TAILIEUCHUNG - Static diagnosis of multiple cracked beam

Model of crack was studied by many authors. Adams R. D. and Cawley P. in 1978 have proposed an axial spring model [1] to investigate the problem of location of crack in a bar using natural frequencies and mode shape. | Vietnam Journal of Mechanics, NCST of Vietnam Vol. 23, 2001, No4 (224 - 233) STATIC DIAGNOSIS OF MULTIPLE CRACKED BEAM TRAN VAN LIEN University of Civil Engineering NGUYEN TIEN KHIEM Institute of Mechanics, NCST of Vietnam 1. Model of multiple cracked beam Model of crack was studied by many authors. Adams R. D. and Cawley P. in 1978 have proposed an axial spring model [1] to investigate the problem of location of crack in a bar using natural frequencies and mode shape. However, in [1] the stiffness of the equivalent spring has not been calculated from the crack depth. The formula relating the spring stiffness and crack depth has been established due to study of Ju and others [2] in 1982. Subsequent studies by Haisty B. S. and Springer W. T . [3] and Dimaroganas A. D. and Chondros T . G. [4] have made a great progress in improvement of the formula. In this paper the rotational spring model of transverse crack in beam developed in studies of Dimaroganas A. D. and his coworkers is adopted and used for solving the crack detection problem. The beam with single transverse crack has been studied in a lot of publications [5, 6]. Less amount of works [7, 8] devoted to the case of multiple cracked beam, especially to the problem of multi crack detection. Following our study in [8] concerned the multiple cracked beam, the problem of multi crack detection using static displacements measured in a beam is considered in the present paper. The theoretical investigation will be illustrated by a numerical example for a cant ilever beam with two and three cracks. Thus , a crack of the depth a at the position x* (Figure ) , following to the [4] may be modeled as a rotational spring of stiffness 1 K=- · Q' ' a = 67r(l - v EI ·. z 2 )h I (~) c h ' () where 3 + 4 - 5 8 - 9 + 10 , Ic(z) = 2 +- - + 6 - 7 () which is determined experimentally. Therefore, a beam with n cracks of depth aj at

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• Static diagnosis of multiple cracked beam
• Multiple cracked beam
• Natural frequencies and mode shape
• The crack detection problem
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