Application of cross-oscillator, cross-floor response spectrum method of multiply supported systems, considering the correlations between three directional earthquake excitations

Abstract

AbatractResponse spectrum analysis method is widely used for the seismic design of equipment and piping systems of nuclear power plant, or other industrial facilities. Some of the equipment and piping systems are multiply supported with plural floors, or several different points. In these cases, conservative design methods, such as uniform response spectrum (URS) method that envelopes all of the individual response spectra, or independent support motion (ISM) method are commonly accepted. These design methods are not practical, but often mislead to design with unnecessary conservatism. This paper presents the practical seismic analysis methodologies considering the correlation coefficients of seismic responses with multi-directional excitations, which is extended to apply the correlations between modal responses and between support motions, called cross-oscillator, cross-floor response spectrum by Asfura, A. and Kiureghian, A,D., and numerical examples are also presented to examine the validity for the seismic analysis method of multiply supported secondary systems, with simultaneous three directional excitations of each X, Y, Z axis.

Application of Response Spectrum Analysis of Multiply Supported System, with the Multi-Directional Excitations and Residual Rigid Response

“…It should not be forgotten to consider the secondary stress term generated by the quasi-static boundary displacement . Dynamic relative displacement is derived from Equation (10) and Equation (5) and is valid at an arbitrary time. In response spectrum analysis, the maximum value of each mode is calculated by the Duhamel integral, and the maximum response is obtained by combining them.…”

“…In Equation ( 15), 2 / 3 , 4 5 and 2 " 6 " , 4 " 7 are the floor response spectra on the k-th and l-th floors of the primary system shown in Figure 2, and the numerator is the cross spectrum (CCFS) of the hypothetical oscillators k and l of the secondary piping system supported by the primary system. Using the spectra of the basic design earthquake ground motions X, Y, Z direction at the base mat of the primary system, it is concretely expressed by the following equation, by our work [5] and [11].…”

“…(26) Equation ( 26) represents the seismic response of multiply supported system with one-directional excitation, considering the response correlation of two oscillators with natural frequencies ω i and ω j installed on the floor surfaces of the k-th and l-th floors. According to the Equation of our work in [5] with three-directional excitations, it can be developed into Equation (27) to Equation (30) shown below.…”

“…This paper introduces an evaluation formula of response spectrum analysis considering the effect of residual rigid response and multi-directional earthquake excitation in order to improve the analytical accuracy of multiply supported system. The residual rigid response is based on the missing mass method on the previous study [3,4], and the introduction of the multi-directional seismic excitations is based on our work [5]. In addition, in ordinary response spectrum analysis of uniform excited system, the formula is developed in consideration of the effect of the residual rigid response and the multi-directional excitation, corresponding to the above-mentioned multiply supported system.…”

“…But the above effects in the U. S. guidelines are not taken into consideration, and sometime overestimated the seismic responses. In our previous work [5], the multiply supported response spectrum analysis method CCFS (Cross-oscillator, Cross-Floor response Spectrum) based on the theorem [2] was extended, and it was shown that the seismic response considering the correlation coefficient between modes, between seismic excitation directions, and between multiple responses can be evaluated with good accuracy.…”