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Conservatism in summation rules for closely spaced modes

Kelly, James M.; Sackman, Jerome L.

UCB/EERC-79/11, Earthquake Engineering Research Center, University of California, Berkeley, 1979-05, 34 pages (555.2/K39/1979)

It is shown that the method recommended by the U.S. Nuclear Regulatory Commission to be used to combine spectral response in the case of closely spaced modes is unnecessarily conservative for certain systems. Closely spaced modes arise in structures from symmetry and where there is a light appendage with a frequency close to one of the natural frequencies of the structure. In the former case, the closely spaced modes do not interact and the Nuclear Regulatory Commission Guide is reasonable. The latter case, that is when there are closely spaced modes where interaction occurs as in the example of light appendages and in torsionally unbalanced buildings, must be treated by consideration of the interacting system. The approach proposed in this paper is that the modes which are not closely spaced be treated by modal analysis and the closely spaced modes, in the case of two closely spaced modes be treated as a coupled two degree-of-freedom system. If this is done, the beat phenomenon, the most important characteristic of the interaction between the two closely spaced modes, is evident, as is the associated result that the peak response of the coupled system is developed much later than the peak responses obtained in the individual modes by standard analysis. It is shown that the square root of the sum of the squares procedure underestimates, as expected, the response for undamped and very lightly damped systems; but, for damped systems, the square root of the sum of the squares method can be extremely conservative. It follows that the other methods specified by the Nuclear Regulatory Commission for closely spaced modes must be even more conservative.

Available online: http://nisee.berkeley.edu/documents/EERC/EERC-79-11.pdf (1 MB)