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Reliability analysis of slender RC bridge columns under the combined effects of gravity and lateral loads Open Access

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The latest philosophy adopted by the American Association of State Highway and Transportation Officials (AASHTO), and Federal Highway Administration (FHWA) is the Load and Resistance Factor Design (LRFD) method. This philosophy accounts for the inherent uncertainties both in demand and capacity of structural components. Just recently Caltrans initiated its own implementation of a reliability design philosophy in its Bridge Design Practice (BDP), Uncertainties faced in a typical structural engineering problem are the following: (1) uncertainties arise because structural behavior cannot be accurately characterized and predicted and is defined as an epistemic uncertainty, (2) the other uncertainties results from the process of collecting temporal and environmental demands on the structure or aleatory uncertainty. The primary concentration of structural performance is on collapse prevention. The ability to predict the instability point with high accuracy ensures that the response remains in the safe range. Instability point is highly influenced by aleatory and epistemic uncertainties. Although the concept of stability is essentially dynamic in nature, static stability can be studied under assumption of linear elasticity and conservative loading such as gravity and hydrostatic loads. A computational technique that is widely used for evaluating the instability of structures under earthquake motion is the Incremental Dynamic Analysis (IDA). Performing nonlinear time history analysis using sufficiently large number of ground motions provides enough information to better identify the instability limit state for the column.In this research an expression for investigating the dynamic stability of RC bridge columns under the combined effects of gravity and dynamic loads is given in closed-form solution. Formulation of the governing equations of motion was based on Lagrangian mechanics and the closed-form solution (CFS) was derived from poles of the transfer function. The proposed analytical solution explicitly addresses the ductility level at which columns reach instability under dynamic loads. The analytical solution was subsequently validated through a nonlinear IDA of columns with varying ratios of slenderness, axial load, and longitudinal and transverse reinforcement. Reliability analysis in addressing P-Delta effects is performed as a measure of separation between the displacement ductility at the onset of instability and the target design displacement ductility for single column bents. Reliability indexes were computed assuming that both of these probability state variables follow normal distributions. The reliability analysis was subsequently used in specifying lower bound stability indexes. Stability indexes for addressing P-Delta effects are investigated based on a reliability analysis. Additionally, stability indexes were studied to: (1) stipulate threshold limits for neglecting P-Delta effects and, (2) define a collapse-prevention criterion. Collapse prevention of RC bridge columns was stipulated based on a target reliability index of 2. The lower bound stability index at the collapse-prevention threshold limit was calculated. Threshold limits for neglecting P-Delta effects was stipulated based on a target reliability index of 3.5.

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