Static Stability Formulas of a Weakened Timoshenko Column: Effects of Shear Deformations
Publication: Journal of Engineering Mechanics
Volume 136, Issue 12
Abstract
The static stability analysis of two-dimensional Timoshenko columns weakened at an arbitrary section is derived in a classic manner. The effects of shear deformations along the column, influenced by the additional shear force induced by the applied axial load as the member deforms according to the modified shear equation proposed by Haringx, are presented and studied in detail. The proposed model also captures: (1) the influence on the buckling load capacity of the column when an arbitrary weakened section is formed at any location; (2) the tension buckling phenomenon due to the low shear stiffness of columns made of composite materials or elastomeric rubbers; and (3) the beneficial effects of an additional lateral bracing located at the weakened section to alleviate the buckling load reduction of the column. Seven classical and nonclassical cases of columns mostly used in civil and mechanical engineering are summarized in condensed formulas which allow the straightforward determination of buckling loads and shapes.
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References
Arboleda-Monsalve, L. G., Zapata-Medina, D. G., and Aristizabal-Ochoa, J. D. (2007). “Stability and natural frequencies of a weakened Timoshenko beam-column with generalized end conditions under constant axial load.” J. Sound Vib., 307(1–2), 89–112.
Aristizabal-Ochoa, J. D. (2004). “Column stability and minimum lateral bracing: Effects of shear deformations.” J. Eng. Mech., 130(10), 1223–1232.
Aristizabal-Ochoa, J. D. (2005). “Discussion of ‘Tension buckling in multilayer elastomeric bearings’.” J. Eng. Mech., 131(1), 106–108.
Aristizabal-Ochoa, J. D. (2007). “Static and dynamic stability of uniform shear beam-columns under generalized boundary conditions.” J. Sound Vib., 307(1–2), 69–88.
Attard, M. M., and Hunt, G. W. (2008). “Column buckling with shear deformations—A hyperelastic formulation.” Int. J. Solids Struct., 45(14–15), 4322–4339.
Bazant, Z. P. (2003). “Shear buckling of sandwich, fiber composite and lattice columns, bearings, and helical springs: Paradox resolved.” J. Appl. Mech., 70(1), 75–83.
Caddemi, S., and Calio, I. (2008). “Exact solution of the multicracked Euler-Bernoulli column.” Int. J. Solids Struct., 45(5), 1332–1351.
Challamel, N., Casandjian, C., and Lanos, C. (2009). “Localization in the vibration of an axially loaded two-span weakened column.” J. Vib. Control, 15(12), 1827–1851.
Engesser, F. (1889a). “Die Knickfestigkeit gerader Stabe.” Zentralblatt des Bauverwaltung, 11, 483–486.
Engesser, F. (1889b). “Die Knickfestigkeit gerader Stabe.” Z. Architekten und Ing. Verein zu Hannover, 35, 455–462.
Haringx, J. A. (1942). “On the buckling and lateral rigidity of helical compression springs.” Proc., Konink. Ned. Akad. Wetenschap, Vol. 45, Royal Netherlands Academy of Arts and Sciences, Amsterdam, 533.
Haringx, J. A. (1948). “On highly compressible helical springs and rubber rods and their application for vibration-free mountings. I.” Philips Res. Rep., 3, 401–449.
Haringx, J. A. (1949a). “On highly compressible helical springs and rubber rods and their application for vibration-free mountings. II.” Philips Res. Rep., 4, 49–80.
Haringx, J. A. (1949b). “On highly compressible helical springs and rubber rods and their application for vibration-free mountings. III.” Philips Res. Rep., 4, 206–220.
Kelly, J. M. (2003). “Tension buckling in multilayer elastomeric bearings.” J. Eng. Mech., 129(12), 1363–1368.
Li, Q. S. (2001). “Buckling of multistep cracked columns with shear deformation.” Eng. Struct., 23(4), 356–364.
Li, Q. S. (2003). “Classes of exact solutions for buckling of multistep nonuniform columns with an arbitrary number of cracks subjected to concentrated and distributed axial loads.” Int. J. Eng. Sci., 41(6), 569–586.
Loya, J. A., Vadillo, G., and Fernandez-Saez, J. (2010). “First-order solutions for the buckling loads of Euler-Bernoulli weakened columns.” J. Eng. Mech., 136(5), 674–679.
Swamidas, A. S. J., Yang, X., and Seshadri, R. (2004). “Identification of cracking in beam structures using Timoshenko and Euler formulations.” J. Eng. Mech., 130(11), 1297–1308.
Thornton, W. A. (1984). “Bracing connections for heavy construction.” Eng. J., 21(3), 139–148.
Timoshenko, S., and Gere, J. (1961). Theory of elastic stability, 2nd Ed., McGraw-Hill, New York.
Viola, E., Nobile, L., and Federici, L. (2002). “Formulation of cracked beam element for structural analysis.” J. Eng. Mech., 128(2), 220–230.
Viola, E., Ricci, P., and Aliabadi, M. H. (2007). “Free vibration analysis of axially loaded cracked Timoshenko beam structures using dynamic stiffness method.” J. Sound Vib., 304(1–2), 124–153.
Wang, C. Y., Wang, C. M., and Aung, T. M. (2004). “Buckling of a weakened column.” J. Eng. Mech., 130(11), 1373–1376.
Wang, J., and Qiao, P. (2007). “Vibration of beams with arbitrary discontinuities and boundary conditions.” J. Sound Vib., 308(1–2), 12–27.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 136 • Issue 12 • December 2010
Pages: 1528 - 1536
Copyright
© 2010 ASCE.
History
Received: Oct 25, 2009
Accepted: May 25, 2010
Published online: May 27, 2010
Published in print: Dec 2010
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