Flexural Strength Design of RC Beams with Consideration of Strain Gradient Effect

Authors: Mantai Chen, Johnny Ching Ming Ho

Abstract:

The stress-strain relationship of concrete under flexure is one of the essential parameters in assessing ultimate flexural strength capacity of RC beams. Currently, the concrete stress-strain curve in flexure is obtained by incorporating a constant scale-down factor of 0.85 in the uniaxial stress-strain curve. However, it was revealed that strain gradient would improve the maximum concrete stress under flexure and concrete stress-strain curve is strain gradient dependent. Based on the strain-gradient-dependent concrete stress-strain curve, the investigation of the combined effects of strain gradient and concrete strength on flexural strength of RC beams was extended to high strength concrete up to 100 MPa by theoretical analysis. As an extension and application of the authors’ previous study, a new flexural strength design method incorporating the combined effects of strain gradient and concrete strength is developed. A set of equivalent rectangular concrete stress block parameters is proposed and applied to produce a series of design charts showing that the flexural strength of RC beams are improved with strain gradient effect considered.

Keywords: Beams, Equivalent concrete stress block, Flexural strength, Strain gradient.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1093327

References:

[1] E. Hognestad., A study of combined bending and axial load in reinforced concrete members. Bulletin No. 399, Engineering Experiment Station, University of Illinois, Urbana. 1951.
[2] G. M. Sturman, S. P. Shah, and G. Winter, "Effects of flexural strain gradients on microcracking and stress-strain behavior of concrete,” ACI Journal, vol. 62, no. 7, pp. 805-822, 1965.
[3] L. E. Clark, K. H. Gerstle, and L. G. Tulin, "Effect of Strain Gradient on the St-ess-Strain Curve of Motar and Concrete,” ACI Journal, vol. 64, no. 9, pp.580-586, 1967.
[4] S. W. Tabsh, "Elimination of the effect of strain gradient from concrete compressive strength test results,” Computers and Concrete, vol. 3, no. 6, pp. 375-388, 2006.
[5] T. Tan and N. Nguyen, "Determination of stress-strain curves of concrete from flexure tests,” Magazine of Concrete Research, vol. 56, no. 4, pp. 243-250, 2004.
[6] J. C. M. Ho, H. J. Pam, J. Peng, and Y. L. Wong, "Maximum concrete stress developed in unconfined flexural RC members,” Computers and Concrete, vol. 8, no. 2, pp. 207-227, 2011.
[7] J. Peng, J. C. M. Ho, H. J. Pam, and Y. L. Wong, "Equivalent stress block for normal-strength concrete incorporating strain gradient effect,” Magazine of Concrete Research, vol. 64, no. 1, pp. 1-19, 2012.
[8] J. C. Ho and J. Peng, "Strain-Gradient-Dependent Stress-Strain Curve for Normal-Strength Concrete,” Advances in Structural Engineering, vol. 16, no. 11, pp. 1911-1930, 2013.
[9] M. T. Chen and J. C. M. Ho, "Concurrent flexural strength and ductility design of RC beams via strain-gradient-dependent concrete stress-strain curve,” The Structural Design of Tall and Special Buildings, submitted for publication.
[10] M. M. Attard and S. Setunge, "Stress-strain relationship of confined and unconfined concrete,” ACI Materials Journal, vol. 93, no. 5, pp. 432-442, 1996.
[11] H. H. Abrishami, W. D. Cook, and D. Mitchell, "Influence of epoxy-coated reinforcement on response of normal and high-strength concrete beams,” ACI structural journal, vol. 92, no. 2, pp. 157-166, 1995.
[12] N. Alca, S. D. Alexander, and J. G. MacGregor, "Effect of size on flexural behavior of high-strength concrete beams,” ACI structural journal, vol. 94, no. 1, pp. 59-67, 1997.
[13] S. A. Ashour, "Effect of compressive strength and tensile reinforcement ratio on flexural behavior of high-strength concrete beams,” Engineering Structures, vol. 22, no. 5, pp. 413-423, 2000.
[14] C. Bosco, A. Carpinteri, and P. G. Debernardi, "Minimum reinforcement in high-strength concrete,” Journal of Structural Engineering, vol. 116, no. 2, pp. 427-437, 1990.
[15] P. G. Debernardi and M. Taliano, "On evaluation of rotation capacity for reinforced concrete beams,” ACI Structural Journal, vol. 99, no. 3, pp. 360-368, 2002.
[16] M. Y. Ko, S. W. Kim, and J. K. Kim, "Experimental study on the plastic rotation capacity of reinforced high strength concrete beams,” Materials and Structures, vol. 34, no. 5, pp. 302-311, 2001.
[17] P. S. Kumar, M. Mannan, and K. John, "High Performance Reinforced Concrete Beams made with Sandstone Reactive Aggregates,” Open Civil Engineering Journal, vol. 2, no., pp. 41-50, 2008.
[18] C. Lee, S. M. Jeong, and J. W. Park, "Use of fibre sheet strip stirrups for internal shear reinforcement of concrete beams,” Magazine of Concrete Research, vol. 61, no. 9, pp. 731-743, 2009.
[19] H. J. Pam, A. K. H. Kwan, and M. S. Islam, "Flexural strength and ductility of reinforced normal-and high-strength concrete beams,” Proceedings of the Institution of Civil Engineers, vol. 146, no. 4, pp. 381-389, 2001.
[20] M. Pecce and G. Fabbrocino, "Plastic rotation capacity of beams in normal and high-performance concrete,” ACI Structural Journal, vol. 96, no. 2, pp. 290-296, 1999.
[21] M. A. Rashid and M. A. Mansur, "Reinforced high-strength concrete beams in flexure,” ACI Structural Journal, vol. 102, no. 3, pp. 462-471, 2005.
[22] K. J. Shin, J. H. Lim, Y. S. Oh, and J. H. Moon, "An experimental study on the flexural behaviour of RC beams strengthened with high-strength bars,” Magazine of Concrete Research, vol. 59, no. 7, pp. 469-482, 2007.
[23] S. W. Shin, S. K. Ghosh, and J. Moreno, "Flexural ductility of ultra-high-strength concrete members,” ACI Structural Journal, vol. 86, no. 4, pp. 394-400, 1989.
[24] S. W. Shin, S. H. Yoo, J. M. Ahn, and K. S. Lee, "The ductile behaviour including flexural strength of high-strength concrete members subjected to flexure,” ACI Special Publication, vol. 172, no., pp. 247-280, 1999.
[25] W. J. Weiss, K. Guler, and S. P. Shah, "Localization and size-dependent response of reinforced concrete beams,” ACI Structural Journal, vol. 98, no. 5, pp. 686-695, 2001.
[26] ACI Committee 318, Building code requirements for structural concrete and commentary ACI 318M-08, Manual of Concrete Practice, American Concrete Institute, Michigan, USA, 2008.
[27] European Committee for Standardization, Design of concrete structures: Part 1-1: General rules and rules for buildings Eurocode 2, British Standards Institution, Brussels, UK, 2004.
[28] Standards New Zealand, Concrete structures standard: Part 1: The design of concrete structures NZS 3101, Wellington, New Zealand, 2006.