Yes! The computed displacements at a limit stop can "exceed"
the specified gap (in Acceleration load case). Sounds strange! But, let
us see how and why such a thing could happen. (Note: The Acceleration
load case is also called "lateral static coefficients" or "static
seismic" load case).
Assume that an acceleration of 0.25g was applied in X, Y and Z directions.
CAEPIPE internally applies an X acceleration (of 0.25g) first and solves
the case ensuring that the displacements at the limit stop do not exceed
the specified gap. This procedure is then applied independently to the
accelerations in Y and Z directions.
The above procedure results in three sets of solutions (displacements,
element forces and moments, and support loads) to accelerations in X,
Y and Z directions, which are typically combined in some manner. In CAEPIPE,
two directional combination methods are available: SRSS (Square root of
sum of squares) and ABS (Absolute). The SRSS summation method employed
in Acceleration load case and other simplified dynamic analysis methods,
such as response spectrum method, is statistically based.
In the SRSS method, all three displacements and support loads from the
X, Y and Z accelerations are squared individually and added. The square
roots of these respective sums are the displacement and support load at
the given node. In the ABS method, all absolute values of displacements
and support loads are added to get the total displacement and support
load.
It is possible that the SRSS (or ABS) result may exceed the specified
gap at a given limit stop. This is because a given limit stop may act
differently for different loads (such as for each of the three accelerations
in X, Y and Z directions). For example, the limit stop may be inactive
(gap is open) for X and Z accelerations, but may be active (gap is closed)
for Y acceleration.
If the limit stop gap is closed, then the corresponding limit stop load
is combined by the SRSS method to compute the summed support load. On
the other hand, if the limit stop gap is open, then there is no limit
stop load contribution to the summed SRSS support load. So, at each support,
the SRSS loads are computed by taking into account loads from all active
limit stops from each of the three "independent" accelerations.
This is consistent with the assumption of time-independency upon which
the SRSS method is based.
Further, the non-linearity of the gapped support introduces the apparent
contradiction that displacements exceed the value of the limit stop gap.
This is because there is no logical way to determine which directional
effects should be combined when one of the directional displacement is
less than the limit stop gap but the SRSS of all three directional displacements
is greater than the limit stop gap.
See PDF file.
Tip for the Month (Dec 1998)See PDF file.
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