Dynamic instability of castellated beams subjected to transverse periodic loading

In this study, an analytical solution is developed for the investigation of free vibra-tion, static buckling and dynamic instability of castellated beams subjected to trans-verse periodic loading. Bolotin’s method is used to perform the dynamic instability analysis. By assuming the instability modes, the mass, stiffness, and geometric stiff-ness matrices are derived using the kinetic energy, strain energy and potential of ap-plied loads. Analytical equations for determining the free vibration frequency, critical buckling moment, and excitation frequency of castellated beams are derived. In ad-dition, the influences of the flange width of the castellated beam and the static part of the applied load on the variation of dynamic instability zones are discussed.


Bolotin VV (1964). The Dynamic Stability of Elastic Systems. San Fran-cisco, CA, Holden-day, Inc. Yeh JY, Chen LW, Wang CC (2004). Dynamic stability of a sandwich beam with a constrained layer and electrorheological fluid core. Composite Structures, 64(1), 47-54.

Chen LY, Lin PD, Chen LW (1991). Dynamic stability of thick bimodulus beams. Computers & Structures, 41(2), 257-263.

Demirdjia S (1999). Stability of Castellated Beam Webs. Ph.D thesis, McGill University Montreal, Canada.

Gao K, Gao W, Wu BH, Song CM (2019). Nondeterministic dynamic sta-bility assessment of Euler–Bernoulli beams using Chebyshev surro-gate model. Applied Mathematical Modelling, 66, 1-25.

Gürgöze M (1985). On the dynamic stability of a pre-twisted beam sub-ject to a pulsating axial load. Journal of Sound and Vibration, 102(3), 415-422.

Hsu CS (1966). On dynamic stability of elastic bodies with prescribed ini-tial conditions. International Journal of Engineering Science, 4(1), 1-21.

Huang CC (1980). Dynamic stability of generally orthotropic beams. Fi-bre Science and Technology, 13(3), 187-198.

Huang JS, Hung LH (1984). Dynamic stability for a simply supported beam under periodic axial excitation. International Journal of Non-linear Mechanics, 19(4), 287-301.

Kar RC, Sujata T (1991). Dynamic stability of a rotating beam with var-ious boundary conditions. Computers & Structures, 40(3), 753-773.

Kazemi Nia Korrani HR, Kabir MZ, Molanaei S (2010). Lateral Torsional Buckling of Castellated Beams Under End Moments. Amirkabir Uni-versity of Technology.

Kerdal D (1982). Lateral-torsional buckling strength of castellated beams. Ph.D thesis, Civil and Structural Engineering, Faculty of En-gineering (Sheffield), University of Sheffield, Sheffield, UK.

Kim B, Li LY, Edmonds A (2016). Analytical solutions of lateral-tor-sional buckling of castellated beams. International Journal of Struc-tural Stability and Dynamics, 16(8), 1-16 (1550044).

Kratzig WB, Li LY, Nawrotzki P (1991). Stability conditions for non-con-servative dynamical systems. Computational Mechanics, 8(3), 145-151.

Kwani S, Wijaya PK (2017). Lateral torsional buckling of castellated beams analyzed using the collapse analysis. Procedia Engineering, 171, 813–820.

Lagerqvist O, Hedman-Pétursson E, Unosson E, Feldmann M (2006). Large web openings for service integration in composite floors. De-sign Guide (En), Technical Steel Report.

Li LY (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.

Morris NF (1965). The dynamic stability of beam-columns with a fixed distance between supports. Journal of the Franklin Institute, 280(2), 163-173.

Müller C, Hechler O, Bureau A, Bitar D, Joyeux D, Cajot LG, Demarco T, Lawson RM, Hicks S, Devine P, Showkati H, Ghazijahani TG, Noori A, Zirakian T (2012(. Experiments on elastically braced castellated beams. Journal of Constructional Steel Research, 77, 163-172.

Nethercot D, Kerdal D (1982). Lateral-torsional buckling of castellated beams. The Structural Engineer, 60B(3), 53-61.

Park YP (1987). Dynamic stability of a free Timoshenko beam under a controlled follower force. Journal of Sound and Vibration, 113(3), 407-415

Patel SN, Datta PK, Sheikh AH (2006). Buckling and dynamic instability analysis of stiffened shell panels. Thin-Walled Structures, 44(3), 321-333.

Showkati H, Ghazijahani TG, Noori A, Zirakian T (2012). Experiments on elastically braced castellated beams. Journal of Constructional Steel Research, 77, 163-172.

Sonck D, Van Impe R, Belis J (2014). Experimental investigation of re-sidual stresses in steel cellular and castellated members. Construc-tion and Building Materials, 54, 512-519.

Uang CM, Fan CC (2001). Cyclic stability criteria for steel moment con-nections with reduced beam section. Journal of Structural Engineer-ing, 127(9), 1021-1027.

Yoon SJ, Kim JH (2002). A concentrated mass on the spring uncon-strained beam subjected to a thrust. Journal of Sound and Vibration, 254(4), 621-634.

Zhu J, Qian S, Li LY (2017). Dynamic instability of laterally-restrained zed-purlin beams under uplift loading. International Journal of Me-chanical Sciences, 131–132, 408–413.

Zhu J, Qian S, Li LY (2018). Dynamic instability of channel-section beams under periodic loading. Mechanics of Advanced Materials and Structures, (in press).

Kaynak Göster