Structural Reliability Analysis Based On Ultimate Bearing Capacity And Seismic Ductility Demand

Ultimate bearing capacity and seismic ductility demand are two important indices representing strength and ductility performance of engineering structures, which are also key parameters for safety and applicability evaluation as well as structural seismic design. In this study, the Elastic Modulus Reduction Method (EMRM) was proposed to evaluate ultimate bearing capacity of complex structures based on the generalized yield criterion and limit analysis theory. Two novel methods including the Influence Coefficient Method (ICM) and Stochastic Elastic Modulus Reduction Method (SEMRM) were developed for system reliability analysis of large complicated structures based on theories of stochastic finite flement, limit analysis and component reliability. Furthermore, three new Bouc-Wen models for nonlinear seismic dynamic analysis of inelastic systems under unidirectional-, bidirectional-, and lateral-torsional coupling excitations were developed by improving the traditional uniaxial model. The influences of P-â–³and pinching effects as well as strength and stiffness degradations on probabilistic characteristics of seismic ductility demand and Park-Ang damage index of inelastic system were also quantitatively investigated using 69 earthquake records. The probability distribution type and prediction equation of seismic ductility demand for inelastic system with strength and stiffness degradations as well as P-â–³and pinching effects were also developed. This study provides significative foundation of theory research and guidance of engineering application in safety and applicability evaluation as well as seismic reliability analysis. The main contents of this thesis are as follows:(1) The element bearing ratio (EBR), degree of uniformity of EBRs, and the reference EBR were defined based on the generalized yield criterion and limit analysis theory. By adopting the EBR as a governing parameter, the Elastic Modulus Reduction Method (EMRM) was developed based on the Strain Energy Equilibrium Principle (SEEP). Numerical examples show that the EMRM is accurate and efficient for limit analysis of complex structures constructed with multi-material and with complicated configuration.(2) Four strategies including the Fixed Strain Method (FSM), the Circular Arc Method (CAM), the Strain Energy Conservation Law (SECL), and the Strain Energy Equilibrium Principle (SEEP) were proposed to determine the elastic modulus reduction factor. The applications and limitations of above four strategies in limit analysis of spatial frame and truss as well as thin plate and shell structures were investigated. Numerical results show that flexibility and accuracy of the SEEP is most satisfied, which provides a rational way to determine the elastic modulus reduction factor.(3) A novel method to calculate ultimate bearing capacity of frame structure under combined action of initial constant and proportional loads was developed by modifying the proposed Elastic Modulus Reduction Method (EMRM), which eliminates the assumption of proportional loading existed in various analytical and mathematical programming methods as well as traditional elastic modulus adjustment procedures for limit analysis. Numerical results show that the method is accurate and efficient to evaluate ultimate bearing capacity of frame structure under both dead and live loads.(4) A new uniaxial Bouc-Wen model for nonlinear seismic dynamic response analysis of inelastic single-degree-of-freedom (SDOF) system under unidirectional ground motion excitation was developed considering P-A effect, pinching effect, strength and stiffness degradations, and strain hardening. The influences of P-A and pinching effects on probabilistic characteristics of seismic ductility demand and Park-Ang seismic damage index of inelastic SDOF system were quantitatively investigated using 69 earthquake records. The probability distribution type and prediction equation of seismic ductility demand for inelastic SDOF system with P-A and pinching effects were also developed.(5) Adopting the normalized displacement as governing parameter, a new biaxial Bouc-Wen model for nonlinear seismic dynamic analysis of inelastic two-degree-of-freedom (2DOF) system under bidirectional ground motion excitations was developed using circular yield surface to describe coupling effect of biaxial normalized restoring forces. The influences of bidirectional excitation and P-A effect on statistical characteristics of seismic ductility demand and Park-Ang seismic damage index of inelastic 2DOF system were discussed using 69 earthquake records. Approximate prediction equations for seismic ductility demand and cumulative dissipated energy of inelastic 2DOF system under bidirectional excitation and with P-â–³effect were also developed.(6) By adopting the circular yield surface to describe the coupling effect between biaxial normalized lateral restoring forces and the pyramidal or spheriform yield surface to describe the coupling effect of normalized biaxial lateral restoring forces and torsion, a new lateral-torsional coupling Bouc-Wen model for nonlinear seismic dynamic analysis of planar asymmetric structure under bidirectional ground motion excitations was developed. The influences of the normalized yield strength, uncoupled translational frequency ratio, normalized stiffness eccentricity, uncoupled lateral-to-torsional frequency ratio, and post-yield stiffness to initial stiffness ratio on statistical characteristics of seismic ductility demand and Park-Ang seismic damage index of planar asymmetric structure were also investigated using 69 earthquake records.(7) The Influence Coefficient Method (ICM) was proposed to evaluate system reliability of frame structure by combining elastic modulus adjustment procedure and component reliability theory. The relationship between internal forces and external loads was determined by determinate linear elastic finite element analysis and the element reliability index was adopted as governing parameter to define the degree of uniformity of reliability indices and reference reliability index. A new procedure for elastic modulus adjustment was proposed to simulate redistribution of element reliability indices and transition of failure modes. The failure probability of complex structural system can be achieved based on iterative linear elastic finite element analyses. Numerical results show that the ICM is accurate and efficient for system reliability analysis of large complicated structures, and overcomes difficulties for simulation of failure transition and identification of dominant failure modes in traditional methods.(8) The Stochastic Elastic Modulus Reduction Method (SEMRM) for system reliability analysis of spatial variance frame was proposed based on theories of random field, limit analysis and component reliability. The structural parameters and external loads were modeled as random fields to account for their spatial variations and the covariance matrix of local averages of random fields was calculated using the numerical integration method. The stochastic response and reliability index of each element were achieved by the Perturbation Stochastic Finite Element Method (PSFEM). By adopting the element reliability index as governing parameter, a new strategy for elastic modulus adjustment in system reliability analysis was developed. The collapse mechanism and system reliability index of stochastic frame can be determined through iterative stochastic finite element analyses. Comparing with traditional failure mode approaches, the SEMRM is accurate and efficient, which also avoids modification of element stiffness matrix and artificial loading to simulate failure mode transition and accounts for spatial variations of both structural parameters and external loads rationally.