Studies On Performance-based Seismic Design Methods Of Structures Subjected To Multi-dimensional Earthquake Excitations

Both theoretical analysis and seismic disasters indicate that the torsional response canaggravate destroying of the asymmetry plan structures. The torsional coupling response willinduce the structure's dimensional effects that shouldn't be resolved in the two dimensions(2D). Presently, the seismic design has been shifted from force-based seismic design(FBSD)to performance-based seismic design (PBSD), but the existing research findings of PBSDalmost belong to 2D analysis. So it is significant to develop performance-based seismicdesign theories and methods for the asymmetry plan structures subjected to multi-dimensionalearthquake excitations. The theories and procedures of PBSD for asymmetric plan structuressubjected to multi-dimensional earthquake excitations are established and discussed, the mainfindings are listed as follows:(1) A seismic design approach is presented where the design procedure attempts to createstructures with a specified limited objective under a specified level of seismic intensity. Thelimited objective may be directly defined by limiting damage state of the weakness storey.The famous Park model, constant ductility inelastic response spectra and the traditionaryseismic design method are combined to determine families of structures whose initial strengthand stiffness characteristics will ensure that the desired limited damage performance objectivefor each seismic level is, as closely as possible, achieved. Furthermore, the applicability ofusing the parameterγ_h for storey response of multiple degree-of-freedom structures isanalyzed, and the corresponding equation is established. Finally, a design example shows thatthe design approach is feasible and accurate.(2) The formula of hysteretic energy between the MDOF structures and equivalentSDOF systems is developed. The procedure for estimating hysteretic energy of MDOFstructures subjected to severe ground motions employing the energy relation equation basedon equivalent SDOF systems is proposed. Finally, eight examples for two regular and sixirregular MDOF structures which includes three stiffness distribution irregular structures andthree yield ratio distribution irregular structures show that the procedure to obtain thehysteretic energy demands of MDOF structures may be used as a simple and effective energyestimation method.(3) The traditionary design for structural members' section sizes depends on the concept design absolutely which is difficult to answer the purpose of multi-performance objective forperformance-based seismic design. So, the constant ductility strength reduction factorinelastic statistical spectra is analyzed, and the simplified inelastic spectra equation ispresented, based on which the traditionary two stages seismic design is developed to threestages seismic design: stiffness design stage, strength design stage, displacement checkingstage. In the stiffness design stage, the displacement-based stiffness design procedure ofsymmetry structures is proposed, firstly. For asymmetry plan structures, the adjustmentprocedure of storey stiffness distribution is presented, by which the floor quality center andstiffness center are concurrent and the torsion response is reduced. The displacement-basedseismic design procedure of eccentric structures is presented for those which it is difficult toremove the structural eccentricity by adjusting stiffness distribution. Finally, the three stagesseismic design procedures for multi-dimensional structures are proposed.(4) The constant ductility strength reduction factor inelastic statistical spectra forbi-directional ground motions is established and effects on structural nonlinear response underbi-directional earthquake excitations are discussed based on statistic analysis of 178recordings for hard site, medium site and soft site. By the sufficient statistic analysis, thesimplified model of constant ductility strength reduction factors design spectra is established,which is the foundation for forming the inelastic design demand spectra for structuressubjected to bi-directional ground motions.(5) A multiple modal pushover analysis method to estimate seismic demands forasymmetric plan structures subjected to bi-directional ground motions is presented. Theassumption of equivalent systems for asymmetric plan structures is developed fromequivalent SDOF systems for symmetric structures. The displacement response of asymmetricplan structures is supposed to equate to the combined responses of modal equivalent systems.The multiple modal pushover analysis procedure is proposed, and an example for comparingstructural response results of multiple modal pushover analysis with the results of nonlineardynamic time history analysis shows that the multiple modal pushover analysis proceduremay be used as a simple and effective seismic demands estimation method for asymmetricplan structures subjected to bi-directional ground motions.(6) The capacity spectra methods for estimating the earthquake demands of asymmetricplan structures which based on the multiple modal pushover analysis and bi-directionalinelastic response demand spectra presented in the paper is proposed. Finally, the engineeringexample is provided to show the method is simple, feasible and accurate.