Structural Engineering and Mechanics

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Large deflection of simple variable-arc-length beam subjected to a point load

  • Chucheepsakul, S. (Department of Civil Engineering, King Mongkut's Institute of Technology Thonburi) ;
  • Thepphitak, G. (Department of Civil Engineering, King Mongkut's Institute of Technology Thonburi) ;
  • Wang, C.M. (Department of Civil Engineering, The National University of Singapore)
  • Published : 1996.01.25
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Abstract

This paper considers large deflection problem of a simply supported beam with variable are length subjected to a point load. The beam has one of its ends hinged and at a fixed distance from this end propped by a frictionless support over which the beam can slide freely. This highly nonlinear flexural problem is solved by elliptic-integral method and shooting-optimization technique, thereby providing independent checks on the new solutions. Because the beam can slide freely over the frictionless support, there is a maximum or critical load which the beam can carry and it is dependent on the position of the load. Interestingly, two possible equilibrium configurations can be obtained for a given load magnitude which is less than the critical value. The maximum arc-length was found to be equal to about 2.19 times the fixed distance between the supports and this value is independent of the load position.

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References

  1. Chucheepsakul, S., Buncharoen, S., and Wang, C.M. (1994), "Large deflection of beams under moment gradient," J. Engrg. Mech., ASCE, 120(9), 1848-1860. https://doi.org/10.1061/(ASCE)0733-9399(1994)120:9(1848)
  2. Chucheepsakul, S., Buncharoen, S., and Huang, T. (1995), "Elastica of simple variable-arc-length beam subjected to end moment," J. Engrg. Mech., ASCE, 121(7), 767-772. https://doi.org/10.1061/(ASCE)0733-9399(1995)121:7(767)
  3. Conway, H. D. (1947), "The large deflection of a simple supported beam," Phil. Mag., Series 7, 38, 905-911. https://doi.org/10.1080/14786444708561149
  4. Fertis, D.G. and Afonta, A. (1990), "Large deflection of determinate and indeterminate bars of variable stiffness," J. Engrg. Mech., ASCE, 116(7), 1543-1559. https://doi.org/10.1061/(ASCE)0733-9399(1990)116:7(1543)
  5. Frisch-Fay, R. (1962), Flexible bars, Butterworths, London, England.
  6. Gospodnetic, D. (1959), "Deflection curve of a simple supported beam," J. Appl. Mech., 26(4), 675-676.
  7. Kempf, J. (1987), Numerical software tools in C, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, N.J.. 178-180.
  8. Nelder, J. A. and Mead, R. (1964), "A simplex method for function minimization," Comp. J., 7, 308-313.
  9. Prathap, G. and Varadan, T. K. (1975), "Large deformation of simply supported beam," J. Engrg. Mech. Div., ASCE, 101 (EM6), 929-931.
  10. Schile, R. D. and Sierakowski, R. L. (1967), "Large deflection of a beam loaded and supported at two points," Int. J. Non-linear Mech., 2, 61-68. https://doi.org/10.1016/0020-7462(67)90019-4
  11. Theocaris, P. S. and Panayotounakos, D. E. (1982), "Exact solution of the nonlinear differential equation concerning the elastic line of a straight rod due to terminal loading," Int. J. Non-linear Mech., 17(5/6), 395-402. https://doi.org/10.1016/0020-7462(82)90009-9
  12. Timoshenko, S. P. and Gere, J. M. (1961), Theory of elastic stability, McGraw-Hill Book Co., Inc., New York, N. Y., 79-80.
  13. Wang, C. M. and Kitipornchai, S. (1992), "Shooting-optimization technique for large deflection analysis of structural members," Engrg. Struct., 14(4), 231-240. https://doi.org/10.1016/0141-0296(92)90011-E
  14. Wang, T.M. (1968), "Nonlinear bending of beam with concentrated loads," J. of Franklin Institute, 285, 386-390. https://doi.org/10.1016/0016-0032(68)90486-9

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