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changes.mady.by.user Mike Abell

Saved on May 14, 2012

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changes.mady.by.user Ondrej

Saved on Oct 21, 2022

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Why

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are

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response-spectrum

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base

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reactions

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different

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from

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the

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sum

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of

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individual

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reactions?

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Answer:
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Response-spectrum
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base
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reactions
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will
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not
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match
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the
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sum
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of
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individual
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joint
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reactions
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because
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their
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formulations
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differ.
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Base
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reactions
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are
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calculated
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for
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each
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mode
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before
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modes
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are
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combined
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using
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the
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CQC
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or
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SRSS
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modal-combination
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rule.
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Joint
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reactions,
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on
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the
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other
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hand,
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are
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calculated
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using
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modal
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combinations
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which
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are
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applied
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to
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each
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individual
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joint.
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For
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example,
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consider
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a
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structural
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system
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with
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four
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joints
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and
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two
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modes.
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The
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SRSS
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formulation
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is
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used.
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Base
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and
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point
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reactions
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are
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generated
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as
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follows:
Mode 1:

Point 1 reaction = R(1,1)
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Point
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2
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reaction
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=
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R(2,1)
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Point
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3
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reaction
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=
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R(3,1)
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Point
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4
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reaction
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=
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R(4,1)
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Mode
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2:
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Point 1 reaction = R(1,2)
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Point
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2
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reaction
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=
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R(2,2)
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Point
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3
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reaction
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=
...
R(3,2)
...
Point
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4
...
reaction
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=
...
R(4,2)
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Base
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reaction:
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Mode 1:
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SUM
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mode
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1
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=
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R(1,1)
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+
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R(2,1)
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+
...
R(3,1)
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+
...
R(4,1)
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Mode
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2:
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SUM
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mode
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2
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=
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R(1,2)
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+
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R(2,2)
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+
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R(3,2)
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+
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R(4,2)
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Base
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Reaction
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=
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√((SUM
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mode
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1)
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² +
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(SUM
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mode
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2)
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²)
Point reactions:

Point 1 reaction = √(R(1,1)
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² +
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R(1,2)
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²)
Point 2 reaction = √(R(2,1)
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² +
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R(2,2)
...
²)
Point 3 reaction = √(R(3,1)
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² +
...
R(3,2)
...
²)
Point 4 reaction = √(R(4,1)
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² +
...
R(4,2)
...
²)

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Related Incidents:
Incident 26870: response spectrum base reactions (by fs, tg)