Limit Analysis for Reinforced Concrete Beams with Rectangular Cross-Section under Bending and Torsion

Abstract

Abstract: A new limit analysis method for rectangular reinforced concrete (RC) beams subjected to combined bending and torsion was given. Based on the warped failure surface determined by external loads, with an assumed reasonable stress distribution, a new strength equation on torsion-bending interaction was derived from the equilibrium conditions, which should be a lower bound in limit analysis. The new equation is simple and conceptually clear. Comparing with the existing test results it is shown that the new method is in good agreement with the existing test results, and may also be used in more complex external loadings case.

Key words: reinforced concrete, beams, rectangular section, limit analysis, bending and torsional capacity

CLC Number:

TU 375.1

CHEN Xi-a, LIU Xi-La-b. Limit Analysis for Reinforced Concrete Beams with Rectangular Cross-Section under Bending and Torsion [J]. Journal of Shanghai Jiaotong University, 2012, 46(10): 1573-1580.

References

［1］刘西拉.结构工程学科的进展与前景［M］.北京：中国建筑工业出版社， 2007:216226.
［2］Hsu T T C. Toward a unified nomenclature for reinforcedconcrete theory［J］. Journal of Structural Engineering, 1996， 122(3): 275283.
［3］Hsu T T C, Mo Y L . Unified theory of concrete structures［M］. Chichester, West Sussex, UK: John Wiley and Sons， 2010.
［4］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.
［5］刘彬，张建仁，王磊，等, 钢筋混凝土梁抗剪承载力计算理论综述(上)［J］. 中外公路, 2011，

31(2): 150158.
LIU Bin, ZHANG Jianren, WANG Lei, et al. A review of theories for reinforced concrete beams under shear (I)［J］.

Journal of China & Foreign Highway, 2011，31(2): 150158.
［6］刘彬，张建仁，王磊，等, 钢筋混凝土梁抗剪承载力计算理论综述(下)［J］. 中外公路, 2011.

31(3): 109114.
LIU Bin, ZHANG Jianren, WANG Lei, et al. A review of theories for reinforced concrete beams under shear (II)［J］. Journal of China & Foreign Highway, 2011(2): 150158.
［7］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.
［8］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.
［9］Navarro Gregori J, Miguel Sosa P, Fernández Prada M A, 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.
［10］门进杰，史庆轩，刘继明. 钢筋混凝土复合受扭构件抗扭承载力统一方程的研究［J］. 西安建筑科技大学学报：自然科学版, 2006， 38(2): 227231.
MEN Jinjie, SHI Qingxuan, LIU Jiming. Unity equation of torsional capacity for reinforced concrete members subjected to combined torsion［J］. Journal of Xi’an University of Architecture & Technology：Natural Science Edition, 2006， 38(2): 227231.
［11］王岚，周晓蕾，刘霖，等. “板—桁模型”计算预应力混凝土复合受力构件抗扭强度［J］. 工程力学, 2005, 22(3): 198203.
WANG Lan, ZHOU Xiaolei, LIU Lin, et al. The calculation of torsional strength of prestressed concrete members under combined forces based on platetruss model［J］. Engineering Mechanics, 2005, 22(3): 198203.
［12］刘西拉，陈溪. 关于建立拉压弯剪扭统一计算公式的讨论［J］.四川建筑科学研究, 2012, 38(1): 14.
LIU Xila, CHEN Xi. Discussion on building of carrying capacity of reinforced concrete members under combined load effects［J］. Sichuan Building Science, 2012， 38(1): 14.
［13］Elfren L, Karlsson I, Losberg A. Torsion bendingshear interaction for concrete beams［J］. Journal of Structural Division, 1974， 100(8): 16571676.
［14］Chen W F. Limit analysis and soil plasticity［M］. Fort Lauderdale, USA: J Ross Publishing， 2007.
［15］陈惠发，萨里普A F. 弹性与塑性力学［M］. 北京: 中国建筑工业出版社， 2004.
［16］蓝宗建，梁书亭，孟少平. 混凝土结构设计原理［M］. 南京: 东南大学出版社， 2002.
［17］Baikov V, Sigalov E. Reinforced concrete structures［M］. Moscow: Mir Publishers， 1981.
［18］Ndai . Theory of Flow and Fracture of Solids［M］. New York: McGrawHill， 1950.
［19］Rausch E. Berechnung des eisenbetons gegen Verdrehung［M］. Berlin: Technische Hochschule， 1929.
［20］Hsu T T C. Torsion of reinforced concrete［M］. New York: Van Nostrand Reinhold， 1984.
［21］殷芝霖，张誉，王振东. 抗扭［M］. 北京: 中国铁道出版社， 1990.
［22］GB50010—2002，混凝土结构设计规范［S］.
［23］McMullen A E, Warwaruk J. The torsional strength of rectangular reinforced concrete beams subjected to combined loading［R］. Edmonton: University of Alberta, 1967.
［24］Gesund H, Schuette F J, Buchanan, 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.

