Carrying capacity of edge-cracked columns under concentric vertical loads

• Published in: Acta mechanica Vol. 198; no. 1-2; pp. 1 - 19
• Main Authors: Yazdchi, Kazem, Gowhari Anaraki, A. R.
• Format: Journal Article
• Language: English
• Published: Vienna Springer-Verlag 01.06.2008; Springer; Springer Nature B.V
• Subjects: Buckling; Classical and Continuum Physics; Control; Cracks; Dynamical Systems; Eigenvalues; Engineering; Engineering Thermodynamics; Exact sciences and technology; Flexibility; Fracture mechanics (crack, fatigue, damage...); Fundamental areas of phenomenology (including applications); Heat and Mass Transfer; Mathematical models; Mechanical engineering; Physics; Solid Mechanics; Structural and continuum mechanics; Theoretical and Applied Mechanics; Vibration; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Circular Cross Section; Crack Depth; Edge Crack; Transfer Matrix Method; Rectangular Cross Section; J integral; Transfer matrix; Rupture; Transverse load; Vertical load; Modeling; Edge crack; Finite element method; Load capacity; Column; Critical load; Matrix method; Eigenvalue problem; Buckling
• ISSN: 0001-5970; 1619-6937
• DOI: 10.1007/s00707-007-0523-z

Summary This paper analyses the carrying capacity of edge-cracked columns with different boundary conditions and cross sections subjected to concentric vertical loads. The transfer matrix method, combined with fundamental solutions of the intact columns (e.g. columns with no cracks) is used to obtain the capacity of slender prismatic columns. The stiffness of the cracked section is modeled by a massless rotational spring whose flexibility depends on the local flexibility induced by the crack. Eigenvalue equations are obtained explicitly for columns with various end conditions, from second-order determinants. Numerical examples show that the effects of a crack on the buckling load of a column depend strongly on the depth and the location of the crack. In other words, the capacity of the column strongly depends on the flexibility due to the crack. As expected, the buckling load decreases conspicuously as the flexibility of the column increases. However, the flexibility is a very important factor for controlling the buckling load capacity of a cracked column. In this study an attempt was made to calculate the column flexibility based on two different approaches, finite element and J-Integral approaches. It was found that there was very good agreement between the flexibility results obtained by these two different methods (maximum discrepancy less than 2%). It was found that for constant column flexibility a crack located in the section of the maximum bending moment causes the largest decrease in the buckling load. On the other hand, if the crack is located just in the inflexion point at the corresponding intact column, it has no effect on the buckling load capacity. This study showed that the transfer matrix method could be a simple and efficient method to analyze cracked columns components.