Study of Shear Behavior of RC Beams: Non Linear Analysis

Transcription

1 Study of Shear Behavior of RC Beams: Non Linear Analysis 3477 Study of Shear Behavior of RC Beams: Non Linear Analysis Umer Farooq and K.S. Bedi1 Abstract Shear Failure of reinforced concrete beam more properly called diagonal tension failure, is difficult to predict accurately. In spite of many years of experimental research and the use of highly sophisticated computational tools, it is not fully understood. Shear stresses generate in beams due to bending or twisting. The two types of shear stress are called flexural shear stress and torsional shear stress, respectively. Shear mode of failure in beams is undesired mainly being a brittle failure. The thesis deals with Study of Shear behaviour of RC beams with the help of ATENA. The ATENA is new FEM based software which helps in Non Linear analysis of RCC structure. In this research, the first phase is to model the beams so that they represent the true experimental setup in loading and supporting conditions. The variables introduced in the study are amount of longitudinal steel reinforcement, concrete strength, and a/d ratio while the constants are cross sectional area of beam, doubly reinforced in the central 0.6 m and yield strength of steel. In this study fifteen models were analysed to represent true experimental conditions. For a constant a/d ratio of 1.5, 2.5 and 3.5 shear behaviour was studied for longitudinal reinforcement of 0.5, 1, 2, 3 and 4% respectively. ATENA gave the load deflection curve, the ultimate load and the ultimate deflection, stress strain values, cracking behaviour at each steps etc. All the results of the stressed retrofitted beams are collected and compare with the experimental beam results. The second phase of this research was to study the Umer Farooq M. Tech Structural Engineering, Guru Nanak Dev Engineering College, Gill Park, Ludhiana , Punjab, India faumijk@gmail.com K.S. Bedi Department of Civil Engineering, Guru Nanak Dev Engineering College, Gill Park, Ludhiana , Punjab, India Bloomsbury Publishing India Pvt Ltd., 2015 V. Matsagar (ed.), Modeling, Simulation and Analysis ISBN:

2 3478 Umer Farooq and K.S. Bedi effect of beam length on shear strength of RC beam. For this, beam length of 1.65, 2.2 and 2.7 m was taken. The third phase of this research was to compare the results with the experimental results and try to identify the various effects on the RCC structural members. In addition to comparing the empirical data with the software results, graphs were plotted between shear stress and a/d ratio and also between shear stress and percentage of longitudinal reinforcement to derive a relation between them. The results show good agreement with the experimental results. 1 Introduction In spite of the numerous research efforts directed at the shear capacity of concrete, there is still great discord concerning the mechanisms that govern shear in concrete. Proposed theories vary radically from the simple 45" truss model to the very complex non-linear fracture mechanics. Yet nearly al1 the resulting design procedures are empirical or semi- empirical at best and are obtained by a regression fit through experimental results or through proposed models using artificial neural network. Nowhere is this lack of understanding more evident than in the shear design provisions of the ACI Code (ACI committee ) which consists of 43 empirical equations for different types of members and different loading conditions. Moreover, there is great discrepancy between design codes of different countries. Many of these codes do not even account for some basic and proven factors affecting the shear capacity of concrete members. Of these factors, much confusion is expressed with regards to the effect of absolute member size on the shear capacity of beam elements. On this subject, there is a lack of consensus in the approach to the problem due to the limited amount of experiments dedicated to this effect, especially when it comes to high-strength concrete elements. The mechanism of shear failure in reinforced concrete structures is known to be complicated and a number of factors affect it. Especially concerning diagonal tension failure of reinforced concrete beams without shear reinforcement, a lot of experimental as well as numerical research has been carried out to explain the complicated mechanism. However, very few lucid explanations of the failure mechanism have been achieved through numerical research. The focus of this research is to evaluate the "size effect" in Reinforced concrete beams in order to better understand the mechanisms involved and compare the results obtained from software ATENA with the experimental results. As well, the closely related subject of "amount of longitudinal steel" is investigated as it has been shown to greatly affect the shear behavior of concrete beam or one-way slab elements.

