Torsional Rigidities of Reinforced Concrete Beams Subjected to Elastic Lateral Torsional Buckling

Authors: Ilker Kalkan, Saruhan Kartal

Abstract:

Reinforced concrete (RC) beams rarely undergo lateral-torsional buckling (LTB), since these beams possess large lateral bending and torsional rigidities owing to their stocky cross-sections, unlike steel beams. However, the problem of LTB is becoming more and more pronounced in the last decades as the span lengths of concrete beams increase and the cross-sections become more slender with the use of pre-stressed concrete. The buckling moment of a beam mainly depends on its lateral bending rigidity and torsional rigidity. The nonhomogeneous and elastic-inelastic nature of RC complicates estimation of the buckling moments of concrete beams. Furthermore, the lateral bending and torsional rigidities of RC beams and the buckling moments are affected from different forms of concrete cracking, including flexural, torsional and restrained shrinkage cracking. The present study pertains to the effects of concrete cracking on the torsional rigidities of RC beams prone to elastic LTB. A series of tests on rather slender RC beams indicated that torsional cracking does not initiate until buckling in elastic LTB, while flexural cracking associated with lateral bending takes place even at the initial stages of loading. Hence, the present study clearly indicated that the un-cracked torsional rigidity needs to be used for estimating the buckling moments of RC beams liable to elastic LTB.

Keywords: Lateral stability, post-cracking torsional rigidity, uncracked torsional rigidity, critical moment.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1340330

References:

[1] R. G. Oesterle, M. J. Sheehan, H. R. Lotfi, W. G. Corley, and J. J. Roller, Investigation of Red Mountain Freeway bridge girder collapse. CTL Group Project No. 262291 Final Report, Arizona Department of Transportation, Arizona, USA, 2007.
[2] A. H. Zureick, L. F. Kahn, K. M. Will, I. Kalkan, J. Hurff, and J. H. Lee, Stability of precast prestressed concrete bridge girders considering sweep and thermal effects. GDOT Project No. RP 05-15 Final Report, Georgia Department of Transportation, Atlanta, Georgia, USA, 2009.
[3] ACI Committee 318, Building Code Requirements for Structural Concrete and Commentary (ACI 318M-05), American Concrete Institute, Farmington Hills, Michigan, U.S.A., 2005.
[4] B. de Saint-Venant, “Mémoire sur la torsion des prismes (lu à l’académie le 13 juin 1853) (in French)”, Mémoires des Savants Etrangers, Mémoires Présentés par Divers Savants à l’Académie des Sciences, de l’Institut Impérial de France et Imprimé par son Ordre, v. 14, p. 233-560, 1856.
[5] C. Wang, Applied elasticity, McGraw-Hill Book Co. Inc., New York, pp. 85-89, 1953.
[6] S. P. Timoshenko and J. N. Goodier, Theory of elasticity (International ed.), McGraw-Hill Book Co., New York, pp. 309-313, 1970.
[7] A. Siev, “The lateral buckling of slender reinforced concrete beams,” Magazine of Concrete Research (London), vol. 12, no. 36, pp. 155-164, 1960.
[8] E. Rausch, Berechnung des eisenbetons gegen verdrehung (in German), Ph.D. thesis, Technische Hochschule, Berlin, Germany,1929.
[9] P. Lampert, “Postcracking rigidity of reinforced concrete beams in torsion and bending,” ACI SP 35: Analysis of Structural Systems for Torsion, pp. 385-433, 1973.
[10] T. T. C. Hsu, “Post-cracking torsional rigidity of reinforced concrete sections,” ACI Journal, Proceedings, vol. 70, no. 5, pp. 352-360, 1973.
[11] T. T. C. Hsu, “Shear flow zone in torsion of reinforced concrete,” Journal of Structural Engineering, ASCE, vol. 116, no. 11, pp. 3206-3226, 1990.
[12] Tavio and S. Teng, “Effective torsional rigidity of reinforced concrete members,” ACI Structural Journal, vol. 101, no. 2, pp. 252-260, 2004.
[13] I. Kalkan, “Lateral torsional buckling of rectangular reinforced concrete beams,” ACI Structural Journal, vol. 111, no. 1, pp.71-81, 2014.