Lumped parameter macroscopic structural models, such as those consisting of springs and rigid sticks, are useful for parametric studies and probabilistic analyses of individual building structures as well as for regional-level assessments on building stock. The existing lumped parameter models (LPMs) for shear wall–frame dual systems exhibit some drawbacks. There is a discrepancy in their arrangement of springs. They are calibrated to match only two modal periods of the original multi-story or even high-rise building structure. The existing models also have limitations when confronted with the P-Δ effect. After a careful investigation, this paper developed new schemes of spring-stick assemblies that accurately reproduce the elastic stiffness matrix of a two-dimensional Euler–Bernoulli or Timoshenko beam–column element and cope with geometric and material nonlinearities. The developed assemblies, which are essentially lumped parameter substitutes for beam–column elements, can be used to build LPMs for moment frames and shear walls. For moment frames, the traditional fishbone model is converted into a LPM that not only reflects the beam-to-column stiffness ratio and strength ratio but also captures the P-Δ effect. Combining the LPM for shear wall with the lumped parameter fishbone model results in an improved LPM for wall–frame dual systems. Together with lumped floor masses, the improved LPM is able to accurately predict all the global vibration modes and nonlinear seismic responses of a dual system. The proposed LPM possesses distinct advantages when simplified macroscopic models are preferred for building structures.
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