Static Displacement of Complex Piping System Using Modal Participation Spatial Vectors

Abstract The static displacement of complex piping systems is calculated using the natural frequencies, mode shapes, and modal participation vectors. The author has recently developed the theoretical analysis method for the natural frequencies and mode shapes of three dimensional complex piping systems with elbows and tees. The results of the method agree with those obtained by finite element analysis. The authors have also proposed the concept of the modal participation spatial vector. The modal participation spatial vector represents the direction of input motions that excites the mode the most. The elastic response spectrum of a three dimensional system for a three dimensional acceleration is improved using the unidirectional seismic motion that is parallel to the modal participation spatial vector. In this paper, two methods are combined for the static displacement of three dimensional complex piping systems. The frequency response function of a multi degree of freedom system are calculated from the natural frequencies, modal vectors, and modal participation spatial vectors of the system. The value of the frequency response function at zero frequency represents the static displacement. However, the problem of convergence remains. Therefore, the number of the modes used to calculate the static displacement are discussed.