Implementing Multiplicative Dimensional Reduction Method For Probability Based Seismic Analysis Of RCC Frames

Abstract

Likelihood of the presence of uncertainties in engineering systems is an unhidden, yet, widely accepted fact. Uncertainties are usually encountered in input variables (Loading, Material properties, Geometrical properties, etc.), in response variables (Displacements, Stresses, etc.), and in the relationships between them. All these uncertainties can be dealt with the aid of ‘Reliability Analysis’, thereby, providing the engineers accurate predictions of the probability of a structure performing adequately during its lifetime. Hence, it can be ascertained that ‘Uncertainty Analysis’ of any structural system is an important part of engineering probabilistic analysis. Uncertainty analysis incorporates: (a) Evaluation of the statistical moments of the response, (b) Assessment of the entire probabilistic distribution of the response, and (c) Computation of the parametric sensitivity analysis of the sytem. The actual model of system’s response is usually a high-dimensional function of input variables. Although Monte Carlo Simulation (MCS) has been standardized for the same purpose, yet, it may necessitate extra analytical efforts to achieve an acceptable level of accuracy, especially for the analysis of complex deterministic systems. Hence, development of a robust, computationally effective and easy-to-implement framework is genuinely necessitated to overcome the potential inhibitions involved in the MCS’ implementation for the reliability analysis of structures. As an effective substitute to MCS, this study proposes “Multiplicative Dimensional Reduction Method (MDRM)” to ease out the reliability analysis of structural systems. Further, this study advances ‘MDRM’ by combining it with the “Maximum Entropy (MaxEnt) Principle”, wherein, ‘Fractional Moments’ and not traditional ‘Integer Moments’ are considered as constraints. This novel computational approach allows fairly accurate estimations of both the statistical moments and the probabilistic distribution of the response of interest. In addition, the proposed scheme provides the ‘Global-Variance based Sensitivity Indices’ as a by-product. Therefore, no extra computational efforts are necessitated for sensitivity analysis. The entire work is performed by integrating Microsoft Excel and MATLAB. The efficiency and efficacy of the proposed approach for the structural reliability analysis is demonstrated through pilot study and two main studies. The pilot study is based upon the ‘Minimum Tensile Reinforcement Required in Beams’. The main studies implement MDRM for probability based “Seismic Analysis of a 4—Storeyed RCC Frame”, with a different pattern of input variables. To sum up, it can be envisaged that the proposed approach is computationally affordable without compromising accuracy, as it saves lot of time, thereby yielding similar results with reasonable accuracy as provided by time consuming and computationally expensive standard technique like MCS. The results of such work have significance in future studies for the estimation of the probability of the response exceeding a safety limit and for establishing safety factors related to acceptable probabilities of structural failures.