3 Study of Shear Behavior of RC Beams: Non Linear Analysis Shear Failure Shear failure of reinforced concrete beam more properly called diagonal tension failure is difficult to predict accurately. In spite of many years of experimental research and the use of highly sophisticated computational tools, it us not fully understood. If a beam without properly designed for shear reinforcement is overloaded to failure, shear collapse is likely to occur suddenly. Analysis of Reinforced concrete for shear is more difficult compare to the analysis for axial load and flexure. The analysis for axial load and flexure are based on the following principles of mechanics. 1. Equilibrium of internal and external forces 2. Compatibility of strains in concrete and steel 3. Constitutive relationships of materials. The conventional analysis for shear is based on equilibrium of forces by a simple equation. The compatibility of strains is not considered. The constitutive relationships (relating stress and strain) of the materials, concrete or steel, are not used. The strength of each material corresponds to the ultimate strength. The strength of concrete under shear although based on test results, is empirical in nature. Shear stresses generate in beams due to bending or twisting. The two types of shear stress are called flexural shear stress and torsional shear stress, respectively. 3 Principal Tensile Stress in RC Beam Before cracking, RC beam can be considered as an elastic body. Hence, the maximum principal tensile stress occurs at the extreme tension fiber within the mid span, and its direction is parallel to the member axis. As this principal tensile stress increases and exceeds the tensile strength of concrete, crack occurs in the direction perpendicular to the direction of principal tensile stress. This crack is called flexural crack. After the flexural crack is formed, a RC beam is no longer considered to be an elastic body. However, since the tensile force is carried by longitudinal reinforcement, the state of stress even after flexural cracking is still similar to that of the principal stress of an elastic beam. When applied load is increased, the flexural crack propagates to the compression zone of the cross section. Also in both of side spans, the formulation of cracks occurs with an inclination with respect to the member axis. This crack is called "diagonal crack". When this diagonal crack occurs, the tensile force carried by concrete is released, and if reinforcement effective in the direction of principal tensile stress is not provided, the RC beam fails suddenly under the so-called "diagonal tension failure "mode. Another type of failure following the diagonal crack is "shear compression failure". A RC beam can resist increasing loads after the diagonal crack. The stress state becomes like a compression arch formed by diagonal cracks. In this case the beam fails when this arch crushes under

4 3480 Umer Farooq and K.S. Bedi diagonal compression. These two types of failure modes depend largely on the shear span-effective depth ratio (a/d). If the shear span-effective depth ratio is large, diagonal tension failure occurs, but when small, shear compression failure occurs. For the case of so called deep beam, i.e., the shear span-effective depth ratio is very small (a/d < 1.0), the tiedarch shear resisting mechanism is formed as a compression strut joining the loading and support points, and this failure mode is called deep beam failure. Since all of these failures are preceded by diagonal cracking of web concrete, so they are called as "shear failure". Fig. 1 Typical shear failure modes of RC beams 4 Objective of Research The present investigation of the Non Linear analysis of reinforced concrete beams under two point loading is initiated with the intent to investigate the relative importance of several factors in influencing the shear failure of RC beams: these include the variation in load displacement graph, crack patterns, propagation of cracks and the crack width and the effect of size of finite element mesh on analytical results and the effect of Non Linear behaviour of concrete and steel on the response of deformed beam. The main aim of the research is to improve the understanding about the behaviour of Reinforced concrete members in shear, based on the literature review and experimental work The various objectives of the Thesis were: 1. To predict the shear strength of RC beams at different percentage of tensile steel. For this longitudinal steel of 0.5, 1, 2, 3 and 4% was studied/analysed. 2. To study the effect of beam length on shear strength of RC beam. for this beam length of 1.65, 2.2 and 2.7 m were studied/analysed 3 To validate the numerical results with the experimental results done till date. 5 Methodology To study the shear behavior of beams, 15 beams of size 150 mm 265 mm were studied without shear reinforcement having central 600 mm portion doubly reinforced.

