Evaluation of combination rules for maximum response calculation in multicomponent seismic analysis

Abstract

The paper in discussion [1] presents an interesting comparison of various combination rules for maximum response calculation under two-component horizontal earthquake motions. The authors should be commended for their contribution, in particular for the error bounds they have presented for each of the combination rules examined.The purpose of this discussion is to bring to the authors' attention some past pertinent work by the writer [2], who addressed not the same but a similar problem 20 years ago, and also to suggest one way for making the critical response approach compatible with current codes and design practices. Apparently that publication has escaped the attention of the authors.In that work, eight modal-spatial combination rules were examined, including those by the authors, with the exception of the CQC rule, which had just appeared in a 1979 Berkeley report. However, the double summation rule, very similar to the CQC, had been considered, but gave results very close to the SRSS rule, since the structures examined had no close lower modes.While the present paper addresses the problem of maximum value of any response parameter under two-component horizontal motions acting along the worst possible direction for the parameter, Reference [2] deals with the more traditional problem of peak response under three component earthquake motions acting along three principal structural axes. Although maximum member response, considering all possible earthquake incident angles is certainly of practical interest, a structure should not be designed with each of its members sized to such maximum forces, as this would lead to an over-designed but not necessarily safer structure. The structure would be safer if its response remained elastic. However, under design level earthquakes the structure will respond inelastically and its safety margins will be determined by capacity design procedures requiring consistent sets of member forces. Thus, before the useful concept of critical response is introduced into practice, it should be made compatible with capacity design procedures.The comparisons in Reference [2] were carried out using results from time history analyses with 30 real, three-component earthquake motions, acting on three di erent structures. In addition, the problem of maximum stresses, which requires proper combination of maximum member forces, thus introducing a third level of uncertainty beyond the modal and spatial * Correspondence to:

The impact of the earthquake incident angle on the seismic loss estimation

“…The CQC3 response spectrum rule for combining the contributions from three orthogonal components of ground motion to the maximum value of a response quantity is presented in the work by Menun and Der Kiureghian [18]. In two works by Lopez et al [19,20] it is proposed an explicit formula, convenient for code applications, in order to calculate the critical value of the structural response to the two principal horizontal components acting along any incident angle with respect to the structural axes, and the vertical component of ground motion. In two works by Menun and Der Kiureghian [21,22] a response spectrum based procedure for predicting the envelope that bounds two or more responses in a linear structure is developed.…”

Structural Design Challenges in Design Certification Applications for New Reactors

“…In typical concrete design, however, multiple interacting response quantities are often considered. The combination methods for multiple interacting response quantities are distinctly different from those for a single response quantity [10][11][12][13][14][15][16].…”

Extreme inputs/outputs for multiple input multiple output linear systems.

“…This is the largest possible peak output for any input with a spectral envelope equal to or less than a specified envelope. Other authors [Baratta et al, 1998, Lopez et al, 2000and 2001 The contribution of x~( t ) to the total response will be the same as given by equation 4.3. The relative phases between the inputs are given by FH.…”

“…Other cases with single inputs and responses have also been studied are called the critical response [Lopez et al, 2000and 2001, Baratta et al, 1998 In the examples of this paper the input is force and the output is acceleration. But it is important to understand that the method is much more general.…”