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Dynamic Instability Analysis of Axially Compressed Castellated Columns

  • Jin-song LeiEmail author
  • Boksun Kim
  • Long-yuan Li
Article
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Abstract

This paper presents an analytical study on the dynamic instability of castellated columns subjected to axial excitation loading. By assuming the instability modes, the kinetic energy and strain energy of the columns and the loss of the potential of the axially applied load are evaluated, from which the mass matrix, stiffness matrix, and geometric stiffness matrix of the system are derived. These matrices are then used for deriving dynamic equations and carrying out the analysis of dynamic instability of castellated columns by using Bolotin’s method. The analytical expression for determining the critical excitation frequency of the columns is derived, which takes account for not only the shear influence of web openings but also the rotary inertia effect on the transverse vibration of the columns. Numerical examples are also provided for illustrating the dynamic instability behaviour of castellated columns when subjected to axial excitation loading. The results show that the consideration of the shear effect in castellated columns results in a shaft of the dynamic instability zone to low frequency side and a reduction of the width of the dynamic instability zone. The shear effect on the dynamic instability zone becomes more significant in the short column than in the long column, and in the wide flange column than in the narrow flange column.

Keywords

Dynamic instability Vibration Buckling Castellated column Shear effect Inertia effect 

Notes

References

  1. Bolotin, V. V. (1964). The dynamic stability of elastic systems. San Francisco, CA: Holden-day Inc.zbMATHGoogle Scholar
  2. Chen, J. K., Kim, B., & Li, L. Y. (2014). Analytical approach for transverse vibration analysis of castellated beams. International Journal of Structural Stability and Dynamics,14(3), 1–13.MathSciNetCrossRefGoogle Scholar
  3. Chen, L. Y., Lin, P. D., & Chen, L. W. (1991). Dynamic stability of thick bimodulus beams. Computers & Structures,41(2), 257–263.CrossRefGoogle Scholar
  4. Ellobody, E. (2011). Interaction of buckling modes in castellated steel beams. Journal of Constructional Steel Research,67(5), 814–825.CrossRefGoogle Scholar
  5. El-Sawy, K., Sweedan, A., & Martini, M. (2009). Major-axis elastic buckling of axially loaded castellated steel columns. Thin-Walled Structures,47(11), 1295–1304.CrossRefGoogle Scholar
  6. Gandomi, A. H., Tabatabaei, S. M., Moradian, M., Radfar, A., & Alavi, A. H. (2011). A new prediction model for the load capacity of castellated steel beams. Journal of Constructional Steel Research,67(7), 1096–1105.CrossRefGoogle Scholar
  7. Gholizadeh, S., Pirmoz, A., & Attarnejad, R. (2011). Assessment of load carrying capacity of castellated steel beams by neural networks. Journal of Constructional Steel Research,67(5), 770–779.CrossRefGoogle Scholar
  8. Gu, J. Z. (2014). Free vibration of castellated beams with web shear and rotary inertia effects. International Journal of Structural Stability and Dynamics, 14(6), 1–10 (1450011).MathSciNetCrossRefGoogle Scholar
  9. Gu, J. Z., & Cheng, S. S. (2016). Shear effect on buckling of cellular columns subjected to axially compressed load. Thin-Walled Structures,98(Part B), 416–420.CrossRefGoogle Scholar
  10. Hsu, C. S. (1966). On dynamic stability of elastic bodies with prescribed initial conditions. International Journal of Engineering Science,4(1), 1–21.CrossRefGoogle Scholar
  11. Huang, C. C. (1980). Dynamic stability of generally orthotropic beams. Fibre Science and Technology,13(3), 187–198.CrossRefGoogle Scholar
  12. Huang, J. S., & Hung, L. H. (1984). Dynamic stability for a simply supported beam under periodic axial excitation. International Journal of Nonlinear Mechanics,19(4), 287–301.CrossRefGoogle Scholar
  13. Kar, R. C., & Sujata, T. (1991). Dynamic stability of a rotating beam with various boundary conditions. Computers & Structures,40(3), 753–773.CrossRefGoogle Scholar
  14. Kerdal, D., & Nethercot, D. A. (1984). Failure modes for castellated beams. Journal of Constructional Steel Research,4(4), 295–315.CrossRefGoogle Scholar
  15. Kim, B., Li, L. Y., & Edmonds, A. (2016) Analytical solutions of lateral-torsional buckling of castellated beams. International Journal of Structural Stability and Dynamics, 16(8), 1–16 (1550044).Google Scholar
  16. Kratzig, W. B., Li, L. Y., & Nawrotzki, P. (1991). Stability conditions for non-conservative dynamical systems. Computational Mechanics,8(3), 145–151.MathSciNetCrossRefGoogle Scholar
