Stochastic free vibration analysis of RC buildings

Background/Objectives: Free vibration response of RC structures is random in nature due to the uncertainties exist in geometry, material properties and loading. Stochastic analysis methods can represent this randomness in responses. Methods: The Monte Carlo Simulation is a widely accepted method for stochastic structural analysis but the computational effort and cost associated with it is a limitation and hence in the present study, it is used as a method for the comparison and verification of the results obtained by other metamodel based approaches such as the response surface method. The number of analysis samples required depends on the type of approach adopted. Findings: Three different design of experiments approaches, Central Composite Design, Box Behnken Design and Full Factorial Design, where used in response surface modelling. The present study is an evaluation of these metamodel based approaches. The natural frequencies obtained by these methods of analysis were comparable with the results from Monte Carlo Simulation. However, the latter required one million analyses, making it computationally cumbersome. The Central Composite Design proved to be the most efficient method as it yielded the most accurate results even though the number of runs were marginally more than the 62 required for Box Behnken Design. Improvements: These response surface based metamodel approaches can be further applied to nonlinear stochastic analysis of structures where the cost and effort of analysis is significantly higher