Abstract
To address the irrationality of making a structure subjected to bidirectional ground motions equivalent to an SDOF system, a new approach method is presented in this paper. The ratio between modal participation factors of the two components of the structure is expressed as γ, and the superposition of bidirectional ground motions is regarded as one-directional earthquake excitation for the equivalent SDOF system. Based on this, an energy balance equation is established, and a method used to estimate normalized hysteretic energy (NHE) is proposed. Analysis of the ratio between NHE (γ ≠ 0) and NHE (γ = 0) is suggested in order to analyze the influence of bidirectional ground motions on hysteretic energy demand, and then, “α1 = NHE (γ ≠ 0)/NHE (γ = 0)” is defined, and bidirectional ground motion records for different soil sites are selected for establishing superimposed excitations. In addition, the period range of 0–5 s for the energy spectrum is divided into 6 ranges. In each period range, the means of α1 are defined as α. The curves of α of constant ductility factors for different soil sites are established, in which α is the vertical coordinate and γ is the horizontal coordinate. Through nonlinear response history analysis, the influence of soil types at different sites, the ductility factor, the ratio of modal participation factors, and the period on the values of α are analyzed. According to the analytical results, correction coefficient αs (the simplified value of α) is obtained so that the hysteretic energy demand under bidirectional ground motions can be determined.
Highlights
Proper design of earthquake-resistant structures is extremely important for seismically active areas because it can be a key instrument that shapes economic and social opportunities
Wang and Li [26] proposed a method to solve this problem, in which a structure under bidirectional ground motions (GMs) was made equivalent to a single-mass system with two degrees of freedom, and the hysteretic energy (HE) and earthquake input energy spectra were established based on this equivalent system; further research studies about the energy relationship between this equivalent system and the structure were required for application of this theory
Considering the irrationality of the equivalent SDOF system of a structure subjected to bidirectional GMs. e superposition of bidirectional GMs is regarded as the one-directional excitation of the equivalent SDOF system of a structure
Summary
Proper design of earthquake-resistant structures is extremely important for seismically active areas because it can be a key instrument that shapes economic and social opportunities. Response spectra have been recorded in practice since the 1971 San Fernando earthquake [3, 4], are considered a basic tool for determining cutting forces and dimensioning structures, and are used in preliminary calculations of important structures [3, 5]. Wang and Li [26] proposed a method to solve this problem, in which a structure under bidirectional GMs was made equivalent to a single-mass system with two degrees of freedom, and the HE and earthquake input energy spectra were established based on this equivalent system; further research studies about the energy relationship between this equivalent system and the structure were required for application of this theory. A novel approach is proposed, in which the superposition of bidirectional GMs is applied as one-directional excitations of the equivalent SDOF systems, and used to analyze the HE demand of structures
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