...
Why
...
are
...
response-spectrum
...
base
...
reactions
...
different
...
from
...
the
...
sum
...
of
...
individual
...
reactions?
...
Answer:
...
...
base
...
reactions
...
will
...
not
...
match
...
the
...
sum
...
of
...
individual
...
...
reactions
...
because
...
their
...
formulations
...
differ.
...
Base
...
reactions
...
are
...
calculated
...
for
...
each
...
...
before
...
modes
...
are
...
combined
...
using
...
the
...
CQC
...
or
...
SRSS
...
modal-combination
...
rule.
...
Joint
...
reactions,
...
on
...
the
...
other
...
hand,
...
are
...
calculated
...
using
...
modal
...
combinations
...
which
...
are
...
applied
...
to
...
each
...
individual
...
joint.
...
For
...
example,
...
consider
...
a
...
structural
...
system
...
with
...
four
...
joints
...
and
...
two
...
modes.
...
The
...
SRSS
...
formulation
...
is
...
used.
...
Base
...
and
...
point
...
reactions
...
are
...
generated
...
as
...
follows:
- Mode 1:
- Point 1 reaction = R(1,1)
...
- Point
...
- 2
...
- reaction
...
- =
...
- R(2,1)
...
- Point
...
- 3
...
- reaction
...
- =
...
- R(3,1)
...
- Point
...
- 4
...
- reaction
...
- =
...
- R(4,1)
...
- Mode
...
- 2:
...
- Point 1 reaction = R(1,2)
...
- Point
...
- 2
...
- reaction
...
- =
...
- R(2,2)
...
- Point
...
- 3
...
- reaction
...
- =
...
- R(3,2)
...
- Point
...
- 4
...
- reaction
...
- =
...
- R(4,2)
...
- Base
...
- reaction:
...
- Mode 1:
...
- SUM
...
- mode
...
- 1
...
- =
...
- R(1,1)
...
- +
...
- R(2,1)
...
- +
...
- R(3,1)
...
- +
...
- R(4,1)
...
- Mode
...
- 2:
...
- SUM
...
- mode
...
- 2
...
- =
...
- R(1,2)
...
- +
...
- R(2,2)
...
- +
...
- R(3,2)
...
- +
...
- R(4,2)
...
- Base
...
- Reaction
...
- =
...
- √((SUM
...
- mode
...
- 1)
...
- 2 +
...
- (SUM
...
- mode
...
- 2)
...
- 2)
- Point reactions:
- Point 1 reaction = √(R(1,1)
...
- 2 +
...
- R(1,2)
...
- 2)
- Point 2 reaction = √(R(2,1)
...
- 2 +
...
- R(2,2)
...
- 2)
- Point 3 reaction = √(R(3,1)
...
- 2 +
...
- R(3,2)
...
- 2)
- Point 4 reaction = √(R(4,1)
...
- 2 +
...
- R(4,2)
...
- 2)
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