[1]	ZHAO Pengfei, XUE Xin, YANG Cheng. Simulation of Influence of End Anchorage Degradation of Stirrups Caused by Alkali Aggregate Reaction on Shear Performance of Reinforced Concrete Beams [J]. Journal of Shanghai Jiao Tong University, 2021, 55(6): 681-688.
[2]	YANG Shuyan ∗ (杨淑雁), SONG Xiaobing (宋晓冰), JIA Hongxue (贾红学),CHEN Xi (陈溪), LIU Xila (刘西拉). Hysteretic Model for Corroded Rectangular Reinforced Concrete Bridge Column Under Seismic Loading [J]. J Shanghai Jiaotong Univ Sci, 2021, 26(6): 794-803.
[3]	ZHA Zhixiang, LIU Xila, XU Bo. Collapse Patterns and Their Discrimination of Reinforced Concrete Shear Wall Under Combined Stresses of Compression and Shear due to Strong Earthquake [J]. Journal of Shanghai Jiao Tong University(Science), 2020, 25(4): 495-508.
[4]	REN Chenhui,YANG Deqing. Performance of the Centrally-Clamped Cosine-Shaped Beam as a Nonlinear Vibration Isolator [J]. Journal of Shanghai Jiaotong University, 2019, 53(7): 852-859.
[5]	WANG Pu (王璞), ZHOU Dai (周岱), HUANG Zhen* (黄真). Ultimate Strength of Annular Reinforced Concrete Members Under Combined Actions [J]. Journal of Shanghai Jiao Tong University (Science), 2019, 24(4): 430-438.
[6]	YIN Xiaojun (尹小军), WANG Lanmin (王兰民). Block Limit Analysis Method for Stability of Slopes During Earthquakes [J]. Journal of Shanghai Jiao Tong University (Science), 2018, 23(6): 764-769.
[7]	XU Liqin (徐丽琴), LI Yong (李勇). Angle Estimation in Monostatic MIMO Radar with Low-Complexity Beamspace Unitary ESPRIT [J]. Journal of Shanghai Jiao Tong University (Science), 2018, 23(2): 256-263.
[8]	LUO Jingjinga,YU Haidonga,ZHAO Chunzhanga,b,WANG Haoa,b. Study on Motion Stability of Variable CrossSection Flexible Beams Based on the Absolute Nodal Coordinate Formulation [J]. Journal of Shanghai Jiaotong University, 2017, 51(10): 1174-1180.
[9]	OUYANG Fang, ZHANG Jianjing, DENG Xiaoning, HAN Jianwei, BI Junwei, DU Lin. Analysis of Load Capacity Behaviors of Steel Fiber Reinforced Concrete Piles Through Model Tests [J]. Journal of Shanghai Jiao Tong University, 2016, 50(03): 364-369.
[10]	REN Wei1,GAI YiTing2,ZHANG Gang1. Analysis of RC Arch Strengthen by Bonded FRP Under Initial Stress [J]. Journal of Shanghai Jiaotong University, 2015, 49(02): 232-238.
[11]	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.
[12]	HUANG Ke-feng* (黄科锋), LIU Xi-la (刘西拉). Effects of Temperature Variations on Safety of Reinforced Concrete Structures During Construction [J]. Journal of shanghai Jiaotong University (Science), 2014, 19(2): 139-145.
[13]	HAN Chang-yu1,2 (韩长玉), CHEN Jin-jian1 (陈锦剑), WANG Jian-hua1 (王建华), XIA Xiao-he1* (夏小和). Three-Dimensional Stability Analysis of Excavation Using Limit Analysis [J]. Journal of shanghai Jiaotong University (Science), 2013, 18(6): 646-649.
[14]	LUO Hua-xun* (骆华勋), LIU Xi-la (刘西拉). Advanced Unified Failure Model on Uniformly Reinforced Concrete Box Section Members [J]. Journal of shanghai Jiaotong University (Science), 2013, 18(5): 563-569.
[15]	LUO Hua-xun* (骆华勋), LIU Xi-la (刘西拉). New Unified Failure Model on Evenly Distributed Reinforced Concrete Members with Box Section [J]. Journal of shanghai Jiaotong University (Science), 2013, 18(1): 76-83.