5 Study of Shear Behavior of RC Beams: Non Linear Analysis 3481 Percentage of longitudinal steel ratio (0.5%, 1%, 2%, 3% and 4%) was selected to study the effect of longitudinal steel ratio on the shear strength of RC beams. Shear span to depth ratio (a/d) of three values were selected as 1.5, 2.5 and 3.5 mainly to check the behavior of RC beams in shear. Beam lengths of 1.65 m, 2.2 m and 2.7 m were studied for the effect of length on the shear behavior of RC beams. Observations were taking in ATENA software as monitoring points were used at the centre of the beam to check for deflection and another monitoring point was taken at the point of application of load to take the readings of loading and deflection after each iteration and load step. 6 Modelling Procedure in Atena Following are the steps to be followed for modelling a beam in ATENA: 1. Analysis Information: It includes details and notes about the model. Analysis information is the first step in modelling and after it we save the file in our preferred location. 2. Material definition: This step involves adding the material properties involved in making the model. For the current model the material properties of concrete, steel and steel plates were used. For concrete a material of 3D NonLinear Cementitious was chosen. For adding reinforcement, Atena has a reinforcement material included in its library. Bilinear reinforcement material was used for current analysis. Steel plates were used having 3d elastic isotropic material type. The purpose of using steel plates is safe and uniform load distribution of loads. 3. Adding Macro elements: Beam construction, construction of reinforcement and construction of steel plates starts in topology. Construction of reinforcements is to be done by first fixing the nodes at the joints and then connecting the joints with the line segments and giving the number and diameter of Reinforcement bars. For constructing concrete, surfaces are to be added by adding the line segments or by extraction of solid in single step. Similarly steel plates were added using joints, line segments and surfaces. 4. Adding Load cases: In this step loads are to be added and then added to the joints or lines, or surfaces. There are various load cases in ATENA which can be applied for different types of load cases. 5. Meshing: The purpose of meshing is to convert a continuum to a discrete set of elements joined by nodes. The 3D mesh elements used in ATENA are Linear with 8 nodes and quadratic with 20 nodes. In a linear element the dispalcement across the element is considered linear. In other words, you can use simple interpolation between nodes to find the displacement

6 3482 Umer Farooq and K.S. Bedi at any point on a linear element. In case of a quadratic or second order element the displacement has a quadratic variation. So, in case of a linear element you have only two nodes along an edge while you need three nodes in case of a quadratic element. 6. Solution parameters: Standard Newton Raphson method and standard arc length methods are the two methods by which solution can be performed in ATENA. For current study Standard Newton Raphson method was used with each step having 40 iterations. 7. Analysis steps: depending on the tpe of problem, the analysis steps can be performed. For current study 8. Monitoring points: The points are to be placed where results are to be recorded. Fig. 2 Actual Reinforcement Arrangement. Fig. 3 Modelling of Reinforcement in ATENA 5 Experimental Study Following table shows the shear span, total length and effective length for a/d ratios varying from 1.5, 2.5 and 3.5 a/d a(mm) Lef(mm) L(mm) Following table shows the cross sectional dimensions of concrete beam and different percentage of steel having the number of reinforcement bars with the diameter.

7 Study of Shear Behavior of RC Beams: Non Linear Analysis 3483 d 265 mm pt bd = mm2 Steel area(mm2) Bars (226) (385) (804) (1206) (1608) 6 Results and Discussions 6.1 Experimental Data Following table shows the results for deflection, shear and shear strength for different percentages of steel and shear span-depth ratio. Sr No Reinf ratio ρ = Ast/bd a/d Table 1 Shear stress obtained for different beam specimens Ast Cube Str (Mpa) Ult. Shear, Vu(kN) Ult. Sh. Stress vu = Vu/bd (N/mm2) Deflection at 1st crack (mm) Deflection at Ult. Shear (mm)

8 3484 Umer Farooq and K.S. Bedi 7 Relation between Shear Stress and a/d Ratio for Constant Values of Pt In these figures, shear stress is plotted along X-axis and a/d is plotted along Y- axis Fig. 4 Shear stress v/s shear span-depth ratio for Pt = 0.5% Pt = 1% Fig. 5 Shear stress v/s shear span-depth ratio for Pt = 1%

