Abstract— In the present work the effect of transverse cracks on natural frequencies of a simply supported beam with symmetric overhangs is investigated and an algorithm has been developed for identifying damage in the same. In the numerical example, single and triple cracks are considered in the dynamic analysis. Flexibility matrix of the intact beam and an additional flexibility matrix due to damaged beam is derived and added up to obtain the flexibility matrix of the cracked beam element. Stiffness matrix of cracked beam element is derived by multiplying a transformation matrix with the inverse of the final flexibility matrix of the cracked beam element. The natural frequencies and the corresponding mode shapes of vibration are obtained by solving eigen value problem. It is found that for a simply supported beam with symmetric overhangs, the 1 st frequency decreases with an increase in the crack depth, and, it decreases the most at mid span. In case of 2 nd and 3 rd frequency, these decreases the most at 20% and 80% of the total length from the left support. For triple cracks several important observations are also made. Keywords—Damage Detection, Structural Health Monitoring, Modal Analysis, Cracks, Beams. I. INTRODUCTION Engineering Structures withstand loads during their service life. Buildings are usually designed on strong column, weak beam concept. So, beams are more vulnerable to cracks. Vibrational measurements are an efficient means of crack detection. Crack leads to reduction in stiffness of beam, thereby reducing its natural frequency. A lot of research work has been done to develop effective methods for crack detection. Pandey and Biswas (1991) have evaluated changes in flexibility matrix in order to locate damage. Pandey et.al. (1990) have used curvature mode shape to detect and locate damage in structure. It is shown that curvature mode shape localizes in the damage region whereas the displacement mode shapes are not localized. Further, MAC and COMAC are not sensitive enough to detect damage in its earlier stage. Morassi and Rovere (1997) have identified localized damage in a multistory steel frame. Vibration tests were performed on a five story steel frame with a notch of fixed position and variable depth. Damage is localized by considering frequencies related to shear type modes only. Rizos et.al. (1989) have used the measurement of flexural vibrations of a cantilever beam with rectangular cross section having transverse surface crack extending uniformly along the width of the beam to locate crack location and crack depth. The method requires amplitude measurements at two positions of the structure only. The application of this method is limited to moderate cracks only. Liang et.al (1992) have developed theoretical relationship between eigen frequency changes, crack location and crack depth of damaged cantilever and simply supported beam. This theory can be more specifically applied to steel frame structures. Chondros and Dimarogonas (1979) have discussed the influence of crack in a welded joint on the dynamic behavior of a structural member. Local flexibility was used to establish relationship between crack depth to the change of natural frequency for the cases of a cantilever beam with a transverse crack at the welded root of the beam and of a beam welded (clamped) at both ends with a transverse crack at one welded end. This method is applicable to members of simple geometry. It is applied to individual members of large structures where member flexibility is larger than flexibility of supporting members. Mostafa Attar (2012) has used an analytical approach to investigate natural frequencies and mode shapes of a stepped beam with an arbitrary number of cracks and general form of boundary conditions. A simple transfer matrix is used to obtain general form of characteristic equation for the cracked beam. It is a function of crack location, crack depth, frequency, boundary conditions, geometrical and physical parameters of the beam. Boltezar et.al. have shown the crack identification procedure for free-free uniform beams in flexural vibrations. Khiem and Toan (2014) have proposed a novel method for calculating the natural frequencies of a multiple cracked beam and detecting unknown number of multiple cracks from measured natural frequencies. An explicit expression for natural frequencies through crack parameters is derived as modification of Rayleigh quotient for multiple cracked beams. Hu and Liang (1993) have developed two damage modeling techniques. First modeling technique involves use of massless, infinitesimal springs to represent discrete cracks and other employs a continuum damage concept. In spring model, castigliano’s theorem and perturbation technique are used to derive crack location, extent of crack and eigen frequency changes. In continuum damage model, effective stress concept together with Hamilton’s principle are used to derive similar relationship in continuum form. Antonino Morassi (1993) has shown that frequency sensitivity for any beam like structure can be evaluated on the basis of undamaged system by general Identification of Damages in Skeletal Structures using Modal Data Abhishek Kumar Sahu National Institute of Technology Agartala, India Dr. Surajit Das National Institute of Technology Agartala,India Department of Civil Engineering Assistant Professor M.Tech Scholar Department of Civil Engineering International Journal of Engineering Research & Technology (IJERT) ISSN: 2278-0181 http://www.ijert.org IJERTV5IS060248 (This work is licensed under a Creative Commons Attribution 4.0 International License.) Published by : Vol. 5 Issue 06, June-2016 www.ijert.org 168