A new technique in the modal analysis of cracked reinforced concrete (RC) beams through the finite element method

Abstract

In this paper, the natural frequency of the cracked reinforced concrete (RC) beams in the first and second modes are investigated using the finite element method. In this research, the modelling of the crack is made based on continuity conditions, the correction of the moment of inertia and considering the stress intensity factor (SIF) at the crack point. In this study, the crack in opening mode is corresponded to a rotational spring. The stiffness factor of the spring is derived as a function in terms of the stress intensity factor and geometric and material characteristics of a cracked cross-section. In the present technique, the stiffness and mass matrices of a cracked element are enriched using convert matrices obtained by applying continuity conditions in the crack point. Natural frequencies of the cracked reinforced concrete Euler-Bernoulli beam are determined by inserting enriched stiffness and mass matrices in the eigenvalue equation. The effect of different depths and positions of crack and various boundary conditions are studied on the first and second vibration modes. A comparison between the results of the present work with experimental results and fully simulation in Abaqus clearly demonstrates the accuracy of the proposed technique in the determination of the natural frequency of the cracked reinforced concrete beams.

Keywords

• modal analysis
• reinforced concrete beam
• crack
• finite element method
• rotational spring