Reliability in OpenSees
OpenSees (Open System for Earthquake Engineering Simulation) is a general-purpose nonlinear finite element code developed by researchers in the Pacific Earthquake Engineering Research (PEER) Center. We have developed and implemented modules for sensitivity analysis, uncertainty propagation, reliability assessment and determining variable importance measures. C++ programming in an object-oriented architecture is used with special attention devoted to the maintainability and extensibility of the code. The program is capable of performing sensitivity analysis by the direct differentiation method (DDM), uncertainty propagation analysis by the first-order second-moment (FOSM) method, and reliability analysis by the first-order reliability method (FORM), importance sampling, and Monte Carlo simulation. Several variable importance measures are provided as part of the standard output. Linear and nonlinear static and dynamic problems can be analyzed. This program can be freely downloaded.

FERUM (Finite Element Reliability Using Matlab) has been developed primarily for pedagogical purposes, though it is also useful for research and engineering production. It is developed as a set of functions under Matlab to carry out finite element reliability analysis, as well as reliability analysis for prescribed analytical limit-state functions. It is under constant development by members of the research group. It serves as a testbed to implement and visualize methods and solution strategies in a relatively simple programming environment. FERUM is intended for use by other researchers interested in reliability analyses. The program - the set of Matlab functions, that is - can be downloaded for free under a GNU licence. Comments, questions and suggestions for further development will be received with gratitude.

CalREL - is a general purpose structural reliability analysis program. It is designed to work on its own or to operate as a shell program in conjunction with other structural analysis programs. Structural failure criteria are defined in terms of one or more limit-state functions. The specification is by the user in user-defined subroutines. CalREL is capable of computing the reliability of structural components as well as systems. Specific macro commands are available for the following types of analyses: (1) First-order component and system reliability analysis; (2) Second-order component reliability analysis by both curvature-fitting and point-fitting methods; (3) First-order reliability bounds for series systems; (4) First-order reliability sensitivity analysis with respect to distribution and limit-state function parameters; (5) Directional simulation for components and general systems, employing first or second-order fittings of the limit-state surfaces; and (6) Importance sampling and Monte Carlo simulation for components and general systems. CalREL has a large library of probability distributions for independent as well as dependent variables. Additional distributions may be included through a user-defined subroutine. CalREL is available for purchase from UC Berkeley in both object and source code. For more information about this program please write to

FSG (Floor Spectrum Generator) is a FORTRAN code used for generating floor response spectra (plot of the maximum response of an oscillator attached to a structure as a function of its frequency) directly in terms of the input ground response spectrum and including the effect of oscillator-structure interaction. It uses minimal information about the structure (i.e., modal frequencies, modal masses and components of mode shapes at the attachment point). It is based on the theory developed by T. Igusa and A. Der Kiureghian (see Earthquake Engineering & Structural Dynamics, 13(5), 661-676). For more information about this program please write to