Large Deflection of Determinate and Indeterminate Bars of Variable Stiffness
Publication: Journal of Engineering Mechanics
Volume 116, Issue 7
Abstract
The research here deals with the development of an analytical method for the computation of large deflections and rotations of members with varying stiffness along their length. The member may be statically determinate, or statically indeterminate, and its loading may be arbitrary. This method involves the use of equivalent nonlinear and equivalent pseudolinear systems of uniform stiffness that replace the original variable‐stiffness member. The large deflections and rotations of the equivalent system are identical to the corresponding ones of the original variable‐stiffness member, and they can be obtained by either: (1) Using the equivalent pseudolinear system and applying elementary linear analysis; or (2) using a simplified equivalent nonlinear system and applying nonlinear analysis. A mathematical proof regarding the existence of equivalent nonlinear and equivalent pseudolinear systems is obtained by using the nonlinear second‐order differential equation. The use of equivalent systems simplifies a great deal the mathematical complexity of the variable‐stiffness problem. The Young's modulus of elasticity is assumed to be constant, but the method applies equally well when this modulus varies along the length of the member.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Fertis, D. G. (1956). “Theoretical and experimental investigations on vibration susceptibilities of various highway bridges.” Res. Rept., Michigan Dept. of Transp., Lansing, Mich.
2.
Fertis, D. G. (1964). “Contribution to the deflection and free vibration of uniform and variable stiffness members.” Thesis presented to the National Technical University of Athens, at Athens, Greece, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
3.
Fertis, D. G. (1966). “Dynamic hinge concept for beam vibrations.” J. Struct. Div., ASCE, 92(2).
4.
Fertis, D. G. (1973). Dynamics and vibration of structures. John Wiley and Sons, New York, N.Y.
5.
Fertis, D. G. (1984). “Dynamics and vibrations of structures.” Revised Ed., Robert E. Krieger Publishing Co., Malabar, Fla.
6.
Fertis, D. G., and Keene, M. E. (1990). “Elastic and inelastic analysis of nonprismatic members.” J. Struct. Engrg., ASCE, 116(2).
7.
Fertis, D. G., and Pallaki, S. (1989). “Pseudolinear and equivalent systems for large deflections of members.” J. Engrg. Mech., ASCE, 115(11).
8.
Fertis, D. G., and Zobel, E. (1958). “Equivalent systems for the deflection of variable stiffness members.” J. Struct. Div., ASCE.
9.
Fertis, D. G., and Zobel, E. (1961). Transverse Vibration Theory, Applications of Equivalent Systems. Ronald Press Co., New York, N.Y.
10.
Frisch‐Fay, R. (1962). Flexible bars. Butterworth and Co., Publishers, Washington, D.C.
Information & Authors
Information
Published In
Copyright
Copyright © 1990 ASCE.
History
Published online: Jul 1, 1990
Published in print: Jul 1990
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.