| Summary: | 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.
The functionality of risk minimization is demonstrated with two example structures, with the framework provided for a third. The first is an example previously solved in Rt, which confirms functionality of the implementations in Rts. The second model uses an analytical model of a single-storey timber-steel hybrid frame, which utilizes the novel structural “Finding the Forest Through the Trees” (FFTT) design concept that has been proposed in Vancouver and studied at UBC. The minimum mean cost of this structure, subject to the cost functions and structural simplification, was determined by optimizing two decision variables that represent the fundamental geometry of the frame. Optimization of this frame converged to one point throughout many analyses, utilizing both the steepest descent and BFGS search methods. Finally, the framework for a future 6-storey FFTT example was developed. This example is inspired from modern tall timber design concepts, which are discussed in a literature review and demonstrates unique features within Rts, including the deep parameterization and nested model structure. === Applied Science, Faculty of === Civil Engineering, Department of === Graduate
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