  17. Li, L. Y. (1991). Interaction of forced and parametric loading vibrations. Computers & Structures,40(3), 615–618.MathSciNetCrossRefGoogle Scholar
  18. Mohebkhah, A. (2004). The moment-gradient factor in lateral–torsional buckling on inelastic castellated beams. Journal of Constructional Steel Research,60(10), 1481–1494.CrossRefGoogle Scholar
  19. Mohebkhah, A., & Showkati, H. (2005). Bracing requirements for inelastic castellated beams. Journal of Constructional Steel Research,61(10), 1373–1386.CrossRefGoogle Scholar
  20. Najafi, M., & Wang, Y. C. (2017). Behaviour and design of steel members with web openings under combined bending, shear and compression. Journal of Constructional Steel Research,128, 579–600.CrossRefGoogle Scholar
  21. Nethercot, D. A., & Kerdal, D. (1982). Lateral-torsional buckling of castellated beams. The Structural Engineer,60, 53–61.Google Scholar
  22. Park, Y. P. (1987). Dynamic stability of a free Timoshenko beam under a controlled follower force. Journal of Sound and Vibration,113(3), 407–415.CrossRefGoogle Scholar
  23. Patel, S. N., Datta, P. K., & Sheikh, A. H. (2006). Buckling and dynamic instability analysis of stiffened shell panels. Thin-Walled Structures,44(3), 321–333.CrossRefGoogle Scholar
  24. Pattanayak, U. C., & Chesson, E. (1974). Lateral instability of castellated beams. AISC Engineering Journal,11(3), 73–79.Google Scholar
  25. Showkati, H., Ghazijahani, T. G., Noori, A., & Zirakian, T. (2012). Experiments on elastically braced castellated beams. Journal of Constructional Steel Research,77, 163–172.CrossRefGoogle Scholar
  26. Soltani, M. R., Bouchaïr, A., & Mimoune, M. (2012). Nonlinear FE analysis of the ultimate behaviour of steel castellated beams. Journal of Constructional Steel Research,70, 101–114.CrossRefGoogle Scholar
  27. Sonck, D., & Belis, J. (2016). Weak-axis flexural buckling of cellular and castellated columns. Journal of Constructional Steel Research,124, 91–100.CrossRefGoogle Scholar
  28. Sonck, D., Van Impe, R., & Belis, J. (2014). Experimental investigation of residual stresses in steel cellular and castellated members. Construction and Building Materials,54, 512–519.CrossRefGoogle Scholar
  29. Sorkhabi, R. V., Naseri, A., & Naseri, M. (2014). Optimization of the castellated beams by particle swarm algorithms method. APCBEE Procedia,9, 381–387.CrossRefGoogle Scholar
  30. Sweedan, A. M. I. (2011). Elastic lateral stability of I-shaped cellular steel beams. Journal of Constructional Steel Research,67(2), 151–163.CrossRefGoogle Scholar
  31. Tsavdaridis, K. D., & D’Mello, C. (2012). Optimisation of novel elliptically-based web opening shapes of perforated steel beams. Journal of Constructional Steel Research,76, 39–53.CrossRefGoogle Scholar
  32. Uang, C. M., & Fan, C. C. (2001). Cyclic stability criteria for steel moment connections with reduced beam section. Journal of Structural Engineering,127(9), 1021–1027.CrossRefGoogle Scholar
  33. Van Oostrom, J., & Sherbourne, A. N. (1972). Plastic analysis of castellated beams—II. Analysis and tests. Computers & Structures,2(1/2), 111–140.CrossRefGoogle Scholar
  34. Wang, P., Guo, K., Liu, M., & Zhang, L. (2016). Shear buckling strengths of web-posts in a castellated steel beam with hexagonal web openings. Journal of Constructional Steel Research,121, 173–184.CrossRefGoogle Scholar
  35. Wang, P., Wang, X., & Ma, N. (2014). Vertical shear buckling capacity of web-posts in castellated steel beams with fillet corner hexagonal web openings. Engineering Structures,75, 315–326.CrossRefGoogle Scholar
  36. Yeh, J. Y., Chen, L. W., & Wang, C. C. (2004). Dynamic stability of a sandwich beam with a constrained layer and electrorheological fluid core. Composite Structures,64(1), 47–54.CrossRefGoogle Scholar
  37. Yoon, S. J., & Kim, J. H. (2002). A concentrated mass on the spring unconstrained beam subjected to a thrust. Journal of Sound and Vibration,254(4), 621–634.CrossRefGoogle Scholar
  38. Yuan, W. B., Kim, B., & Li, L. Y. (2014). Buckling of axially loaded castellated steel columns. Journal of Constructional Steel Research,92, 40–45.CrossRefGoogle Scholar
  39. Zirakian, T., & Showkati, H. (2006). Distortional buckling of castellated beams. Journal of Constructional Steel Research,62(9), 863–871.CrossRefGoogle Scholar

Copyright information

© Korean Society of Steel Construction 2020

Authors and Affiliations

  1. 1.College of Civil Engineering and ArchitectureSouthwest University of Science and TechnologyMianyangChina
  2. 2.Shock and Vibration of Engineering Materials and Structures Key Laboratory of Sichuan ProvinceSouthwest University of Science and TechnologyMianyangChina
  3. 3.School of EngineeringUniversity of PlymouthPlymouthUK

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