Session: SE-03-01 Damping and Vibration Control

Paper Number: 61395

Start Time: Tuesday, July 13, 2021, 05:00 PM

61395 - Modified Response Spectrum Accounting for Seismic Load Categorization as Primary or Secondary in Multi-Modal Piping Systems 

This proposed paper follows up on previous PVP papers that were dealing with perfect plasticity (2017) and plasticity with hardening (2018) for single degree of freedom systems. After a theoretical approach of stress categorization for multi-modal piping systems was presented (2020), the purpose is to present its practical implementation.

Categorizing the inertial part of seismic load requires calculating the input level associated with the ultimate capacity and comparing it to the level associated with the plastic yield. For this purpose, an analysis of the seismically induced ductility demand in elastic-plastic oscillators of variable frequencies and variable hardening slope (10% and 20%) is carried out by running time response analyses. The seismic input motion is simulated as samples of a stochastic process of central frequency fc. The response of oscillators with natural frequencies, f0, varying from 0.1 fc to 10 fc, is systematically analyzed. For every oscillator, 10000 time-responses are performed, corresponding to 1000 input samples multiplied by 10 input levels, covering a wide range of ductility demand up to 20. 

A remarkable output is that seismic loads should be regarded as secondary for flexible oscillators (f0 < fc) while it should be regarded as primary for very stiff oscillators (f > fcut, cut-off frequency of the input motion), with intermediate situations for fc < f0 < fcut. On this basis, we derive an evaluation of the primary part of the seismically induced inertia stresses, which appear as strongly dependent on f0/fc. Dependence on the hardening slope is less significant, although not negligible.

A practical implementation of this result is presented in the frame of the conventional linear modal analysis method. It consists of a simple modification of the input response spectrum: spectral ordinates at the peak frequency (or plateau) and lower frequencies are lowered by a factor that depends on the ductile capacity and the hardening slope. The spectrum ordinate is unchanged at frequencies larger than fcut (the zero-period spectrum ordinate is unchanged), and a coefficient, linear versus frequency, applies between the peak and fcut.

This practical engineering approach is validated against nonlinear time-response analyses of the multimodal piping system ELSA., which is used in the framework of “Seismic Risk” project of EDF Research & Development Division with the objective of reducing conservatism of piping design criteria by performing seismic nonlinear analysis. This 6’’ pipeline, consisting of six elbows and seven straight lines, is made of 316L austenitic steel and underwent high level seismic load (up to 18g).

Presenting Author: Pierre LABBÉ LABBE Consultant

Authors:

Pierre LABBÉ LABBE Consultant
Thuong Anh Nguyen EDF Lab Paris-Saclay