Limit Analysis for Reinforced Concrete Rectangular Members Under Bending, Shear and Torsion

doi:10.1007/s12204-014-1481-y

Abstract

Abstract: The ultimate strength of reinforced concrete (RC) rectangular members subjected to combined bending, shear and torsion is obtained from the limit analysis proposed in the present paper. Based on a warped failure surface determined by external loads, and a reasonable assumed stress distribution balancing external loads but not violating the yield condition, the bending-shear-torsion interaction can be derived from equilibrium conditions. According to the definition of lower-bound theorem in limit analysis, the calculated ultimate loads will be carried safely by the structure. The present method is a simple approach to obtain carrying capacities for RC elements under complex external loads. After comparing with the test results, a good agreement has been observed. The present method can be extended to explain the failure mechanism of RC members subjected to axial loads, and it is possible to develop a simple unified theory of RC members for engineering.

摘要： The ultimate strength of reinforced concrete (RC) rectangular members subjected to combined bending, shear and torsion is obtained from the limit analysis proposed in the present paper. Based on a warped failure surface determined by external loads, and a reasonable assumed stress distribution balancing external loads but not violating the yield condition, the bending-shear-torsion interaction can be derived from equilibrium conditions. According to the definition of lower-bound theorem in limit analysis, the calculated ultimate loads will be carried safely by the structure. The present method is a simple approach to obtain carrying capacities for RC elements under complex external loads. After comparing with the test results, a good agreement has been observed. The present method can be extended to explain the failure mechanism of RC members subjected to axial loads, and it is possible to develop a simple unified theory of RC members for engineering.

CLC Number:

TU 375.1

CHEN Xia* (陈溪), LIU Xi-lab (刘西拉). Limit Analysis for Reinforced Concrete Rectangular Members Under Bending, Shear and Torsion[J]. Journal of shanghai Jiaotong University (Science), 2014, 19(2): 129-138.

References

[1] Liu X L. Going to mature: The theoretical development of reinforced concrete structures [C]// International Conference on Advances in Concrete and Structures (ICACS). Xuzhou, China: RILEM Publications, 2003: 1115-1124.
[2] Chen Xi, Liu Xi-la. Limit analysis for reinforced concrete beams with rectangular cross-section under bending and torsion [J]. Journal of Shanghai Jiaotong University, 2012, 46(10): 30-37 (in Chinese).
[3] Hsu T T C. Toward a unified nomenclature for reinforced-concrete theory [J]. Journal of Structural Engineering, 1996, 122(3): 275-283.
[4] Hsu T T C, Mo Y L. Unified theory of concrete structures [M]. Chichester, UK: John Wiley and Sons Ltd., 2010.
[5] Jeng C H, Hsu T T C. A softened membrane model for torsion in reinforced concrete members [J]. Engineering Structures, 2009, 31(9): 1944-1954.
[6] Greene Jr G, Belarbi A. Model for reinforced concrete members under torsion, bending, and shear. I. Theory [J]. Journal of Engineering Mechanics, 2009, 135(9): 961-969.
[7] Greene Jr G, Belarbi A. Model for reinforced concrete members under torsion, bending, and shear. II. Model application and validation [J]. Journal of Engineering Mechanics, 2009, 135(9): 970-977.
[8] Gregori J N, Sosa P M, Prada M A F, et al. A 3D numerical model for reinforced and prestressed concrete elements subjected to combined axial, bending, shear and torsion loading [J]. Engineering Structures, 2007, 29(12): 3404-3419.
[9] Wei Wei-wei, Gong Jin-xin. Shear strength of reinforced concrete members based on modified compression field theory [J]. Engineering Mechanics, 2011, 28(2): 111-117 (in Chinese).
[10] Arslan G. Shear strength of reinforced concrete beams with stirrups [J]. Materials and Structures, 2008, 41(1): 113-122
[11] Luo Hua-xun, Liu Xi-la. Unified failure model on the reinforced concrete members with annular section [J]. Journal of Shanghai Jiaotong University, 2012, 46(1): 152-157 (in Chinese).
[12] Elfren L, Karlsson I, Losberg A. Torsionbending-shear interaction for concrete beams [J]. Journal of Structural Division, 1974, 100(8): 1657-1676.
[13] Chen W F. Limit analysis and soil plasticity [M]. Fort Lauderdale, USA: J. Ross Publishing, Inc., 2007.
[14] Chen W F, Saleeb A F. Elasticity and plasticity [M]. Beijing: China Architecture & Building Industry Press, 2004.
[15] Baikov V, Sigalov E. Reinforced concrete structures: Vol. 1. Reinforced concrete strength and members[M]. Moscow, Russia: Mir Publishers, 1981.
[16] Nadai A. Theory of flow and fracture of solids [M]. New York: McGraw-Hill, 1963.
[17] Kim W, Kim D J. Analytical model to predict the influence of shear on longitudinal steel tension in reinforced concrete beams [J]. Advances in Structural Engineering, 2008, 11(2): 135-150.
[18] Hsu T T C. Torsion of reinforced concrete [M]. New York: Van Nostrand Reinhold, 1984.
[19] Mcmullen A E, Warwaruk J. The torsional strength of rectangular reinforced concrete beams subjected to combined loading [R]. Edmonton, Canada: Department of Civil Engineering at the University of Alberta, 1967.
[20] Gesund H, Schuette F J, Buchanan G R, et al. Ultimate strength in combined bending and torsion of concrete beams containing both longitudinal and transverse reinforcement [J]. Journal of the American Concrete Institute, 1964, 61(12): 1509-1522.