This thesis presents a probability model to predict the maximum rotation of rocking bodies exposed to seismic excitations given specific earthquake intensity measures. After obtaining the nonlinear equations of motion and clarification of the boundaries applied to a rocking body to avoid sliding, a complete discussion is provided on the estimation of approximate period and equivalent damping ratio for the rocking motion. Thereafter, instead of using an iterative solution, which was previously proven defective, a new approximate technique is developed by finding the best representative ground motion intensities. Suitable transformation and normalization are applied to these intensities, and the Bayesian Updating approach is employed to construct a probability model. The proposed probability model is capable of accurately predicting the maximum rotation of a symmetric rocking block given displacement design spectra, peak ground acceleration, peak ground velocity, and arias intensity of an earthquake. This probabilistic model along with the approximate capacity of rocking blocks are used to estimate the fragility curves for rocking blocks with specific geometrical parameters. At the end, a comprehensive and practical form of fragility curves and numerical examples are provided for design purposes.

Sliding is recognized as a dominant response mode for unanchored stocky components in nuclear facilities. Although unanchored components are themselves not safety-critical, their interaction with safety-critical systems and components during earthquake shaking can have significant consequences. It is therefore important to be able to accurately estimate the peak sliding displacement demands on unanchored components so that sufficient clearance is provided around them. In lieu of nonlinear time history analysis, the ASCE/SEI 43-05 standard provides an approximate method to estimate the maximum sliding displacement of sliding objects in nuclear facilities. The present paper assesses the procedure of the approximate method and compares its results to those of nonlinear time history analysis. The study finds that the ASCE 43-05 approximate method provides conservative sliding estimates overall and that is based on the three components of 7 modified and 159 real earthquake motions used in this study. It is concluded that the ASCE 43-05 approximate method offers reasonable sliding estimates of components in nuclear facilities. / Thesis / Master of Applied Science (MASc)

Cable-stayed bridges are popular these days in spite of their complexity in shape and design. Cable-stayed bridges are ideal for a navigational channel due to their high clearance and long central span. These types of bridges also possess advantages over suspension bridges, especially when local site conditions are not suitable for anchoring the towers. In most of the cases, cable-stayed bridges are self-supportive or require less anchorage. Although symmetrical cable-stayed bridges are dominant, asymmetrical bridges are also common as well due to ground layouts and other restrictions like economy, aesthetic purpose. Added counter weight and eccentricity of asymmetrical bridge may highly affect the response of the structure under earthquake loading. For the same length span bridge, the response of the asymmetric one may have an amplified response compared to the symmetric one with the same span length and also, may not follow any predictable trend. This study presents a multi-support analysis for four models, which are, 200 m symmetrical, 400 m symmetrical, 200 m asymmetrical and 400 m asymmetrical bridges. Ground motions has been recorded by using accelerometers. The recorded ground motion depends on the direction of the accelerometer. To remove this dependency, the principal components of each ground motion were found and used for the analysis and the models were excited in the transverse direction. The models were run under both multi-support excitation and identical-support excitation for displacement time-history analysis using SAP2000. Ratio of stresses and deflections were compared for the bridges with the same span length. According to this study, on 200 m asymmetrical bridge, multi-support excitation factored responses up to 4%, while on 400 m asymmetrical bridge, responses are factored up to 20% compared to the identical-support excitation. It is noted that responses of asymmetrical bridges are factored up making identical-support excitation non-conservative.