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TECHNICAL PAPERS

Stability of the Shanley Column Under Cyclic Loading

[+] Author and Article Information
E. Corona

Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556

J. Appl. Mech 68(2), 324-331 (Jun 28, 2000) (8 pages) doi:10.1115/1.1349118 History: Received March 20, 2000; Revised June 28, 2000
Copyright © 2001 by ASME
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References

Bertero,  V. V., and Popov,  E. P., 1965, “Effect of Large Alternating Strains of Steel Beams,” J. Struct. Div. ASCE, 91, pp. 1–12.
Kyriakides,  S., and Shaw,  P. K., 1987, “Inelastic Buckling of Tubes Under Cyclic Bending,” ASME J. Pressure Vessel Technol., 109, pp. 169–178.
Clément,  G., Acker,  D., and Lebey,  J., 1989, “A Practical Rule for Progressive Buckling,” Nucl. Eng. Des., 111, pp. 209–216.
Taylor,  N., and Hirst,  P., 1989, “Strut Behavior: Sub-Buckling Excursion Effects and Risk Assessment,” Res. Mech., 28, pp. 139–189.
Corona,  E., and Kyriakides,  S., 1991, “An Experimental Investigation of the Degradation and Buckling of Circular Tubes Under Cyclic Bending and External Pressure,” Thin-Walled Struct., 12, pp. 229–263.
Vaze,  S. P., and Corona,  E., 1998, “Degradation and Collapse of Square Tubes Under Cyclic Bending,” Thin-Walled Struct., 31, pp. 325–341.
Ellison,  M. S., and Corona,  E., 1998, “Buckling of T-Beams Under Cyclic Bending,” Int. J. Mech. Sci., 40, pp. 835–855.
Shaw,  P. K., and Kyriakides,  S., 1985, “Inelastic Analysis of Thin-Walled Tubes Under Cyclic Bending,” Int. J. Solids Struct., 21, pp. 1073–1100.
Corona, E., 1997, “Cyclic Plasticity Applications in Structural Degradation of Shells Under Cyclic Loading,” Proceedings of Plasticity ’97, A. S. Khan, ed., Neat Press, Fulton, MD, pp. 345–346.
Hassan,  T., and Kyriakides,  S., 1992, “Ratcheting in Cyclic Plasticity, Part I: Uniaxial Behavior,” Int. J. Plast. 8, pp. 91–116.
Hassan,  T., Corona,  E., and Kyriakides,  S., 1992, “Ratcheting in Cyclic Plasticity, Part II: Multiaxial Behavior,” Int. J. Plast. 8, pp. 117–146.
Corona,  E., Hassan,  T., and Kyriakides,  S., 1996, “On the Performance of Kinematic Hardening Rules in Predicting a Class of Biaxial Ratcheting Histories,” Int. J. Plast. 12, pp. 117–145.
Shanley,  F. R., 1947, “Inelastic Column Theory,” J. Aeronaut. Sci., 14, pp. 261–268.
Dafalias,  Y. F., and Popov,  E. P., 1975, “A Model of Nonlinearly Hardening Materials for Complex Loading,” Acta Mech., 21, pp. 173–192.
Dafalias,  Y. F., and Popov,  E. P., 1976, “Plastic Internal Variables Formalism of Cyclic Plasticity,” ASME J. Appl. Mech., 43, pp. 645–651.
Corona, E., 1996, “Buckling of Elastic-Plastic Structural Members Under Cyclic Loading,” NSF Proposal ID CMS-9610510.

Figures

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(a) Shanley column, (b) deflected configuration and free-body diagram
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Plasticity model parameters
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Monotonic response, (a) load-axial deflection response of three models, (b) corresponding load-rotation response
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Cyclic response under symmetric displacement control for a model with L/b=50, (a) load-axial deflection response, (b) corresponding load-rotation response
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Stress-strain response for the case in Fig. 4, (a) link 1, (b) link 2
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Peak values of θ in each cycle as a function of cycle number for various cycle amplitudes under displacement control
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Cyclic response under symmetric displacement control for a model with L/b=100, (a) load-axial deflection response, (b) corresponding load-rotation response
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Stress-strain histories for the first cycle of the response shown in Fig. 7
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Cyclic response under symmetric load control for a model with L/b=50, (a) load-axial deflection response, (b) corresponding load-rotation response
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Stress-strain response under symmetric load control for the case in Fig. 9, (a) link 1, (b) link 2
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Response history under load control for a model with L/b=50 for different load amplitudes, (a) peak values of vertical displacement in each cycle as function of cycle number, (b) peak values of θ in each cycle as function of cycle number
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Response history under load control for a model with L/b=100 for different load amplitudes, (a) peak values of vertical displacement in each cycle as function of cycle number, (b) peak values of θ in each cycle as function of cycle number
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Response in terms of peak values of u and θ in each half-cycle for a model with L/b=100 and Ñ/|Ncr|=0.70 under load control
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Response history under load control for a model with L/b=150 for different load amplitudes, (a) peak values of vertical displacement in each cycle as function of cycle number, (b) peak values of θ in each cycle as function of cycle number
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Response history in terms of peak θ values as function of cycle number under load control for different values of initial imperfection, (a) L/b=50, (b) L/b=100

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