Structural Engineering and Mechanics

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Elastic buckling of end-loaded, tapered, cantilevered beams with initial curvature

  • Wilson, James F. (Department of Civil and Environmental Engineering, Duke University) ;
  • Strong, Daniel J. (North Carolina Department of Transportation)
  • Published : 1997.05.25
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Abstract

The elastic deflections and Euler buckling loads are investigated for a class of tapered and initially curved cantilevered beams subjected to loading at the tip. The beam's width increases linearly and its depth decreases linearly with the distance from the fixed end to the tip. Unloaded, the beam forms a circular are perpendicular to the axis of bending. The beam's deflection responses, obtained by solving the differential equations in closed form, are presented in terms of four nondimensional system parameters: taper ratio ${\kappa}$, initial shape ratio ${\Delta}_0$, end load ratio f, and load angle ${\theta}$. Laboratory measurements of the Euler buckling loads for scale models of tapered initially straight, corrugated beams compared favorably with those computed from the present analysis. The results are applicable to future designs of the end structures of highway guardrails, which can be designed to give the appropriate balance between the capacity to deflect a nearly head-on vehicle back to its right-of-way and the capacity to buckle sufficiently that penetration of the vehicle may be averted.

Keywords

References

  1. Allen, H.G. and Bulson, P.S. (1980), Background to Buckling, McGraw-Hill.
  2. Bronstad, M.E., Meyer, J.B., Hatton, J.H. and Meczkowski, L.C. (1986), "Crash test evaluation of eccentric loader guardrail terminals", Transportation Research Record 1065, TRB, National research Council.
  3. DeWolf, J.T., Peokoz, T. and Winter, G. (1974), "Local and overall buckling of cold-formed members", J. of Struct. Div., Proc. ASCE, 100(ST10).
  4. Dinnik, A. (1929), "Design of columns of varying cross-section", Trans. ASME, 51.
  5. Dinnik, A. (1932), "Design of columns of varying cross-section", Trans. ASME, 54.
  6. Ermopoulos, J.C. (1986), "Buckling of tapered bars under stepped axial loads", J. Struct. Engr., 112(6).
  7. Kalyanaraman, A.M.. Pekoz, T. and Winter, G. (1977), "Unstiffened compression elements", J. Struct. Div., Proc. ASCE, 103(ST9).
  8. Moore, R.A. (1962), Introduction to Differential Equations, Allyn and Bacon, Inc, Boston.
  9. Sicking, D.L., Qureshy, A.B., Bligh, R.P., Ross, H.E. Jr. and Buth, C.E. (1988), "Development of new guardrail end treatments", Texas Transportation Institute, Texas A & M Univ.
  10. Siginer, A. (1992), "Buckling of columns of variable flexural rigidity", J. Eng. Mech., 18(3).
  11. Southwell, R.V. (1912), "The strength of struts", Engineering, 94.
  12. Strong, D.J. (1994), "Tapered eccentric beam subjected to end loading", Master of Science Thesis, Dept. of Civil and Environmental Eng., Duke Univ., Durham, N.C.
  13. Timoshenko, S.P. and Gere, J.M. (1961), Theory of Elastic Stability, McGraw-Hill.
  14. Williams, F.W. and Aston, G. (1989), "Exact or lower bound tapered column buckling loads", J. Struct. Eng. 115(5).

Cited by

  1. Buckling analysis of semi-rigid gabled frames vol.55, pp.3, 2015, https://doi.org/10.12989/sem.2015.55.3.605
  2. Plastic collapse of tapered, tip-loaded cantilevered beams vol.9, pp.6, 2000, https://doi.org/10.12989/sem.2000.9.6.569