Seismic analysis of piping systems

Abstract

Seismic analysis of piping systems has been reviewed based on the single degree response spectrum curve technique and lumped mass parameters. Using the design of the primary coolant loop of a typical nuclear power plant as an example, both stiffness and flexibility formulations have been discussed in detail, in which the pipes, valves, steam generator, and coolant pump are included in the three dimensional model. Since it is a general practice to choose only part of the six degrees-of-freedom in each concentrated mass, the flexibility matrix constructed based on this reduced system is not complete. Consequently, the usual approach of obtaining shear forces from a stiffness matrix may be in error when the latter has to be computed by inverting the reduced flexibility matrix. This difficulty can be overcome by reducing the stiffness matrix after inverting the complete flexibility matrix. However, this is not always practical because the size of the matrix, which has to be inverted, may be large. On the other hand, whether the use of stiffness matrix together with the maximum relative displacement vector will give a maximum reverse effective force vector is uncertain. Consequently, the stiffness method may not always yield satisfactory results. In the light of these difficulties, to compute an approximate but conservative absolute acceleration vector becomes more attractive in the sense that this process does not require inverting any matrix. The reverse effective force vector obtained by multiplying the diagonal mass matrix with the maximum absolute acceleration vector will, indeed, be a maximum.