Structural Engineering and Mechanics

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Large deflections of variable-arc-length beams under uniform self weight: Analytical and experimental

  • Pulngern, Tawich (Department of Civil Engineering, King Mongkut's University of Technology Thonburi) ;
  • Halling, Marvin W. (Department of Civil and Environmental Engineering, Utah State University) ;
  • Chucheepsakul, Somchai (Department of Civil Engineering, King Mongkut's University of Technology Thonburi)
  • Received : 2004.04.07
  • Accepted : 2004.11.10
  • Published : 2005.03.10
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Abstract

This paper presents the solution of large static deflection due to uniformly distributed self weight and the critical or maximum applied uniform loading that a simply supported beam with variable-arc-length can resist. Two analytical approaches are presented and validated experimentally. The first approach is a finite-element discretization of the span length based on the variational formulation, which gives the solution of large static sag deflections for the stable equilibrium case. The second approach is the shooting method based on an elastica theory formulation. This method gives the results of the stable and unstable equilibrium configurations, and the critical uniform loading. Experimental studies were conducted to complement the analytical results for the stable equilibrium case. The measured large static configurations are found to be in good agreement with the two analytical approaches, and the critical uniform self weight obtained experimentally also shows good correlation with the shooting method.

Keywords

References

  1. Chucheepsakul, S., Buncharoen, S. and Huang, T. (1995), 'Elastica of simple variable-are-length beam subjected to end moment', J. Engrg. Mech., 121(7), 767-772 https://doi.org/10.1061/(ASCE)0733-9399(1995)121:7(767)
  2. Chucheepsakul, S., Theppitak, G. and Wang, C.M. (1996), 'Large deflection of simple variable-are-length beams subjected to a point load', Struet. Engrg. Mech., 4(1),49-59
  3. Chucheepsakul, S., Theppitak, G. and Wang, C.M. (1997a), 'Exact solution of variable-are-length elastica under moment gradient', Struet. Engrg. Mech., 5(5), 529-539
  4. Chucheepsakul, S. and Huang, T. (1997b), 'Finite element solution of variable-are-length beam under a point load', J. Struet. Engrg., 123(7), 968-970 https://doi.org/10.1061/(ASCE)0733-9445(1997)123:7(968)
  5. Chucheepsakul, S., Wang, C.M., He, X.Q. and Monprapussom, T.(1999), 'Double curvature bending of variable-are-length elasticas', J. Appl. Mech., 66, 87-94 https://doi.org/10.1115/1.2789173
  6. Golley, B.W. (1997), 'The solution of open and closed elasticas using intrinsic coordinate finite elements', J. Comp. Meth. Appl. Mech. Engrg., 146,127-134 https://doi.org/10.1016/S0045-7825(96)01231-5
  7. Hartono, W (2000), 'Behavior of variable-are-length elastica with frictionless support under follower force', Mech. Res. Comm., 27(6), 653-658 https://doi.org/10.1016/S0093-6413(00)00142-7
  8. Huang, T. and Chucheepsakul, S. (1985), 'Large displacement analysis of a marine riser', J. Energy Resources Tech., 107(3), 54-59 https://doi.org/10.1115/1.3231163
  9. Malvern, L.E. (1969), Introduction to the Mechanics of Continuous Media, Prentice-Hall, Inc
  10. Neider, J.A. and Meade, R. (1965), 'A simplex method for the function minimization', Comp. J., 7, 308-313 https://doi.org/10.1093/comjnl/7.4.308
  11. Press, W.H., Teukolsky, S.A., Vettering, W.T. and Flannery, B.P. (1992), Numerical Recipes in Fortran, 2nd ed., Cambridge University Press
  12. Wang, C.M., Lam, K.Y., He, X.Q. and Chucheepsakul, S. (1997), 'Large deflections of an end supported beam subjected to a point load', Int. J. Nonl. Mech., 32(1), 63-72 https://doi.org/10.1016/S0020-7462(96)00017-0

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