Adaptive numerical method algorithms are presented for the numerical simulation of the hysteretic behavior of nonlinear viscous and bilinear oil dampers within a finite element program for nonlinear dynamic analysis of frame structures under earthquake excitations. The adaptive algorithms are applicable for computing high-precision solutions for nonlinear viscous and bilinear oil dampers with valve relief that are typically represented mathematically with a nonlinear Maxwell model. The algorithms presented possess excellent convergence characteristics for viscous dampers with a wide range of velocity exponents and axial stiffness properties. The algorithms are implemented in an open source finite element software, and their applicability and computational efficiency is demonstrated through a number of validation examples with data that involve component experimentation as well as the utilization of fullscale shake table tests of a 5-story steel building equipped with nonlinear viscous and bilinear oil dampers.
This paper presents quantitative information on the effectiveness of seismic retrofit solutions using bilinear oil dampers for seismically deficient existing tall steel buildings. For this purpose, a benchmark 40-story steel space moment-resisting frame building is studied that represents 1970s design practice in North America. Rigorous seismic performance assessment based on ASCE 41 recommendations reveals a high collapse risk for the existing building. The local engineering demand parameters are comprehensively assessed to quantify the impact of seismic retrofit on steel columns and column splices, which are particularly vulnerable due to the time of construction. Multiple retrofit schemes are explored with numerous damping levels and vertical damping distribution methods. The dampers are designed via a recently developed multi-degree-of-freedom performance curves method. A new balanced vertical damping method is proposed to account for the effects of frame inelasticity. This strongly depends on the supplemental damping level, and it determines the effectiveness of the employed vertical damping distribution method. The results indicate that the proposed retrofit strategies can minimize the collapse risk of the tall building. It is shown that the balanced vertical damping distribution method provides the most uniform drift distribution along the building height. Despite the reduction in story drift ratios, the axial force demand in exterior columns remains relatively high in the bottom stories regardless of the seismic retrofit solution. On the other hand, bilinear oil dampers produce relative constant forces despite exhibiting higher velocity demands than expected.
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