Solving the conundrum of recovering sufficient participating mass for complex structures

Abstract

An enduring question for response spectrum analysis of complex structural models is obtaining modes of vibration with a sufficient participating mass to represent the overall seismic response of the structure. Codes of practice for seismic design typically prescribe that a modal dynamic analysis captures a number of modes with a cumulative participating mass of at least 90% of the total model mass. Whilst this might be relatively straightforward for standard, regular structures whose seismic behaviour is governed by a few sway modes, it is far from trivial for complex geometries and models such as multiple towers built on a podium. In these structural models, in which the structure has multiple ‘parts’, each part can have relatively independent modes of vibration, which must be included in the response spectrum calculation. Effectively, we seek to satisfy the 90% minimum, not just for the entire structure but also for each individual part. In such scenarios, the computational cost (time and memory) of computing these modes can be prohibitively high.

We introduce a new eigensolver algorithm, implemented in Oasys GSA, that uses a novel filtering technique to compute only the most relevant modes that contribute to the required mass participation. The algorithm also allows for parts of the model to be identified, and mass participation requirements to be checked and enforced on each part. The algorithm is called MASIL, which stands for Mass Accumulating Shift Invert Lanczos, and it returns only those eigenvectors that contribute mass above a certain threshold for each part specified by the engineer.

Using numerical experiments we demonstrate that MASIL can identify the important modes on a part-by-part basis, and that using the conventional method (of checking mass participation only on the structure as a whole can lead to significantly underestimated element forces for design. We conclude that seismic design codes should take into account mass participation requirements for parts of a structure, and further guidance or requirements should be introduced for large irregular structures, especially those made up of many connected parts.