Assessment of diagonal-tension failure load in reinforced concrete beams without stirrups through the study of size effect

This paper proposes an expression to evaluate the load causing diagonal-tension failure of reinforced concrete beams without stirrups. The study is based on experimental tests results and basic concepts of Fracture Mechanics. It is observed that longitudinal reinforced bars modify the trend in size effect as compared to the one shown by un-reinforced notched beams. To quantify this effect, a theoretical model is established and validated against tests of reinforced concrete beams. From the proposed model, an expression is developed to determine the diagonal-tension strength in beams without stirrups. To facilitate the application in structural design, a series of simplifications has been done, so that the final expression is based on the parameters conventionally used in the design of concrete structures.

[1]  Antoni Cladera,et al.  Shear design procedure for reinforced normal and high-strength concrete beams using artificial neural networks. Part II: beams with stirrups , 2004 .

[2]  J. R. Carmona,et al.  Bond and size effects on the shear capacity of RC beams without stirrups , 2014 .

[3]  James K. Wight,et al.  Unified shear strength model for reinforced concrete beams - Part I: Development , 2007 .

[4]  Z. Bažant.  Size Effect in Blunt Fracture: Concrete, Rock, Metal , 1984 .

[5]  Michael P. Collins,et al.  Predicting the Response of Reinforced Concrete Beams Subjected to Shear Using the Modified Compression Field Theory , 1988 .

[6]  Michael P. Collins,et al.  Effect of Concrete Strength and Minimum Stirrups on Shear Strength of Large Members , 2001 .

[7]  Hong-Gun Park,et al.  Analytical model for shear strength of ordinary and prestressed concrete beams , 2013 .

[8]  Aurelio Muttoni,et al.  Effect of load distribution and variable depth on shear resistance of slender beams without stirrups , 2012 .

[9]  Shuaib H. Ahmad,et al.  Shear Capacity of Reinforced High-Strength Concrete Beams , 1986 .

[10]  J. R. Carmona,et al.  Failure Mode Transitions in Reinforced Concrete Beams-Part 1: Theoretical Model , 2011 .

[11]  B. Bresler,et al.  Shear Strength of Reinforced Concrete Beams , 1963 .

[12]  Jaime Planas,et al.  Experimental study of fracture of lightly reinforced concrete beams , 1998 .

[13]  Michael P. Collins,et al.  AN ADEQUATE THEORY FOR THE SHEAR STRENGTH OF REINFORCED CONCRETE STRUCTURES , 2008 .

[14]  F. Vecchio,et al.  THE MODIFIED COMPRESSION FIELD THEORY FOR REINFORCED CONCRETE ELEMENTS SUBJECTED TO SHEAR , 1986 .

[15]  J. R. Carmona,et al.  MIXED-MODE CRACK PROPAGATION THROUGH REINFORCED CONCRETE , 2007 .

[16]  C. P. Siess,et al.  Behavior and Strength in Shear of Beams and Frames Without Web Reinforcement , 1960 .

[17]  Qiang Yu,et al.  Designing Against Size Effect on Shear Strength of Reinforced Concrete Beams without Stirrups: II. Verification and Calibration , 2005 .

[18]  Qiang Yu,et al.  Designing Against Size Effect on Shear Strength of Reinforced Concrete Beams Without Stirrups: I. Formulation , 2005 .

[19]  G. N. J. Kani,et al.  HOW SAFE ARE OUR LARGE REINFORCED CONCRETE BEAMS , 1967 .

[20]  James K. Wight,et al.  Strain-Based Shear Strength Model for Slender Beams without Web Reinforcement , 2006 .

[21]  J. R. Carmona,et al.  Failure Mode Transitions in Reinforced Concrete Beams—Part 2: Experimental Tests , 2011 .

[22]  W. J. Krefeld,et al.  Studies of the Shear and Diagonal Tension Strength of Simply SupportedReinforced Concrete Beams , 1966 .

[23]  Antoni Cladera,et al.  Shear-flexural strength mechanical model for the design and assessment of reinforced concrete beams subjected to point or distributed loads , 2014, Frontiers of Structural and Civil Engineering.

[24]  Karim S. Rebeiz,et al.  Shear Strength Prediction for Concrete Members , 1999 .

[25]  Gregory C. Frantz,et al.  Shear Tests of High- and Low-Strength Concrete Beams Without Stirrups , 1984 .

