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

This paper presents practical implementation of a theoretical approach that was introduced at PVP 2020 conference. Analysis of the seismically induced ductility demand in elastic-plastic oscillators of variable frequencies and hardening slope is carried out by running time response analyses. The input motion consists of 1000 stochastic process samples of central frequency f_c. Oscillators of natural frequencies, f₀, (0.1 f_c ≤ f₀ ≤ 10 f_c) are submitted to a wide range of ductility demand, up to 20. It turns out that seismic loads should be regarded as secondary for flexible oscillators (f₀ < f_c) and primary for very stiff oscillators (f > f_cut, cut-off frequency of the input motion), with intermediate situations. On this basis, we derive a strongly f₀/f_c dependent evaluation of the seismically induced inertial stresses primary part. In the frame of the conventional linear modal analysis method, practical implementation consists of reducing the input response spectrum: spectral ordinates are minimized in the low frequency domain by a factor that depends on the ductile capacity and hardening slope, unchanged at the ZPA frequency and vary linearly in the medium frequency domain. This approach is tested against nonlinear time-response analysis of a multimodal piping system.