crack modeling and vibration analysis of cracked in reinforced concrete beams strengthened with composite sheets

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RAZZAGHI J.; Abadi M.Kh.; ALIJANI A.

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Journal: Modares Civil Engineering journal Year:2018 | Volume:18 | Issue:4 Page(s): 85-99

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Title

crack modeling and vibration analysis of cracked in reinforced concrete beams strengthened with composite sheets

Author(s)

RAZZAGHI J. | Abadi M.Kh. | ALIJANI A. | Issue Writer Certificate

Keywords

Crack ModelingQ1

Vibration AnalysisQ1

Reinforced Concrete BeamsQ1

Composite SheetsQ1

Stress Intensity FactorQ1

Abstract

In this paper, a numerical method is presented for Crack Modeling in the opening mode in which a Vibration Analysis for cracked Reinforced Concrete Beams strengthened with Composite Sheets is carried out by using the fundamental relationships of fracture mechanics and finite element method. A one-dimensional beam is assumed to fulfill the finite element method in which two degrees of freedom (including the transverse displacement and the rotation) are considered at each node. The Hermitian shape functions are applied to interpolate the displacement field. The effects of Composite Sheets, steel bars and cracks are investigated in the analysis of the Euler-Bernoulli beam by correcting the second moment of inertia in cracked and uncracked sections. In this study, the cracked element is divided into two sub-elements. The continuity conditions are defined by equality of the transverse displacement, the moment and the shear force at the right-and left-hand sides of the crack point, while the rotation at there is different. The equations of the two sub-elements are connected together by continuity conditions in the point of the crack simulated by a rotational spring. The stiffness of this spring is regulated as a function of the Stress Intensity Factor. This factor depends on the parameters such as the location of the reinforcement, the distance of the composite sheet from the center of the cross-section, the crack depth and loading conditions. This technique of the problem solution called as “ Conversion Matrix” is implemented in the cracked element according to the expression of the displacement of the two nodes at the crack point in terms of the displacement of the basic nodes of the same element. The stiffness and mass matrices of the beam are enriched by inserting the effects of Composite Sheets, the steel reinforcement and the crack in the equations. These enriched matrices are used to implement the Vibration Analysis and the derivation of the natural frequency; for this purpose, an eigenvalue solution including the enriched stiffness and mass matrices is carried out to determine the natural frequency. In this research, the effects of the crack depth and location, boundary conditions, the composite sheet thickness and the cross-sectional area of steel bars on the response of the natural frequency of beam are discussed. The results show that if the crack depth increases, the value of the natural frequency decreases in which the natural frequency can be expressed in terms of a function of the crack depth. Also, increasing the thickness of the composite sheet results in increasing the natural frequency of the cracked Reinforced Concrete Beams, while the effect of the diameter of the steel bar is negligible on the natural frequency. In this paper, three boundary conditions of simply supported-simply supported (SS-SS), clamped-clamped (C-C) and clamped-free (C-F) are applied in the extraction of results. In the C-C boundary conditions, if the crack is situated at ⁄ ⁄ and ⁄ , the effect of the crack on the natural frequency can be ignored. The accuracy of the results is ensured by performing a full analysis in Abaqus software. The comparison of the results shows that the proposed method is appropriate for analyzing cracked Reinforced Concrete Beams strengthened with Composite Sheets.

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APA: Copy

RAZZAGHI, J., Abadi, M.Kh., & ALIJANI, A.. (2018). crack modeling and vibration analysis of cracked in reinforced concrete beams strengthened with composite sheets. MODARES CIVIL ENGINEERING JOURNAL, 18(4 ), 85-99. SID. https://sid.ir/paper/256616/en

Vancouver: Copy

RAZZAGHI J., Abadi M.Kh., ALIJANI A.. crack modeling and vibration analysis of cracked in reinforced concrete beams strengthened with composite sheets. MODARES CIVIL ENGINEERING JOURNAL[Internet]. 2018;18(4 ):85-99. Available from: https://sid.ir/paper/256616/en

IEEE: Copy

J. RAZZAGHI, M.Kh. Abadi, and A. ALIJANI, “crack modeling and vibration analysis of cracked in reinforced concrete beams strengthened with composite sheets,” MODARES CIVIL ENGINEERING JOURNAL, vol. 18, no. 4 , pp. 85–99, 2018, [Online]. Available: https://sid.ir/paper/256616/en

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