[26]  E. Hognestad,et al.  Shear Strength of Reinforced Concrete Beams Part 1 -Tests of Simple Beams , 1954 .

[27]  Manuel J. Freire Tellado.  Análisis de las formulaciones sobre la resistencia a cortante del hormigón , 2005 .

[28]  W L Gamble,et al.  CONCRETE SHEAR STRENGTH: ANOTHER PERSPECTIVE. DISCUSSION AND CLOSURE , 2004 .

[29]  Bryan E. Little,et al.  American Association of State Highway and Transportation Officials. Highway Drainage Guidelines American Association of State Highway and Transportation Officials. LRFD Bridge Design Specifications , 2000 .

[30]  J. R. Carmona,et al.  Propagation of flexural and shear cracks through reinforced concrete beams by the bridged crack model , 2007 .

[31]  JoDean Morrow,et al.  Shear Strength of Reinforced Concrete Frame Members Without Web Reinforcement , 1957 .

[32]  P. D. Zararis,et al.  Diagonal Shear Failure and Size Effect in RC Beams without Web Reinforcement , 2001 .

[33]  Evan C. Bentz,et al.  Repeating a Classic Set of Experiments on Size Effect in Shear of Members without Stirrups , 2005 .

[34]  Daniel A. Kuchma,et al.  How Safe Are Our Large, Lightly Reinforced Concrete Beams, Slabs, and Footings? , 1999 .

[35]  T. Zsutty.  Beam Shear Strength Prediction by Analysis of Existing Data , 1968 .

[36]  Takeshi Higai,et al.  PROPOSED DESIGN EQUATION FOR SHEAR STRENGTH OF REINFORCED CONCRETE BEAMS WITHOUT WEB REINFORCEMENT , 1980 .

[37]  Aurelio Muttoni,et al.  Shear Strength of Members without Transverse Reinforcement as Function of Critical Shear Crack Width , 2008 .

[38]  Michael P. Collins,et al.  Shear Strength of Members without Transverse Reinforcement , 1996 .

[39]  Jack P. Moehle,et al.  "BUILDING CODE REQUIREMENTS FOR STRUCTURAL CONCRETE (ACI 318-11) AND COMMENTARY" , 2011 .

[40]  Elena Díaz Heredia,et al.  Evaluación del ajuste e introducción de la seguridad en el modelo experimental del EC-2 para estimar la capacidad a cortante en elementos lineales de hormigón armado sin armadura transversal , 2014 .

[41]  A. H. Nilson,et al.  Shear Capacity of Prestressed Concrete Beams Using High-Strength Concrete , 1986 .

[42]  Z. Bažant,et al.  Fracture and Size Effect in Concrete and Other Quasibrittle Materials , 1997 .

[43]  Hong-Gun Park,et al.  Unified shear strength model for reinforced concrete beams-Part II: Verification and simplified method , 2007 .

[44]  Comite Euro-International du Beton,et al.  CEB-FIP Model Code 1990 , 1993 .

[45]  F. Vecchio,et al.  Simplified Modified Compression Field Theory for Calculating Shear Strength of Reinforced Concrete Elements , 2006 .

[46]  Antonio R. Marí,et al.  Estudio del comportamiento del hormigón armado ante esfuerzos normales y tangentes mediante modelos seccionales de interacción completa , 2010 .

[47]  J. K. Kim,et al.  Prediction of Shear Strength of Reinforced ConcreteBeams without Web Reinforcement , 1996 .

[48]  Chanakya Arya,et al.  Buckling resistance of unstiffened webs , 2009 .

[49]  R. Grimm.  Einfluss bruchmechanischer Kenngroessen auf das Biege- und Schubtragverhalten hochfester Betone , 1997 .

[50]  P. Petersson.  Crack growth and development of fracture zones in plain concrete and similar materials , 1981 .

[51]  G. Ruiz.  Propagation of a cohesive crack crossing a reinforcement layer , 2001 .

[52]  Zdenek P. Bazant,et al.  Size Effect in Diagonal Shear Failure: Influence of Aggregate Size and Stirrups , 1987 .

[53]  Kang Su Kim,et al.  Shear Database for Reinforced Concrete Members without Shear Reinforcement , 2003 .

[54]  Akh Kwan,et al.  SHEAR CAPACITY OF HIGH-STRENGTH CONCRETE BEAMS WITH THEIR POINT OF INFLECTION WITHIN THE SHEAR SPAN. , 1998 .