2003
Posts: 703

PostPosted: Mon Nov 10, 2003 12:29 pm    Post subject: Seismic Wt. of Floors Reply with quote

Dear Mr. Upadhyay
Your inference is based on "the reactive force" coming on the bottom floor
for static analysis.

However, it can be proved by energy methods, that in the case of cantilever,
with a uniformly distributed mass Md and a concentrated mass Mc at the free
end, the equivalent mass at the free end would be Mc+f*Md
[considering as an equivalent single degree of freedom system).
f= 0.33  if Md <<Mc
f=0.50  if Md >> Mc

Read Chapter  2 of the book by Jacobsen & Ayre on Vibrations for an
excellant treatment.

For dynamic analysis of buildings in which masses are lumped at nodes, the
method suggested of 50% distribution to top and bottom mass is more correct.

Interestingly, even in Static Analysis, the equivalent loads at the nodes of
a eight noded 2D FEM element would
indicate W/3 at midside nodes and negative W/12 at corner ends !!

Sincerely
ARC

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