The effect of crack on buckling behaviour of weakened column

Document Type : Original Article

Authors

Department of Civil Engineering, Yazd Branch, Islamic Azad University, Yazd, Iran

Abstract

This research deals with the buckling analysis of cracked column with fixed-fixed conditions. The crack is modelled with a unilateral elastic bending-stiffness behaviour, represented by a unilateral rotational spring. This model takes into account the crack closure effect on buckling behaviour of column. The governing equation of the problem is introduced by the variational approach based on energy arguments. Using the variational approach, the governing equation can be formulated as a function of damage index. Damage index is the stiffness of the equivalent rotational spring associated with the crack. A one-crack and a tow-crack are theoretically investigated to illustrate the effects of the crack on the buckling load. For the one crack column, the buckling load increases with the stiffness of the crack section. When the crack-stiffness parameter tends towards an infinite value, the structural model is reduced to the classical Euler column. It is observed that the buckling load increases as the crack get closer to the supports, for constant damage value of the crack parameter (constant crack depth). For the two crack column, the crack closure phenomenon is investigated. In order to two cases are considered. In the first case, the two-crack are located on the same side of column, and in the second case, the cracks are located on the opposite side of the columns. Comparison between two cases show that the crack closure influence on the buckling load. In other words the crack-closure phenomenon tends to increase the buckling load.

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  • Okamura, H., Liu, H.W., Chu, C.S., Liebowitz, H., (1969). A cracked column under compression. Engineering Fracture Mechanics, 1(3), 547-564.
  • Ostachowicz, WM., Krawczuk C. (1991). Analysis of the effect of cracks on the natural frequencies of a cantilever beam. J Sound Vib,150(2), 191–201.
  • Chondros, TJ., Dimarogonas, AD., Yao, J. (1998). A continuous cracked beam vibration theory. J Sound Vib , 215(1),17–24.
  • Biondi, B., Caddemi, S. (2005). Closed form solutions of Euler–Bernoulli beam with singularities. J. Solids Struct, 42, 3027–3044.
  • Biondi, B., Caddemi, S. (2007). Euler–Bernoulli beams with multiple singularities in the flexural stiffness. J. Mech, 26, 789–809.
  • Shifrin, E.I., Ruotolo, R. (1999). Natural frequencies of a beam with an arbitrary number of cracks. Sound Vib, 222, 409–423.
  • Kisa, M. (2011). Vibration and stability of multi-cracked beams under compressive axial loading. Int. J. Phys. Sci. 6, 2681–2696.
  • Caddemi, S., Calió, I. (2011). The influence of the axial force on the vibration of the Euler–Bernoulli beam with an arbitrary number of cracks. Appl. Mech, 82, 1–13.
  • Anifantis, N., Dimarogonas, A., (1983). Stability of columns with a single crack subjected to follower and vertical loads. International Journal of Solids and structures, 19(4), 281-291.
  • Li, Q.S, (2003). Classes of exact solutions for buckling of multi-step non-uniform columns with an arbitrary number of cracks subjected to concentrated and distributed axial loads. International Journal of engineering Science, 41(6), 569-586.
  • Caddemi, S., Calio, I., Cannizzaro, F. (2013). The influence of multiple cracks on tensile and compressive buckling of shear deformable beams. International Journal of Solids and Structures, 50(20-21),3166-3183.
  • Challamel, N., Lanos, C., Casandjian, C. (2006). Localization in the vibration of a two-span weakened column. Engineering Structures, 28(5), 776-782.
  • Dehghani, M.A., Dehghan Manshadi, S.H., Ranjbaran, A., Esfandiari, M.J. Dehghan Manshadi, S.M. (2018). Analysis of localization in the buckling of a two-span column with elastic end connections. European Journal of Environmental and Civil Engineering, 22(7), 811-835.
  • Zhou, L., Huang, Y. (2006).Crack effect on the elastic buckling behavior of axially and eccentrically loaded columns. Struct Engng Mechanics, 22(2), 169-184.
  • Patel, T.H., Darpe, A.K. (2008). Influence of crack breathing model on nonlinear dynamics of a cracked rotor. Sound Vib. 311, 953–972.
  • Caddemi, S., Calió, I. (2011). The influence of the axial force on the vibration of the Euler–Bernoulli beam with an arbitrary number of cracks. Appl. Mech, 82, 1–13.
  • Ariaei, A., Ziaei-Rad, S., Ghayour M. (2009). Vibration analysis of beams with open and breathing cracks subjected to moving masses. Journal of sound and vibration, 326(3-5),709-724.
  • Cicirello, A., Palmeri, A. (2014). Static analysis of Euler-Bernoulli beams with multiple unilateral cracks under combined axial and transverse loads. International Journal of Solids and Structures, 51(5), 1020-1029.