The risk posed to a structure from an earthquake may be minimized by changing the design characteristics of the structure to determine the optimal design. A risk measure, the mean value of the cost functions in this thesis, can be determined using reliability methods to construct a loss curve. This formulation includes the effect of uncertainty in all aspects of the cost, including construction and repair given an event. This risk model also requires no prior information to determine the mean cost and does not define a discrete “failure,” instead using a continuum of possible outcomes in determining the mean of the cost functions. The optimization model allows for different search directions and step sizes in the search for the minimum cost, with steepest descent and BFGS search directions currently implemented. These analyses are performed using the Rts software, which has the capability of performing the optimization, risk, and reliability analyses on input structural models.
