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.
This is a preview of subscription content, log in to check access.
Buy single article
Instant unlimited access to the full article PDF.
Price includes VAT for USA
Bolotin, V. V. (1964). The dynamic stability of elastic systems. San Francisco, CA: Holden-day Inc.
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.
Chen, L. Y., Lin, P. D., & Chen, L. W. (1991). Dynamic stability of thick bimodulus beams. Computers & Structures,41(2), 257–263.
Ellobody, E. (2011). Interaction of buckling modes in castellated steel beams. Journal of Constructional Steel Research,67(5), 814–825.
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.
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.
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.
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).
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.
Hsu, C. S. (1966). On dynamic stability of elastic bodies with prescribed initial conditions. International Journal of Engineering Science,4(1), 1–21.
Huang, C. C. (1980). Dynamic stability of generally orthotropic beams. Fibre Science and Technology,13(3), 187–198.
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.
Kar, R. C., & Sujata, T. (1991). Dynamic stability of a rotating beam with various boundary conditions. Computers & Structures,40(3), 753–773.
Kerdal, D., & Nethercot, D. A. (1984). Failure modes for castellated beams. Journal of Constructional Steel Research,4(4), 295–315.
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).
Kratzig, W. B., Li, L. Y., & Nawrotzki, P. (1991). Stability conditions for non-conservative dynamical systems. Computational Mechanics,8(3), 145–151.
Li, L. Y. (1991). Interaction of forced and parametric loading vibrations. Computers & Structures,40(3), 615–618.
Mohebkhah, A. (2004). The moment-gradient factor in lateral–torsional buckling on inelastic castellated beams. Journal of Constructional Steel Research,60(10), 1481–1494.
Mohebkhah, A., & Showkati, H. (2005). Bracing requirements for inelastic castellated beams. Journal of Constructional Steel Research,61(10), 1373–1386.
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.
Nethercot, D. A., & Kerdal, D. (1982). Lateral-torsional buckling of castellated beams. The Structural Engineer,60, 53–61.
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.
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.
Pattanayak, U. C., & Chesson, E. (1974). Lateral instability of castellated beams. AISC Engineering Journal,11(3), 73–79.
Showkati, H., Ghazijahani, T. G., Noori, A., & Zirakian, T. (2012). Experiments on elastically braced castellated beams. Journal of Constructional Steel Research,77, 163–172.
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.
Sonck, D., & Belis, J. (2016). Weak-axis flexural buckling of cellular and castellated columns. Journal of Constructional Steel Research,124, 91–100.
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.
Sorkhabi, R. V., Naseri, A., & Naseri, M. (2014). Optimization of the castellated beams by particle swarm algorithms method. APCBEE Procedia,9, 381–387.
Sweedan, A. M. I. (2011). Elastic lateral stability of I-shaped cellular steel beams. Journal of Constructional Steel Research,67(2), 151–163.
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.
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.
Van Oostrom, J., & Sherbourne, A. N. (1972). Plastic analysis of castellated beams—II. Analysis and tests. Computers & Structures,2(1/2), 111–140.
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.
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.
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.
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.
Yuan, W. B., Kim, B., & Li, L. Y. (2014). Buckling of axially loaded castellated steel columns. Journal of Constructional Steel Research,92, 40–45.
Zirakian, T., & Showkati, H. (2006). Distortional buckling of castellated beams. Journal of Constructional Steel Research,62(9), 863–871.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Lei, J., Kim, B. & Li, L. Dynamic Instability Analysis of Axially Compressed Castellated Columns. Int J Steel Struct (2020). https://doi.org/10.1007/s13296-020-00306-8
- Dynamic instability
- Castellated column
- Shear effect
- Inertia effect