Probabilistic Dynamic Response of Beams and Frames

This paper presents a method for evaluating the probabilistic dynamic response (distribution of natural frequencies and amplitudes) of reinforced concrete beams and frames. It considers the statistical variation of material properties, geometric parameters, and exciting force. The basic dependent variables that are considered probabilistic are individual geometric parameters, the area of reinforcement and strengths of materials. The dependent variables that are of statistical nature are dynamic modulus of elasticity of concrete, moments of inertia, and areas. The Monte Carlo simulation is used to generate the distribution of the dependent variables from that of the independent parameters. Examples covering a wide range of geometric and load parameters are considered for both beams and frames. Distribution of natural frequencies and response amplitudes are calculated by a specially developed computer program. The results are then reviewed from the practical point of view.