## Tips Oct  Dec 1998

### Can Computed Displacements Exceed Specified Limit stop gaps in CAEPIPE?

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.

See PDF file.