9 Study of Shear Behavior of RC Beams: Non Linear Analysis 3485 Fig. 6 Shear stress v/s shear span-depth ratio for Pt = 2% Pt = 3% Fig. 7 Shear stress v/s shear span-depth ratio for Pt = 3% Fig. 8 Shear stress v/s shear span-depth ratio for Pt = 4%

10 3486 Umer Farooq and K.S. Bedi 8 Relation between Shear Stress and PT for Constant A/D Ratio Reinforcement ratio is plotted along X- axis and Shear stress is plotted along Y-axis Fig. 9 Shear stress v/s Pt for a/d = 1.5 Fig. 10 Shear stress v/s Pt for a/d = 2.5 Fig. 11 Shear stress v/s Pt for a/d = 3.5

11 Study of Shear Behavior of RC Beams: Non Linear Analysis Conclusions The study was carried out to investigate the influence of span-to- depth ratio, percentage of longitudinal reinforcement and concrete grade on the shear strength of Reinforced concrete beams. The 3 different values of span to depth ratio was taken 1.5, 2.5 and 3.5. Longitudinal reinforcement of 0.5%, 1%, 2%, 3%, 4% with different grades of concrete was considered. Yield strength of steel was taken as 415 MPa. The effective depth and width of beams were kept constant. Following conclusions are drawn on the basis of limited experimental investigations: It was concluded from the study that the graph between load and deflection for experimental observations were well in agreement with the values obtained with the software ATENA. Shear stress decreases with increase in a/d ratio from 1.5 to 3.5. Shear stress increases with increase in reinforcement percentage. With the increase in length of beam, shear stress decreases for same reinforcement ratio. 10 Scope of Future Study There is need to carry out further investigations in the following areas: The longitudinal reinforcement in this study was kept at 0.5%, 1%, 2%, 3%, 4%. Other steel percentage like 1.5%, 2.5%, 3.5% could be adopted for more detailed investigations. In this study, the effect of shear on the concrete grades was not studied. Further investigation can be done to establish a relationship for effect of grades of concrete on shear. The dimensional parameters such as depth and width of beam could be varied in order to check the influence of beam sectional area/depth on shear strength. The shear span to depth ratio (a/d) could be increased and its influence on shear strength characteristics needs to be studied. References 1. ACI-ASCE Committee 426, The Shear Strength of Reinforced Concrete Members, ACI Journal Proceedings, July 1973, V. 70, pp Batchelor, B., Shear in R.C. Beams without Web Reinforcement, Journal of Structural Division, 107(ST5) (1981), pp Bazant, Z.P and Kim J.K., (1984) The Size effect in shear Failure of longitudinally reinforced Beams, ACI Structural Journal Vol.81 (5), pp Bazant, Z. P., and Kim, J.K., Size Effect in Shear Failure of Longitudinally Reinforced Beams, ACI Journal, September 1984, V. 81, pp

12 3488 Umer Farooq and K.S. Bedi 5. Singhal, H. (2009), Finite Element Modeling of Retrofitted RCC Beams M.E. Thesis, Thapar University, Patiala. 6. Sharma M.(2011), Finite Element Modelling of Reinforced Cement Concrete Skew Slab M.E. Thesis, Thapar University, Patiala. 7. ATENA 3D and ATENA WIN finite element software manuals 8. ATENA theory manual part 1 from Vladimir Cervenka, Libor Jendele and Jan Cervenka. 9. Tutorial Atena Eng 3D by Jan Červenka 10. Berg, F. J. Shear strength of reinforced concrete beams without web reinforcement. Journal of ACI, 59(11) (1962), pp Elzanty, A.H., Nilson, Slate., F. O., Shear capacity of reinforced concrete beams using high strength concrete. ACI Journal, Marcg-April 1986, v 83,pp Jin Kuen Kim and YonDong Park. Prediction of shear strength of reinforced concrete beams without web reinforcement. ACI Materials Journal V 93, No 3, May Jun 1996, pp Kani, G. N. J, Basic facts concerning shear failure, ACI Journal, June 1996, pp Kani, G. N. J, How safe are our large reinforced concrete beams, ACI March 1967, v64, pp Taylor, H. P. J, The fundamental behavior of reinforced concrete beam and shear, ACI sp 42, 1974, pp