Closed-form critical response of undamped bilinear hysteretic MDOF system under pseudo-double impulse for estimating resonant response under one-cycle sine wave

Approximate closed-form maximum interstory drifts under the critical pseudo-double impulse (PDI) are derived for undamped multi-story shear building models with bilinear hysteresis by using the proposed updated mode-controlled energy-based approach (UMEA). PDI was proposed in the previous paper to simulate the critical responses of elastic-plastic MDOF models under near-fault fling-step motions. Although a double impulse (DI) is treated as a ground motion, PDI is treated as a set of impulsive lateral forces. PDI excites only the fundamental-mode responses of elastic proportionally-damped MDOF models because the fundamental participation vector is applied to the influence coefficient vector of PDI. UMEA is a kind of displacement control analyses, and the displacement increment, which is proportional to the fundamental mode evaluated by the tangent story stiffnesses, is given to the model. It is demonstrated that UMEA effectively captures the main characteristics of the maximum interstory drifts under the critical PDI and the critical one-cycle sine wave because most of the kinetic energy, which the fundamental mode has just before yielding, is given to the plastic fundamental mode just after yielding except for the case that the post-yielding stiffness is almost zero. The use of UMEA leads to much more efficient estimation of the maximum interstory drifts than the time-history response analysis because UMEA requires only 2N-time evaluations of the elastic and plastic fundamental modes at most for N-story shear mass models with bilinear hysteresis. It is shown through numerical examples that the maximum interstory drifts under the critical PDI and the corresponding one-cycle sine wave correspond well to those evaluated by the proposed method. It is also shown that the correspondence of the responses of elastic-plastic MDOF models under recorded near-fault motions and the estimated responses by the proposed method is fairly good