Transversely Cracked Beams with Quadratic Function’s Variation of Height

The receptance function has been studied and applied widely since it interrelates the harmonic excitation and the response of a structure in the frequency domain. This paper presents the derivation of the exact receptance function of continuous cracked beams and its application for crack detection. The receptance curvature is defined as the second derivative of the receptance. The influence of the crack on the receptance and receptance curvature is investigated. It is concluded that when there are cracks the receptance curvature has sharp changes at the crack positions. This can be applied for the crack detection purpose. In this paper, the numerical simulations are provided.

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Stiffness Estimation of Cracked Beams Based on Nonlinear Stress Distributions Near the Crack

Mathematical Problems in Engineering ◽

10.1155/2018/5987973 ◽

2018 ◽

Vol 2018 ◽

pp. 1-12 ◽

Cited By ~ 4

Author(s):

Chunyu Fu ◽

Yuyang Wang ◽

Dawei Tong

Keyword(s):

Crack Depth ◽

Internal Force ◽

Stress Distributions ◽

Cracked Beam ◽

Section Shape ◽

Nonlinear Stress ◽

Crack Depth Ratio ◽

Element Technique ◽

Force Equilibrium ◽

Cracked Beams

The crack presence causes nonlinear stress distributions along the sections of a beam, which change the neutral axis of the sections and further affect the beam stiffness. Thus, this paper presents a method for the stiffness estimation of cracked beams based on the stress distributions. First, regions whose stresses are affected by the crack are analyzed, and according to the distance to the crack, different nonlinear stress distributions are modeled for the effect regions. The inertia moments of section are evaluated by substituting these stress distributions into the internal force equilibrium of section. Then the finite-element technique is adopted to estimate the stiffness of the cracked beam. The estimated stiffness is used to predict the displacements of simply supported beams with a crack, and the results show that both static and vibrational displacements are accurately predicted, which indicates that the estimated stiffness is precise enough. Besides, as the section shape of beam is not limited in the process of modeling the stress distributions, the method could be applicable not only to the stiffness estimation of cracked beams with a rectangular section, but also to that of the beams with a T-shaped section if the crack depth ratio is not larger than 0.7.

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On the Stress Intensity Factors of Cracked Beams for Structural Analysis

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.488-489.379 ◽

2011 ◽

Vol 488-489 ◽

pp. 379-382 ◽

Cited By ~ 5

Author(s):

Erasmo Viola ◽

Yong Li ◽

Nicholas Fantuzzi

Keyword(s):

Stress Intensity ◽

Structural Analysis ◽

Cross Section ◽

Stress Intensity Factors ◽

Circular Cross Section ◽

Bending Moment ◽

Intensity Factors ◽

Close Approximation ◽

Shear Forces ◽

Cracked Beams

In this paper simple engineering methods for a fast and close approximation of stress intensity factors of cracked beams and bars, subjected to bending moment, normal and shear forces, as well as torque, are examined. As far as the circular cross section is concerned, comparisons are made on the base of numerical calculations. The agreement between the present results and those previously published is discussed. New formulae for calculating the stress intensity factors are proposed.

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